Abstract

We investigate the formation and propagation of ultraslow weak-light solitons and their memory in the atomic gas filled in a kagome-structured hollow-core photonic crystal fiber (HC-PCF) via electromagnetically induced transparency (EIT). We show that, due to the strong light-atom coupling contributed by the transverse confinement of the HC-PCF, the EIT and hence the optical Kerr nonlinearity of the system can be largely enhanced, and hence optical solitons with very short formation distance, ultraslow propagation velocity, and extremely low generation power can be realized. We also show that the optical solitons obtained can not only be robust during propagation, but also be stored and retrieved with high efficiency through the switching off and on of a control laser field. The results reported herein are promising for practical applications of all-optical information processing and transmission via the ultraslow weak-light solitons and the kagome-structured HC-PCF.

© 2017 Optical Society of America

1. Introduction

In recent years, tremendous efforts have been paid to the investigation on optical pulse memory, which is important for the realization of fast optical information processing. One of the main techniques to realize optical pulse memory is the utilization of electromagnetically induced transparency (EIT) [1,2], an interesting quantum interference effect typically occurring in three-level atomic systems. EIT can be used not only to cancel optical absorption in resonant quantum systems, but also to bring many novel nonlinear optical effects at weak-light level, including the production of weak-light solitons [3–5]. Based on the dark-state polariton [6] inherent in EIT systems, a signal optical mode can be mapped into an atomic mode, stored temporarily, and then retrieved from atoms by switching off and on of a control laser field [7–10].

However, nearly all researches reported up to now on the storage and retrieval of optical pulses via EIT are limited within linear optical regime. Due to the significant dispersion inherent in resonant systems, linear optical pulses in EIT-based atomic ensembles are not stable, resulting in a serious deformation for retrieved pulses and hence the loss of optical information. For practical applications of light memory, it is desirable to obtain a signal pulse that is robust not only during propagation, but also during storage and retrieval, and hence to acquire high efficiency and fidelity.

Recently, the EIT-based memory has been generalized to weak nonlinear optical regime, where the storage and retrieval of optical soliton pulses have been analyzed [11]. Nevertheless, because the optical pulses and atomic gases considered in Refs. [11] work in free space, the diffraction effect in those systems can not be neglected, which makes the optical soliton pulses unstable during propagation as well as during storage and retrieval. In addition, a larger power is needed for generating the optical soliton pulses in those systems since the coupling between light and atoms is weak in free space.

In this article, we propose a scheme for the formation, propagation, storage and retrieval of the optical soliton pulses in an atomic gas filled in a kagome-structured hollow-core photonic crystal fiber (HC-PCF) [12–16] via EIT. Because of the transverse confinement provided by the fiber, the diffraction effect of the optical pulses is completely eliminated. We show that the EIT and hence the Kerr nonlinearity may be largely enhanced, which can be used to balance the dispersion and hence supports the production of the optical soliton pulses in the system. We prove that the optical soliton pulses obtained with such a scheme have very short formation distance (< 2 cm), ultraslow propagation velocity (∼ 10−5 c), and extremely low generation power (∼ nW); in addition, they are robust during propagation and can be stored and retrieved with high efficiency through the switching on and off of a control laser field. The results reported here are promising for practical applications of all-optical information processing and transmission.

Before preceding, we note that bandgap-structured HC-PCFs [15–17] can also be used to perform EIT (see Refs. [18–25]), and to form an optical soliton pulse as shown recently by Facão et al. [26] where the fiber-core diameter is less than 4 μm. However, the use of the kagome-structured HC-PCF possesses many advantages, including: (i) The kagome-structured HC-PCF has a large core diameter (26 μm–100 μm in our scheme), which is easier not only for fabrication and but also for loading more atoms in the fiber core; (ii) Because of the larger atomic number in the kagome-structured HC-PCF, the coupling between the light field and the atomic gas is stronger, which is desirable for forming optical solitons within a shorter distance and with a lower generation power. (iii) Comparing with bandgap-structured HC-PCFs, the kagome-structured HC-PCF has a larger transverse transit time for the atoms in the fiber core, which admits a smaller dephasing and hence a higher efficiency for the storage and retrieval of the optical soliton pulses (see a further discussion in Sec. 5).

The rest of the article is arranged as follows. In Sec. II, the theoretical model is described. In Sec. III, the formation and propagation of ultraslow weak-light solitons is investigated. In Sec. 4, the storage and retrieval of optical soliton pulses are studied. Finally, in Sec. IV a discussion and a summary on the main results obtained in this work is given.

2. Model

We consider a pulsed signal laser field Es and a continuous-wave (CW) control laser field Ec, both are guided inside a kagome-structured HC-PCF with (hollow) core radius r0 and pitch Λ0 [Fig. 1(a)]. The core of the HC-PCF is filled with an atomic gas with a lambda-type level configuration [Fig. 1(b)]. In the absence of the atomic gas, the HC-PCF allows many eigenmodes of electric field E with the form eα qα(x, y) exp{i[βα(ω)zωt]}, here eα, qα(x, y), and βα are the polarization unit vector, eigenfunction, and propagation constant for the mode with index α (for a simple introduction of the eigenmodes in the kagome-structured HC-PCF, see Appendix A). In the present study, we are interested in the fundamental mode of the HC-PCF made of silica. The blue solid line in Fig. 1(c) is the numerical result of the electric-field distribution in the radius direction (with rx2+y2 the radius coordinate of the system) of the fundamental mode for r0 = Λ0 = 13 μm when the atomic gas is absent. The shape of the fundamental mode can be fitted well by the zeroth-order Bessel function [27] [the red dashed curve in Fig. 1(c)]. One sees that the fundamental mode is well confined in the fiber core, as shown in the inset of Fig. 1(c). In Fig 1(b), |1〉, |2〉, and |3〉 are respectively the metastable, ground, and excited states, Δ3 and Δ2 are respectively one- and two-photon detunings, Γjl (j = 1, 2; l = 3) denotes the spontaneous emission rate from |l〉 to |j〉; ωs and Ωs [ωc and Ωc] are respectively the angular and half Rabi frequencies of the signal (control) field, which is coupled to the transition |1〉 ↔ |3〉 (|2〉 ↔ |3〉). Both of the signal and control fields belong to the fundamental mode of the HC-PCF and propagate along z direction, with the form E=Es+Ec=l=s,celωl20Vleffl(z,t)ql(x,y)ei[βlzωlt]+c.c., where βlβ(ωl), VleffLz|ql(x,y)|2dxdy is the effective mode volume for the mode ω = ωl, Lz is the fiber length, the subscript s (c) denotes the signal (control) field, and c.c. represents complex conjugate.

 figure: Fig. 1

Fig. 1 (a) Kagome-structured HC-PCF with core radius r0 and pitch Λ0. (b) Atoms of a lambda-type three-level configuration are filled within the hollow core of the fiber, and initially prepared in the metastable |1〉 for suppressing four-wave mixing effect. (c) Numerical result of the electric-field distribution of the normalized fundamental-mode amplitude as a function of radius coordinate r in the HC-PCF made of silica when the atoms are absent. (d) Absorption spectrum Im(K) of the signal field as a function of Δω for different core radius r0. The red, blue and green lines are for r0 = 13 μm, 17 μm, and 100 μm, respectively. The other notations in the figure are explained in the text.

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We choose a cesium atomic gas with the energy levels selected as |1〉 = |62S1/2, F = 4〉, |2〉 = |62S1/2, F = 3〉, and |3〉 = |62P3/2, F = 4〉. For such level configuration the wavelengths of the signal and control fields are approximately equal (i.e. λsλc = 852 nm) [28], which means qc(x, y) ≈ qs(x, y) ≡ q(x, y). For an analytical description, in the following the fundamental mode is approximated by the zero-order Bessel function q(x, y) = J0(kr) when rr0 and q(x, y) = 0 when r > r0 with k ≈ 2.405/r0 [27], which gives VceffVseff=πr02J12(kr0)LzVeff. In order to have a quantitative discussion on light-beam confinement effect in the HC-PCF, following the approach in Refs. [29, 30] we define a reference mode volume of free space, i.e. Vref=πR2Lz. The quantity R (determined by input condition) is the transverse radius of laser beams in free space, introduced here for illustrating the confinement effect due to the HC-PCF by comparing the EIT in the HC-PCF and the EIT in free space. Note that experimentally R is usually large (e.g., R = 100 μm [31], which is chosen in the following discussion). Then the electric field can be expressed as

E=l=s,celRr0J1(kr0)l(z,t)ql(x,y)ei[βlzωt]+c.c..
When the atomic gas is filled into the fiber, under electric-dipole and rotating-wave approximations, the Hamiltonian of the system in the interaction picture reads H^int=j=13Δj|jj|[ζ(x,y)Ωs|13|+ζ(x,y)Ωc|23|+h.c.], where ζ(x,y)Rr0J1(kr0)q(x,y), and Ωs = |p13|s/ħc = |p23|c/ħ) is the half Rabi frequency of the signal (control) field, with pjl the electric-dipole moment associated with the state |j〉 and the state |l〉. The equation of motion for the density matrix σ in the interaction picture reads [32]
i(t+Γ)σ=[H^int,σ],
where σ is a 3 × 3 density matrix with matrix elements σjl ≡ |j〉 〈l|, Γ is a 3 × 3 relaxation matrix denoting the spontaneous emission and dephasing. The explicit expression of Eq. (2) is presented in Appendix B.

The equation of motion for Ωs can be obtained by the Maxwell equation ∇2E − (1/c2)2E/∂t2 = [1/(0c2)]2Pp/∂t2, with the electric polarization intensity given by Pp = Phost + 𝒩p13σ31 exp[i(βszωst)] + c.c., where 𝒩 is the atomic density, Phost = 0χhostE is the electric polarization intensity, with χhost = χhost(x, y) is the susceptibility of HC-PCF in the absence of the atomic gas. According to the expression of the electric field [i.e. the Eq. (1)] and using Eq. (18), the Maxwell equation under a slowly varying envelope approximation is reduced to

i(z+n2cnefft)Ωs+κ13σ˜31=0,
where n ≡ [1 + χhost(x, y)]1/2 is the refractive index [χhost(x, y) is the electric susceptibility] of the HC-PCF in the absence of the atomic gas, κ13𝒩ωs|p13|2/(2ħ∊0cneff) is light-atom coupling coefficient with neff the effective refractive index. In Eq. (3) we have defined σ31 = σ̃31ζ(x, y) and 〈ψ〉 = ∬ |ζ(x, y)|2ψ(x, y)dxdy/ ∬ |ζ(x, y)|2dxdy, with ψ an arbitrary function of x and y (for the detailed derivation of Eq. (3), see Appendix A). We see that, the diffraction effect of the signal field is effectively canceled due to the transverse (mode) confinement of the HC-PCF.

For simplicity, the following assumptions are made for our theoretical calculations presented below: (i) To suppress Doppler effect, the atoms are assumed to be cooled to low temperature and the signal and the control fields are injected with opposite directions. (ii) To reduce the dephasing rate caused by the adsorption of atoms to the inner walls of the fiber core, the inner walls are coated with some materials, or a light-induced atomic desorption process is used to release the atoms into the center of fiber core, or a dipole trap along the fiber axis is employed to attract the atoms away from the inner walls of the fiber. (iii) The atoms are initially populated on the metastable state |1〉 by an optical pumping to suppress four-wave mixing effect. These assumptions are realistic because related experiments have already been done in recent years [19,21,33].

3. Ultraslow weak-light solitons in the HC-PCF

3.1. Linear dispersion relation and EIT enhancement

We first solve the Maxwell-Bloch (MB) equations (2) and (3) in the linear regime and discuss the linear property of the system. The steady state before the signal field opens is σ11 = 1 and all other σjl are zero. When the signal field is switched on but very weak, the system will evolve into a time-dependent state and the solution of the MB equations (2) and (3) have the solution σ11 = 1, σj1 ∼ exp() (j = 2, 3), Ωs ∼ exp(), and σ22 = σ33 = σ32 = 0, with θ = Kω)z − Δωt [34]. The linear dispersion relation is given by

K=Δωcn2neff+κ13(Δω+d21)|ζ(x,y)Ωc|2(Δω+d21)(Δω+d31),
here the definitions of the parameters d21 and d31 have been given in Appendix B. Because the signal field is resonant with the atoms in the fiber, in usual cases one expects that a significant absorption will happen. However, the absorption can be made very low in the present system. Fig. 1(d) shows the calculation result on the imaginary part of K, i.e. Im(K), as a function of Δω, where the blue, red and green lines are respectively for the core radius r0 = 13 μm, 17 μm, and 100 μm. From Fig. 1(d) we see that: (i) A transparency window (i.e., the dip near Δω = 0) is opened, which is due to the quantum interference (i.e. EIT) effect induced by the control field; (ii) For different core radius r0, the width of the transparency window (called EIT transparency window) is different. The smaller the value of r0, the wider the EIT transparency window, which means that the EIT effect is enhanced when the core radius r0 is reduced. The physical reason of the enhancement of EIT effect is due to the existence of the (geometrical) confinement effect in the kagome-structured HC-PCF. By the confinement, the control field Ωc has an enhanced factor (R/r0)[J1(kr0)]−1, which leads to a larger EIT transparency window for smaller r0. For instance, the transparency window is very wide for r0 = 13 μm, which will be used in our following calculations.

When plotting Fig. 1(d), the system parameters are chosen as Ωc = 1.0 × 107 s−1, Δ2 = Δ3 = 0, |p13| ≃ |p23| = 3.8 × 10−27 C · cm [28], 𝒩 = 2.0 × 1010 cm−3, R = 100 μm, Γ3 ≃ 2γ31 = π × 5.23 MHz, γ31 = γ32. Note that the ground-state dephasing rate γ21dep for the atoms filled in the HC-PCF may be caused by many physical factors, widely discussed in literature (see, e.g., [18, 20, 25, 35–37]). Here we take γ21dep=γ212π×0.05MHz in our numerical calculations carried out here and below, which is slightly larger than that given in the recent experiment [25] in order to account for the factors causing the dephasing not included in our model.

3.2. Nonlinear envelope equation

The approach above is valid not only for CW but also for pulsed signal fields. However, vanishing one- and two-photon detunings assumed there usually cannot be satisfied in reality, which will result in a dispersion effect in the system and hence the spreading of the signal pulse. In particular, in light memory what we need is to store and retrieve a signal pulse within a finite time duration. The sideband components of the pulse are detuned from the energy-level difference of the related transition (|1〉 to |3〉 in the present system), which brings a non-negligible dispersion effect to the system. Such effect brings not only a deformation of the signal pulse but also a reduction of the quality of light memory in the system.

In order to suppress the dispersion effect and obtain a shape-preserving signal pulse useful for light memory, one can exploit the Kerr effect of the system to balance the dispersion [3, 4]. In fact, the Kerr nonlinearity of the system can be largely enhanced in the present system by both the EIT effect and the confinement effect of the HC-PCF, as shown below.

To this end, based on the MB equations (2) and (3) we derive a nonlinear envelope equation describing the nonlinear evolution of the signal field by using the method developed in Ref. [4]. Taking the asymptotic expansion σjk=l=0lσjk(l) (j, k =1, 2, 3; σjk(0)=δj1δk1), and Ωs=l=1lΩs(l). Here is a dimensionless small parameter characterizing the typical amplitude of the signal pulse. All the quantities on the right-hand side of the expansion are considered as functions of the multi-scale variables zl = lz (l = 0, 1, 2, · · ·) and tl = lt (l = 0, 1, 2, · · ·). Substituting the expansions into the Eqs. (2) and (3) and comparing the coefficients of m (m=1, 2, 3), we obtain a set of linear but inhomogeneous equations which can be solved order by order.

The first-order (m = 1) solution is given by

Ωs(1)=Fexp(iθ),
σj1(1)=δj3(Δω+d21)δj2ζ*(x,y)Ωc*|ζ(x,y)Ωc|2(Δω+d21)(Δω+d31)ζ(x,y)Feiθ,(j=2,3)
with all other σjl(1)=0. Here θKω)z0 − Δωt0, with F a yet to be determined envelope function depending on the indicated slow variables t1, z1, and z2 and Kω) the same as (4). At the second order (m = 2), we obtain the solvability condition i[∂F/∂z1 + (∂K/∂Δω)∂F/∂t1] = 0, which shows that the signal-pulse envelope F travels with the group velocity VgK11=(K/Δω)1, given by
Vg={1cn2neff+κ13(Δω+d21)2+|ζ(x,y)Ωc|2[|ζ(x,y)Ωc|2(Δω+d21)(Δω+d31)]2}1.
The explicit expressions of the second-order approximation solutions are given in Appendix C.

With the above results we go to the third order (m = 3). A solvability condition in this order yields the equation for the signal-pulse envelope iF/z2(1/2)[2K/Δω2]2F/t12W|F|2Fe2a¯z2=0, here K22K/∂Δω2 describes the second-order dispersion, and the nonlinear coefficient

W=κ13ζ(x,y)Ωca32*(2)+(Δω+d21)(2a11(2)+a22(2))|ζ(x,y)Ωc|2(Δω+d21)(Δω+d31)
is related to optical Kerr effect describing the self-phase modulation of the signal field.

Combining the solvability conditions in all orders and returning to the original variables, we obtain the equation

iUzK222Uτ2W|U|2U=iaU,
where τ = tz/Vg, U = ∊Feâz2, and a = 2ā, with the definition of ā presented in Appendix C. Note that Eq. (8) is valid for Δωωs. Since we are interested in the evolution of the signal pulse at the center frequency ωs, in the calculations given below all the coefficients in Eq. (8) will be evaluated at Δω = 0.

3.3. Ultraslow weak-light solitons

The third-order nonlinear optical susceptibility χ(3) of the signal field is proportional to the self-phase modulation coefficient W in Eq. (8) via the relation

χ(3)=2cωs|p13|22W.
Using the system parameters given in the last subsection but with Ωc = 3.6 × 106 s−1, Δ2 = 2.5 × 107 s−1, Δ3 = 3.75 × 108 s−1, 𝒩 = 2.0 × 1010 cm−3 and r0 = 13 μm, we obtain W = (−5.38+0.16i)×10−13 cm−1 s2 and Re(χ(3)) = −1.56×10−2 cm2 V−2, which is many orders of magnitude larger than that in conventional fibers [38]. Hence the HC-PCF with the filled atomic gas via EIT possesses greatly enhanced Kerr nonlinearity [39], contributed from the quantum interference effect in the (resonant) atomic gas, which is very useful for practical applications of many nonlinear optical processes, including effective four-wave mixing and formation of weak-light solitons.

Since the system under study is a resonant one, the coefficients in Eq. (8) are generally complex. However, when the system works under the EIT condition, the absorption of the signal field can be largely suppressed, and therefore the imaginary part of these coefficients can be made to be much smaller. Thus Eq. (8), when writing into the dimensionless form, can be approximated by the nonlinear Schrödinger equation i∂u/∂s + 2u/∂σ2 + 2|u|2u = 0, where u = U/U0, s = −z/(2LD), and σ = τ/τ0, with LD=τ02/K˜2 (τ0 is the pulse duration of the signal field) the typical dispersion length of the system. Note that we have taken LN = LD with LN=1/(W˜U02) the typical nonlinear length, and thus U0=(1/τ0)K˜2/W˜ (typical Rabi frequency of the signal field in free space). Here the tilde above K2 and W means taking the real part, 2 = Re(K2) and = Re(W). A single-soliton solution reads u(s, σ) = 2ϑsech[2ϑ(σσ0 + 4δs)] exp [−2iδσ − 4i(δ2ϑ2)s0], where ϑ, σ0, δ, and ϕ0 are real free parameters that determine the amplitude (also width), propagating velocity, initial position, and initial phase of the soliton, respectively. For simplicity, we take ϑ = 1/2, σ0 = δ = ϕ0 = 0. Then, when returning to original variables, we obtain the expression of the signal field Es = esEs, with

Es=τ0|p13|K˜W˜Rr0J1(kr0)J0(2.405rr0)sech[1τ0(tzV˜g)]×exp[i(K˜012LD)zi(ωs+Δω)t]+c.c.,
here 0 ≡ Re(K0), with K0 = Kω)|Δω=0.

We now give a set of system parameter for the formation of the optical soliton given above. By taking Ωc = 3.6 × 106 s−1, τ0 = 1.0 × 10−7 s, Δ2 = 2.5 × 107 s−1, Δ3 = 3.75 × 108 s−1, 𝒩 = 2.0 × 1010 cm−3 and other parameters are the same as those given in the above text, we obtain (evaluated at Δω = 0) K0 = (−3.23 + 0.09i) cm−1, K1 = (4.05 − 0.33i) × 10−8 cm−1 s, K2 = (−3.45 + 0.39i) × 10−15 cm−1 s2, W = (−5.38 + 0.16i) × 10−13 cm−1 s2, U0 = 0.8×106 s−1, and LA = 1/Im(K0) = 10.39 cm (typical absorption length). In particular, the nonlinearity length of the system is given by

LN=2.9cm,
which means that to form the soliton very short fiber length is needed. With these parameters we obtain
V˜g=Re(Vg)=8.17×104c,
which means that the optical soliton has an ultraslow propagating velocity.

The energy flux of the ultraslow optical soliton in the HC-PCF predicted by Eq. (10) can be calculated by using the Poynting vector integrated over the hollow core cross-section, i.e., P = ∬ dxdy(Es × Hs) · ez, where ez is the unit vector in the propagation direction [40]. At leading order the corresponding magnetic field of the soliton, Hs, is transverse and in the es × ez direction. Thus if es = ey then Hs = exHs with Hsneff0cEs. After averaging over the carrier-wave period, we obtain P = Pmax sech2 [(tz/Ṽg)/τ0], where Pmax = 20cneff(ħU0/|p13|)2 ∬ |ζ(x, y)|2dxdy, with neff the effective refractive index of the signal field, given in the Appendix A [i.e. Fig. (6)]. Using the parameters given above, we obtain

Pmax=0.82×109W,
i.e., the optical soliton has extremely low generation power. We see that, very different from the optical solitons obtained in conventional solid-core optical fibers [38], the optical soliton presented here has many attractive characters, including the very short formation distance [given by (11)], the ultra slow propagation velocity [given by (12)], and the extremely low generation power [given by (13)]. Physical reasons for these characters come from the enhanced EIT and Kerr nonlinear effects in the resonant atomic gas confined in the core of the kagome-structured HC-PCF.

Shown in Fig. 2(a) is the propagation of the ultraslow optical soliton with |Ωs (z, τ)τ0| as a function of z/LD and t/τ0. The comparison of waveshapes at z = 0 and at z = 2LD is given by Fig. 2(b). The solution is obtained by numerically solving Eq. (8) with all the imaginary parts of the complex coefficients taken into account. In the simulation, the initial condition is chosen as Ωs(0, τ)τ0 = 0.08 sech(t/τ0). One sees that, although due to the dissipative effect (mainly contributed by the dephsing γ21dep) there is a weak amplitude decay when propagating to z = 2LD, the soliton can keep its shape well for a propagation distance up to 2LD = 5.8 cm.

 figure: Fig. 2

Fig. 2 (a) The propagation of the ultraslow optical soliton, with |Ωs(z, τ)τ0| as a function of z/LD and t/τ0 (LD is dispersion length and τ0 is pulse duration). (b) The comparison of waveshapes between z = 0 (blue curve) and z = 2LD (red curve).

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4. Storage and retrieval of the ultraslow weak-light solitons in kagome structured HC-PCF

4.1. Storage and retrieval of the optical soliton pulse in a small-core kagome-structured HC-PCF

Although many schemes have been proposed and realized in the atomic gases in free space (see Refs. [41–51] and references therein), the light memory using an atomic gas filled in HC-PCFs is more desirable. The reasons are the following. First, guided-wave optics can confine optical modes within a small area over a distance longer than that is possible with diffractive optics in free space, thus the light power required to obtain strong light-atom coupling can be largely reduced, which can increase light memory efficiency. Second, an integrated platform is easier to interface with existing photonic architectures and also easier to scale up. Thus it is nature to seek the possibility of the storage and retrieval of the ultraslow weak-light solitons obtained in the last section.

The principle of EIT-based light memory is as follows [6]. When switching on the control field, the signal pulse propagates in the atomic gas with nearly vanishing absorption; by slowly switching off the control field the signal pulse disappears and gets stored in the atomic gas in the form of atomic coherence; when the control field is switched on again the signal pulse appears again. However, this principle was usually applied for linear optical pulses, which are not stable during propagation and suffer serious deformation due to the dispersion and/or diffraction. In the following, we show that it is available to realize the memory of stable optical soliton pulses in the kagome-structured HC-PCF obtained in the last section.

To this end, we numerically solve the MB equations (2) and (3) by taking the control field to be adiabatically changed with time to realize the function of its switching on and off. The switching-on and the switching-off of the control field are modeled by the combination of two hyperbolic tangent functions with the form

Ωc=Ωc0{112tanh[tTcoffTs]+12tanh[tTconTs]},
where Tcoff and Tcon are respectively the times of switching-off and switching-on of the control field. The switching time of the control field is Ts and the storage time of the signal pulse is approximately given by TconTcoff. We choose Ts = 0.5τ0, Tcoff=10.0τ0, Tcon=20.0τ0, with τ0 = 1.0 × 10−7 s. Note that due to the light confinement in the transverse directions, the MB equations [i.e. (2) and (3)] controlling the motion of the atoms filled in the HC-PCF are different from those in free space. In particular, the mode function ζ(x, y) appears in the coefficients of these equations, making the calculation of light memory more complicated than that in free space.

We first consider the kagome-structured HC-PCF with a relatively small core radius r0 (but much larger than that of the bandgap-structured HC-PCF in Ref. [26]). In this case, the system can be well approximated by a quasi-one-dimensional waveguide since the variation of the electric field on x and y is much faster than that on z, and hence the light memory can be studied by using the Eq. (3) and effective Bloch equation (23) (see Appendixes B and D). Shown in Fig. 3(a) is the result of storage and retrieval of an optical soliton pulse for r0 = Λ0 = 13 μm, where |Ωsτ0| is taken as a function of the propagation distance z and the evolution time t. The wave shape of the input signal pulse is taken as a hyperbolic secant one with a larger amplitude for forming soliton, i.e., Ωsin(t)τ0=0.1sech(1.5t/τ0). The black, red, green, yellow, sky blue, and blue solid lines in each panel are for the soliton pulse propagating to the distance z=0, 1, 2, 3, 4 and 5 cm, respectively; the purple solid line is for the dimensionless half Rabi frequency |Ωcτ0| of the control field. From the figure, we see that in this soliton regime the pulse is narrowed (i.e. the soliton is indeed formed) before its storage because of the balance between the dispersion and nonlinearity in the system. When the control field is switched off at t=Tcoff=10τ0, the soliton pulse disappears, and then appears again when the control field is switched on at t=Tcon=20τ0.

 figure: Fig. 3

Fig. 3 Numerical results on the storage and retrieval of an optical soliton pulse and a linear optical pulse for r0 = Λ0 = 13 μm. (a) [(b)] Evolution of the dimensionless half Rabi frequency |Ωsτ0| of the signal field (atomic coherence σ̃21) as a function of time t for different propagation distance z in the soliton regime. (c) [(d)] Evolution of the dimensionless half Rabi frequency |Ωsτ0| of the signal field (atomic coherence σ̃21) as a function of t for different z in the linear regime. In each panel, the black, red, green, yellow, sky blue, and blue solid lines are for z=0, 1, 2, 3, 4 and 5 cm, respectively; the purple solid line represents the dimensionless half Rabi frequency |Ωcτ0| of the control field.

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During the storage stage, the energy (information) of the optical soliton pulse is transferred into the atomic gas. Fig. 3(b) shows the result of the atomic coherence |σ̃21| as a function of z and t. One sees that σ̃21 is nonzero during the switch-off of the control field. Since the signal pulse is stored in the form of atomic coherence σ̃21 when the control field is switched off and is retained until the control field is switched on again, the atomic coherence σ̃21 can be taken as the intermediary for the memory of the signal pulse.

The efficiency η of the light memory can be described by the energy ratio between the retrieved pulse and the input pulse [52], i.e.,

η=Tcondtrr0dxdy|Esout(x,y,t)|2Tcoffdtrr0dxdy|Esin(x,y,t)|2,
where Esin(x,y,t)=Es(x,y,z,t)|z=0 and Esout(x,y,t)=Es(x,y,z,t)|z=Lz, with Lz the fiber length. Our calculation gives that the optical pulse memory efficiency in this soliton regime is η = 86.3% for Lz = 5 cm. The fidelity of the light memory can be characterized by the quantity ηJ2, here J2 is the overlap integral
J2=|Tcoffdtrr0dxdyEsout(x,y,t+ΔT)Esin(x,y,t)|2Tcoffdtrr0dxdy|Esin(x,y,t)|2Tcondtrr0dxdy|Esout(x,y,t)|2,
where ΔT is the time interval between the peak of the input signal pulse Esin and the peak of the retrieved signal pulse Esout. From Fig. 3(a) we see that the peak of the input signal pulse (the black solid curve) is at t = 0 and the peak of the retrieved signal pulse (the blue solid curve) is at t = 28τ0, and hence ΔT = 28τ0. Using the formula (16) we obtain J2 = 91.9% for Lz = 5 cm. Thus, the fidelity of the optical soliton memory is ηJ2 = 79.4%.

For comparison, the optical pulse memory in a linear regime is also calculated. Fig. 3(c) shows the result of numerical simulation on the evolution of |Ωsτ0| as function of z and t. The input signal pulse is also taken as a hyperbolic secant function but with a much smaller amplitude, i.e., Ωsin(t)τ0=0.01sech(1.5t/τ0). The colored solid lines are for z=0, 1, 2, 3, 4 and 5 cm, respectively. At beginning, the pulse profile for red line (z = 1 cm) in Fig. 3(b) is similar to that in Fig. 3(a) with almost same peak amplitude and pulse width. However, after 5 cm propagation, the peak value of blue line (z = 5 cm) decreases to 6.8 × 104 and its width is more than 2.0τ0. The blue line in Fig. 3(a) still keeps its amplitude and pulse width. From the figure, we see that the retrieved signal pulse is significantly broadened and its amplitude decreases rapidly. Based on Eqs. (15) and (16), we obtain the memory efficiency and fidelity of the linear optical pulse, respectively given by η = 79.8% and ηJ2 = 62.9% for Lz = 5 cm, lower than the optical soliton memory shown in Fig. 3(a). The atomic coherence |σ̃21| of the linear optical pulse during the storage and retrieval is presented in Fig. 3(d).

For a given storage time, the memory efficiency of the optical soliton pulse depends on the fiber length Lz and the fiber core radius r0 when the other system parameters are fixed. Fig. 4 shows the result of η as a function of the fiber length Lz for the storage time TconTcoff=10τ0. The blue, red and green solid curves in the figure are respectively for r0 taking 13, 15, and 17 μm (the pitch Λ0 is fixed to be 13 μm). From the figure we can obtain the following conclusions: (i) For any core radius r0, the memory efficiency η grows rapidly in the small Lz region (i.e. the region on the left side of its peak value), then as Lz increases it reaches to the peak value, and finally drops down slowly in the large Lz region (i.e. the region on the right side of the peak value); (ii) In the large (small) Lz region, the smaller the core radius r0 the higher (lower) the memory efficiency η. The physical reasons are the following. Since the signal pulse in the fiber with a larger core radius has a smaller group velocity, in the small Lz region (where damping due to the spontaneous emission and dephasing is negligible) the compression of the signal pulse is more effective and hence the memory efficiency for the large-core fiber is larger than that of the small-core fiber. However, in the large Lz region (where damping plays a significant role), the attenuation of the signal pulse in the small-core fiber is relatively smaller than in the large-core fiber and thus the memory efficiency is higher for the small-core fiber. Consequently, one can acquire a large memory efficiency of the optical soliton pulse by suitably selecting the core radius and the fiber length.

 figure: Fig. 4

Fig. 4 Memory efficiency η of the optical soliton pulse as a function of the fiber length Lz. Solid lines are fitted curves based on numerical calculation. The blue, red and green solid lines are for the fiber core radius r0=13, 15 and 17 μm, respectively. Dashed-dotted lines for each core radius are the memory efficiencies when a microwave field is coupled to the two lower atomic levels [i.e. |1〉 and |2〉 in Fig. 1(b)].

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The main factor affecting the light memory efficiency and fidelity is the value of the dephasing rate γ21dep. To improve the efficiency and fidelity, one can employ a microwave field to couple the two lower atomic levels [i.e. |1〉 and |2〉 in Fig. 1(b)]. The microwave field is applied within the time interval in which the control field is switched off, which can provide a gain to the atomic coherence σ21 [53]. We have carried out a numerical simulation on the memory of an optical soliton pulse by adding such a microwave field into the system, with the result shown by the dashed-dotted lines in Fig. 4. We see that by using the microwave field the soliton memory efficiency can be increased by 20%, which is valid for the all values of the core-radius r0.

4.2. Storage and retrieval of the optical soliton pulse for a large-core kagome-structured HC-PCF

As pointed out previously, a large-core fiber is desirable to fill more atoms in its core to obtain a strong light-atom coupling in the system. Recently, the core radius r0 of kagome-structured HC-PCF has been extended to 50 μm [54, 55], which encourages us to consider the memory of optical soliton pulse with such large-core fiber.

To this end, we make a numerical simulation to investigate the memory of optical soliton pulse in a kagome-structured HC-PCF with the core radius r0 = 50 μm and the pitch Λ0 = 25 μm. Note that in this situation the distribution range of the mode function ζ(x, y) is relatively large, the effective Bloch equation [i.e. Eq. (23)] is not a good approximation. Nevertheless, the (reduced) Maxwell equation (3) is still valid since the distribution range of ζ(x, y) is still much smaller than the spatial length of the signal pulse in the propagation (i.e. z) direction [56]. Thus the simulation is carried out based on the Eqs. (3) and (19).

Shown in Fig. 5(a) is the result of the storage and retrieval of an optical soliton pulse in the large-core fiber. The switching on and off of the control field is still modeled by the function (14). Panels (i) to (v) in the figure give the electric-field intensity distribution |Es|2 of the soliton pulse in the (x, y) plane for the soliton propagating to the distance z = 0, 1, 2.5, 4, and 5 cm, respectively. t = 0, 3.5τ0, 15τ0, 25τ0, and 28.5τ0 shown respectively in (i) to (v) are the times when the peak of the soliton arrives at the positions z = 0, 1, 2.5, 4, and 5 cm, respectively. We see that the optical soliton pulse can still be stored and retrieved in the system and can keep well its shape during the storage process. The efficiency and fidelity of the light memory in the present case are η = 77.6% and ηJ2 = 71.2% for Lz = 5 cm, respectively.

 figure: Fig. 5

Fig. 5 (a) Storage and retrieval of the optical soliton pulse in the HC-PCF with core radius r0 = 50 μm and pitch Λ0 = 25 μm. The subplots from (i) to (v) give the intensity distribution |Es|2 of the soliton pulse in the (x, y) plane when propagating to the distance z = 0, 1, 2.5, 4, and 5 cm, respectively. t = 0, 3.5τ0, 15τ0, 25τ0, and 28.5τ0 shown respectively in (i) to (v) are the times when soliton’s peak arrives at the positions z = 0, 1, 2.5, 4, and 5 cm, respectively. (b) Storage and retrieval of a linear optical pulse in the same fiber.

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 figure: Fig. 6

Fig. 6 Numerical result for the effective refractive index neff of the kagome-structured HC-PCF as a function of frequency ω with pitch Λ0 = 13 μm and three different core radius r0. The solid (dashed) line is for the fundamental (first higher-order) mode; the blue, red, and green colors are for r0 = 13 μm, r0 = 15 μm, r0 = 17 μm, respectively.

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For comparison, Fig. 5(b) shows the storage and retrieval of a linear optical pulse in the same large-core fiber. One sees that during the storage process the linear optical pulse undergoes a significant decrease of the amplitude. By the formulas (15) and (16) one obtains small memory efficiency (η = 63.8%) and small fidelity (ηJ2 = 50.3%), lower than the optical soliton memory shown in Fig. 5(a).

5. Discussion and summary

From the results described above, we see that the optical soliton pulses in the kagome-structured HC-PCF can not only be robust during propagation, but also be stored and retrieved with relatively higher efficiency and fidelity.

We note that there are two types of HC-PCFs, i.e., bandgap-structured HC-PCFs and kagome-structured HC-PCFs [15–17,57–59]. The bandgap-structured HC-PCFs have a true bandgap for eigenfrequency, which can be taken as a guidance mechanism preventing light from propagating in fibre cladding and confining the light within the fiber core. The EIT and related phenomena based on such HC-PCFs were demonstrated in many previous studies (see, e.g., Refs. [18–25]). The kagome-structured HC-PCFs do not possess a bandgap, so the light is guided by different mechanisms (e.g., anti-resonant reflection) [15]. The EIT and related Raman memory based on such HC-PCFs were also reported [33,60,61].

Our work presented above is different from that considered in Ref. [26], where the authors employed a bandgap-structured HC-PCF with a small core radius and did not discuss the storage and retrieval of optical solitons. In contrast, in our work not only the formation and propagation but also the storage and retrieval of the optical solitons are investigated, both are based on the kagome HC-PCF. In addition, our work is also at variance with those studied in Refs. [18–25,33, 60,61], where no optical solitons and their storage and retrieval were studied. We stress that the light memory using the atomic gas filling into the kagome HC-PCF has higher efficiency and fidelity than those using an atomic gas in free space. For comparison, consider the same cesium atomic gas (used above) works in a free space with the same control field Ωc. If the input signal pulse has the transverse mode profile q(x, y) = J0(kr), the characteristic diffraction length of the system reads LDif=3πr02/λs. If r0 = 13 μm (r0 = 50 μm), one has LDif = 0.1 cm (LDif = 1.6 cm), which is much shorter than the medium length (5 cm) and thus the diffraction effect in the system is very significant. Due to the diffraction, the signal pulse spreads fast in the transverse directions and its amplitude decreases rapidly. As a result, one obtains, for r0 = 13 μm (r0 = 50 μm), the light memory efficiency and fidelity are respectively given by η = 0.997% and ηJ2 = 0.786% (η = 16.65% and ηJ2 = 14.39%), which are much lower than those obtained by using the kagome-structured HC-PCF considered above.

Note that in principle one can take bandgap-structured HC-PCFs [15–17] for generating the ultraslow weak-light soliton pulses and for realizing their storage and retrieval. However, the kagome-structured HC-PCFs, as indicated in Sec. 1, are better for implementing such tasks. For instance, using the core radius r0 = 5 μm and the atomic density 𝒩 = 3.0 × 109 cm−3 in the bandgap-structured HC-PCF given in Ref. [21], under the same control field one obtains the nonlinear coefficient describing Kerr effect [defined by (9)] W = (5.05 + 0.31i) × 10−16 cm−1 s2 and hence the nonlinearity length (describing the formation distance of the optical solitons) LN = 8.62 cm. Nevertheless, using the core radius r0 = 13 μm and 𝒩 = 1.1 × 1011 cm−3 in the kagome-structured HC-PCF given in Ref. [33], one obtains W = (2.17 + 0.44i) × 10−14 cm−1 s2 and hence LN = 0.3 cm. Thus, comparing with the bandgap-structured HC-PCF, the Kerr effect in the kagome-structured HC-PCF can be made much larger, and hence the formation distance of the optical soliton pulses can be made much smaller, which is desirable for generating the solitons with a lower power and a smaller system size. In addition, due to the longer LN and larger dephasing caused by larger transverse transit time, the memory efficiency of the soliton storage in the bandgap-structured HC-PCF is less than 22%, much lower than that in the kagome-structured HC-PCF (> 77%). Due to these reasons, the kagome-structured HC-PCF is chosen in our model. We expect that the result and method reported herein will be useful not only for the understanding of nonlinear optical property of gas-filled HC PCFs, but also for practical applications for manipulating optical information at weak-light level.

In summary, in this work we have investigated the formation and propagation of ultraslow weak-light solitons and their memory in cold atomic gas filled in a kagome-structured HC-PCF via EIT. We have shown that, due to the strong light-atom coupling provided by the transverse confinement of the HC-PCF, the EIT and thus the Kerr nonlinearity of such system can be largely enhanced. As a result, stable optical solitons with ultralow generation power down to nW and the propagation velocity slow to 10−5 c can be realized. We have demonstrated that the optical solitons obtained can not only be robust during propagation, but also be stored and retrieved with high memory efficiency and fidelity through the switching off and on of a control laser field. The energy to generate soliton signals in HC-PCF is very low thus it is possible to realize such light memory in weak nonlinear regime under single photon level. The results reported herein are promising for practical applications of optical information processing and transmission based on the ultraslow weak-light solitons and kagome-structured HC-PCFs.

Appendix

A. Electric-field mode functions of the kagome-structured HC-PCF

When in the absence of the atomic gas, the electric field E of the kagome-structured HC-PCF satisfies the Maxwell equation ∇2E − (1/c2)2E/∂t2 = [1/(0c2)]2P/∂t2, here P is electric polarization intensity. Assuming that the frequency of E is far from the resonant frequency of the HC-PCF material, the electric polarization intensity has the from P = 0χhost(x, y)E, where χhost(x, y) is the electric susceptibility of the HC-PCF. Then the Maxwell equation is simplified into ∇2E − (n2/c2)2E/∂t2 = 0, with n = n(x, y) = [1 + χhost(x, y)]1/2 the refractive index of the HC-PCF without the atomic gas.

The general solution of the Maxwell equation can be written as

E=αωeα(ω)α(ω)qα(x,y)ei[βα(ω)zωt]+c.c.,
where eα, α, qα(x, y), and βα are the polarization unit vector, mode amplitude, eigenfunction, and propagation constant for the mode with index α. The eigenfunction qα satisfies the equation
(2x2+2y2)qα(x,y)+n2(x,y)ω2c2qα(x,y)=βα2(ω)qα(x,y).
Since an analytical solution of Eq. (18) is not available, we resort a numerical simulation. Shown in Fig. 6 is the numerical result for the effective refractive index neff(ω) of the kagome-structured HC-PCF as a function of frequency ω. The solid (dashed) line is for the fundamental (first higher-order) mode; the blue, red, and green colors are for r0 = 13 μm, r0 = 15 μm, r0 = 17 μm, respectively. In the calculation, we assume the fiber is made of silica and the pitch Λ0 (defined by the distance between two adjacent holes) of the HC-PCF [see Fig. 1(a)] is fixed to be Λ0 = 13 μm. Form the figure we see that the first higher-order mode has a lower effective refractive index than the fundamental mode. Based on the effective refractive indexes obtained we can find the corresponding eigenfunctions.

We are interested in the fundamental mode, whose electric-field distribution in the radial direction (i.e. as a function of r=x2+y2) is shown by the blue solid line in Fig. 1(c). When obtaining the figure, r0 = Λ0 = 13 μm is chosen. The shape of the fundamental mode can be fitted well by the zeroth-order Bessel function J0(2.405r/r0) [the red dashed curve in Fig. 1(c)] [27]. One sees that the fundamental mode is well confined in the fiber core, as shown in the inset of Fig. 1(c).

B. Equations of motion for the density-matrix elements

The equation of motion for the density-matrix elements σjl reads [32]

itσ11iΓ13σ33+ζ*(x,y)Ωs*σ31ζ(x,y)Ωsσ31*=0,
itσ22iΓ23σ33+ζ*(x,y)Ωc*σ32ζ(x,y)Ωcσ32*=0,
itσ33+iΓ13σ33+ζ*(x,y)Ωs*σ31+ζ(x,y)Ωsσ31*ζ*(x,y)Ωc*σ32+ζ(x,y)Ωcσ32*=0,
(it+d21)σ21ζ(x,y)Ωsσ32*+ζ*(x,y)Ωc*σ31=0,
(it+d31)σ31ζ(x,y)Ωs(σ33σ11)+ζ(x,y)Ωcσ21=0,
(it+d32)σ32ζ(x,y)Ωc(σ33σ22)+ζ(x,y)Ωsσ21*=0,
where djl = Δj − Δl + jl, Δ3 = ωsω31 and Δ2 = ω12 − (ωcωs) are respectively one- and two-photon detuings, with ωjl = (EjEl)/ħ with Ej the eigenenergy of the state |j〉. The dephasing rates are defined as γjl=(Γj+Γl)/2+γjldep, with Γj=El<EjΓlj representing the rate of spontaneous emission of the state |j〉 to all lower energy states |l〉, and γjldep being the dephasing rate reflecting the loss of phase coherence between |j〉 and |l〉.

Under the slowly varying envelope approximation, the equation of motion for Ωs reads

iζ(x,y)(z+n2cnefft)Ωs+κ13σ31=0,
with n2 = 1 + χhost(x, y) the refractive index of the HC-PCF when the atomic gas is absent. When the spatial distribution range of ζ(x, y) is much smaller than in the spatial length of the signal pulse in the propagation (i.e. z) direction, by using the definition σ31 = σ̃31ζ(x, y) and 〈ψ〉 = ∬ |ζ(x, y)|2ψ(x, y)dxdy/ ∬ |ζ(x, y)|2dxdy, Eq. (20) is reduced into Eq. (3) given in the main text.

C. Second-order approximation solution

The second-order approximation solution reads σ21(2)=a21(2)it1Feiθ, a31(2)=a31(2)it1Feiθ, σjj(2)=ajj(2)|F|2e2a¯z2 (j = 1, 2, 3), σ32(2)=a32(2)|F|2e2a¯z2, with ā = −2Im[Kω)|Δω=0] and

a11(2)=P2P1iΓ13|ζ(x,y)Ωc|2(1d32*132)|ζ(x,y)|2,
a22(2)=G|ζ(x,y)|2iΓ13a11(2)iΓ13,
a21(2)=ζ*(x,y)Ωc*(2Δω+d21+d31)D2ζ(x,y),
a31(2)=(Δω+d21)2+|ζ(x,y)Ωc|2D2ζ(x,y),
a32(2)=ζ(x,y)Ωcd32[|ζ(x,y)|2D*(a11(2)+2a22(2))],
where P1=[iΓ232|ζ(x,y)Ωc|2(1/d321/d32*)]G, P2=iΓ13|ζ(x,y)Ωc|2[1/(Dd32*)1/(D*d32)], with G=(Δω+d21*)/D*(Δω+d21)/D and D = |ζ(x, yc|2 − (Δω + d21)(Δω + d31).

D. Effective Bloch equation

Making the transformation [40]

σ˜jj(z,t)=dxdy|ζ(x,y)|2σjj(x,y,z,t)dxdy|ζ(x,y)|2,(j=1,2,3)
σ˜21(z,t)=dxdy|ζ(x,y)|2σ21(x,y,z,t)dxdy|ζ(x,y)|2,
σ˜31(32)(z,t)ζ(x,y)=σ31(32)(x,y,z,t),
Eq. (19) is reduced into the effective Bloch equation
itσ˜11iΓ13σ˜33+ρΩs*σ˜31ρΩsσ˜31*=0,
itσ˜22iΓ23σ˜33+ρΩc*σ˜32ρΩcσ˜32*=0,
itσ˜33+iΓ3σ˜33ρΩs*σ˜31+ρΩsσ˜31*ρΩc*σ˜32+ρΩcσ˜32*=0,
(it+d21)σ˜21ρΩsσ˜32*+ρΩc*σ˜31=0,
(it+d31)σ˜31Ωs(σ˜33σ˜11)+Ωcσ˜21=0,
(it+d32)σ˜32Ωc(σ˜33σ˜22)+Ωsσ˜21*=0,
with ρ=dxdy|ζ(x,y)|4/dxdy|ζ(x,y)|2, describing the confinement of the HC-PCF in the transverse directions.

Funding

National Natural Science Foundation of China (No. 11474099) and Science and Technology Project of Department of Education of Jiangxi Province (No. GJJ160576).

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32. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Elsevier, 2008).

33. M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014). [CrossRef]  

34. The frequency and wavenumber of the signal field are given by ωs + Δω and ks + K(Δω), respectively. Δω [K(Δω)] is the deviation of the signal-field frequency (wavenumber) when the atoms are present in the fiber core. Thus the point Δω = 0 corresponds to the center frequency of the signal field.

35. M. Graf and E. Arimondo, “Doppler broadening and collisional relaxation effects in a lasing-without-inversion experiment,” Phys. Rev. A. 51, 4030 (1995). [CrossRef]   [PubMed]  

36. M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011). [CrossRef]  

37. C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012). [CrossRef]  

38. G. P. Agrawal, Nonlinear Fiber Optics (4th Edition) (Elsevier, 2007).

39. The Kerr nonlinearity in the HC-PCF in the absence of the atomic gas is many orders of magnitude smaller than the one obatined in the presence of the atomic gas via EIT given here, and hence can be neglected safely.

40. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, CA, 1992), Chap. 5.

41. C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001). [CrossRef]   [PubMed]  

42. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001). [CrossRef]   [PubMed]  

43. I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98, 243602 (2007). [CrossRef]   [PubMed]  

44. U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009). [CrossRef]   [PubMed]  

45. R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009). [CrossRef]  

46. R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009). [CrossRef]  

47. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010). [CrossRef]  

48. Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010). [CrossRef]  

49. F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011). [CrossRef]  

50. H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012). [CrossRef]   [PubMed]  

51. Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013). [CrossRef]   [PubMed]  

52. I. Novikova, N. B. Phillips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78, 021802 (2008). [CrossRef]  

53. A. Eilam, A. D. Wilson Gordon, and H. Friedmann, “Efficient light storage in a Λ system due to coupling between lower levels,” Opt. Lett. 34, 1834 (2009). [CrossRef]   [PubMed]  

54. G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014). [CrossRef]   [PubMed]  

55. C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016). [CrossRef]  

56. The spatial length of the signal pulse in the propagation direction is given by Ṽgτ0, which is about 2.5 mm according to the result (12) and the pulse duration τ0 = 1.0 × 10−7 s.

57. J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998). [CrossRef]   [PubMed]  

58. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011) [CrossRef]  

59. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358 (2003). [CrossRef]   [PubMed]  

60. P. S. Light, F. Benabid, and F. Couny, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323 (2007). [CrossRef]   [PubMed]  

61. N. V. Wheeler, M. D. W. Grogan, P. S. Light, F. Couny, T. A. Birks, and F. Benabid, “Large-core acetylene-filled photonic microcells made by tapering a hollow-core photonic crystal fiber,” Opt. Lett. 35, 1875 (2010). [CrossRef]   [PubMed]  

References

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  15. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87 (2011).
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  17. A. R. Bhagwat and A. L. Gaeta, “Nonlinear optics in hollow-core photonic bandgap fibers,” Opt. Express 16, 5035 (2008).
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  19. S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
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  21. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
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  22. P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
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  23. P. S. Light, F. Benabid, G. J. Pearce, F. Couny, and D. M. Bird, “Electromagnetically induced transparency in acetylene molecules with counterpropagating beams in V and Λ schemes,” Appl. Phys. Lett. 94, 141103 (2009).
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  24. K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
    [Crossref]
  25. F. Blatt, L. S. Simeonov, T. Halfmann, and T. Peters, “Stationary light pulses and narrowband light storage in a laser-cooled ensemble loaded into a hollow-core fiber,” Phys. Rev. A. 94, 043833 (2016).
    [Crossref]
  26. M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
    [Crossref]
  27. F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195 (2002).
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  28. D. A. Steck, Cesium D Line Data, http://steck.us/alkalidata/ .
  29. J. Xu and G. Huang, “Electromagnetically induced transparency and ultraslow optical solitons in a coherent atomic gas filled in a slot waveguide,” Opt. Express 21, 5149 (2013).
    [Crossref] [PubMed]
  30. L. Li, C. Zhu, L. Deng, and G. Huang, “Electromagnetically induced transparency and nonlinear pulse propagation in an atomic medium confined in a waveguide,” J. Opt. Soc. Am. B 30, 197 (2013).
    [Crossref]
  31. Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801(R) (2013).
    [Crossref]
  32. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Elsevier, 2008).
  33. M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
    [Crossref]
  34. The frequency and wavenumber of the signal field are given by ωs + Δω and ks + K(Δω), respectively. Δω [K(Δω)] is the deviation of the signal-field frequency (wavenumber) when the atoms are present in the fiber core. Thus the point Δω = 0 corresponds to the center frequency of the signal field.
  35. M. Graf and E. Arimondo, “Doppler broadening and collisional relaxation effects in a lasing-without-inversion experiment,” Phys. Rev. A. 51, 4030 (1995).
    [Crossref] [PubMed]
  36. M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
    [Crossref]
  37. C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012).
    [Crossref]
  38. G. P. Agrawal, Nonlinear Fiber Optics (4th Edition) (Elsevier, 2007).
  39. The Kerr nonlinearity in the HC-PCF in the absence of the atomic gas is many orders of magnitude smaller than the one obatined in the presence of the atomic gas via EIT given here, and hence can be neglected safely.
  40. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, CA, 1992), Chap. 5.
  41. C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001).
    [Crossref] [PubMed]
  42. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
    [Crossref] [PubMed]
  43. I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98, 243602 (2007).
    [Crossref] [PubMed]
  44. U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
    [Crossref] [PubMed]
  45. R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
    [Crossref]
  46. R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009).
    [Crossref]
  47. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
    [Crossref]
  48. Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010).
    [Crossref]
  49. F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011).
    [Crossref]
  50. H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
    [Crossref] [PubMed]
  51. Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
    [Crossref] [PubMed]
  52. I. Novikova, N. B. Phillips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78, 021802 (2008).
    [Crossref]
  53. A. Eilam, A. D. Wilson Gordon, and H. Friedmann, “Efficient light storage in a Λ system due to coupling between lower levels,” Opt. Lett. 34, 1834 (2009).
    [Crossref] [PubMed]
  54. G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
    [Crossref] [PubMed]
  55. C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
    [Crossref]
  56. The spatial length of the signal pulse in the propagation direction is given by Ṽgτ0, which is about 2.5 mm according to the result (12) and the pulse duration τ0 = 1.0 × 10−7 s.
  57. J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998).
    [Crossref] [PubMed]
  58. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
    [Crossref]
  59. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358 (2003).
    [Crossref] [PubMed]
  60. P. S. Light, F. Benabid, and F. Couny, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323 (2007).
    [Crossref] [PubMed]
  61. N. V. Wheeler, M. D. W. Grogan, P. S. Light, F. Couny, T. A. Birks, and F. Benabid, “Large-core acetylene-filled photonic microcells made by tapering a hollow-core photonic crystal fiber,” Opt. Lett. 35, 1875 (2010).
    [Crossref] [PubMed]

2016 (2)

F. Blatt, L. S. Simeonov, T. Halfmann, and T. Peters, “Stationary light pulses and narrowband light storage in a laser-cooled ensemble loaded into a hollow-core fiber,” Phys. Rev. A. 94, 043833 (2016).
[Crossref]

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

2015 (1)

M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
[Crossref]

2014 (4)

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
[Crossref] [PubMed]

2013 (4)

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

J. Xu and G. Huang, “Electromagnetically induced transparency and ultraslow optical solitons in a coherent atomic gas filled in a slot waveguide,” Opt. Express 21, 5149 (2013).
[Crossref] [PubMed]

L. Li, C. Zhu, L. Deng, and G. Huang, “Electromagnetically induced transparency and nonlinear pulse propagation in an atomic medium confined in a waveguide,” J. Opt. Soc. Am. B 30, 197 (2013).
[Crossref]

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801(R) (2013).
[Crossref]

2012 (3)

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012).
[Crossref]

I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6, 333 (2012).
[Crossref]

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

2011 (6)

F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
[Crossref]

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
[Crossref]

2010 (4)

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

N. V. Wheeler, M. D. W. Grogan, P. S. Light, F. Couny, T. A. Birks, and F. Benabid, “Large-core acetylene-filled photonic microcells made by tapering a hollow-core photonic crystal fiber,” Opt. Lett. 35, 1875 (2010).
[Crossref] [PubMed]

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
[Crossref]

Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010).
[Crossref]

2009 (8)

A. Eilam, A. D. Wilson Gordon, and H. Friedmann, “Efficient light storage in a Λ system due to coupling between lower levels,” Opt. Lett. 34, 1834 (2009).
[Crossref] [PubMed]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706 (2009).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

P. S. Light, F. Benabid, G. J. Pearce, F. Couny, and D. M. Bird, “Electromagnetically induced transparency in acetylene molecules with counterpropagating beams in V and Λ schemes,” Appl. Phys. Lett. 94, 141103 (2009).
[Crossref]

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
[Crossref]

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[Crossref]

2008 (2)

A. R. Bhagwat and A. L. Gaeta, “Nonlinear optics in hollow-core photonic bandgap fibers,” Opt. Express 16, 5035 (2008).
[Crossref] [PubMed]

I. Novikova, N. B. Phillips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78, 021802 (2008).
[Crossref]

2007 (4)

2006 (2)

F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31, 3574 (2006).
[Crossref] [PubMed]

S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

2005 (3)

F. Benabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694 (2005).
[Crossref] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[Crossref]

2004 (1)

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

2003 (2)

T. Hong, “Spatial Weak-Light Solitons in an Electromagnetically Induced Nonlinear Waveguide,” Phys. Rev. Lett 90, 183901 (2003).
[Crossref] [PubMed]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358 (2003).
[Crossref] [PubMed]

2002 (2)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in Hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399 (2002).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195 (2002).
[Crossref] [PubMed]

2001 (2)

C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

2000 (1)

M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. 84, 5094 (2000).
[Crossref] [PubMed]

1998 (1)

J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998).
[Crossref] [PubMed]

1995 (1)

M. Graf and E. Arimondo, “Doppler broadening and collisional relaxation effects in a lasing-without-inversion experiment,” Phys. Rev. A. 51, 4030 (1995).
[Crossref] [PubMed]

Abdolvand, A.

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Afzelius, M.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (4th Edition) (Elsevier, 2007).

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in Hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399 (2002).
[Crossref] [PubMed]

Appe, J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Arimondo, E.

M. Graf and E. Arimondo, “Doppler broadening and collisional relaxation effects in a lasing-without-inversion experiment,” Phys. Rev. A. 51, 4030 (1995).
[Crossref] [PubMed]

Bai, Z.

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

Bajcsy, M.

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Balic, V.

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Bao, X. H.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Behroozi, C.

C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001).
[Crossref] [PubMed]

Benabid, F.

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012).
[Crossref]

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87 (2011).
[Crossref]

N. V. Wheeler, M. D. W. Grogan, P. S. Light, F. Couny, T. A. Birks, and F. Benabid, “Large-core acetylene-filled photonic microcells made by tapering a hollow-core photonic crystal fiber,” Opt. Lett. 35, 1875 (2010).
[Crossref] [PubMed]

P. S. Light, F. Benabid, G. J. Pearce, F. Couny, and D. M. Bird, “Electromagnetically induced transparency in acetylene molecules with counterpropagating beams in V and Λ schemes,” Appl. Phys. Lett. 94, 141103 (2009).
[Crossref]

P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323 (2007).
[Crossref] [PubMed]

P. S. Light, F. Benabid, and F. Couny, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323 (2007).
[Crossref] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31, 3574 (2006).
[Crossref] [PubMed]

F. Benabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694 (2005).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in Hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399 (2002).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195 (2002).
[Crossref] [PubMed]

Bhagwat, A. R.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

A. R. Bhagwat and A. L. Gaeta, “Nonlinear optics in hollow-core photonic bandgap fibers,” Opt. Express 16, 5035 (2008).
[Crossref] [PubMed]

S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Bird, D. M.

P. S. Light, F. Benabid, G. J. Pearce, F. Couny, and D. M. Bird, “Electromagnetically induced transparency in acetylene molecules with counterpropagating beams in V and Λ schemes,” Appl. Phys. Lett. 94, 141103 (2009).
[Crossref]

Birks, T. A.

Blatt, F.

F. Blatt, L. S. Simeonov, T. Halfmann, and T. Peters, “Stationary light pulses and narrowband light storage in a laser-cooled ensemble loaded into a hollow-core fiber,” Phys. Rev. A. 94, 043833 (2016).
[Crossref]

Bloch, I.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Elsevier, 2008).

Broeng, I.

J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998).
[Crossref] [PubMed]

Burger, S.

Campbel, C. J.

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
[Crossref]

Carvalho, M. I.

M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
[Crossref]

Champion, T. F. M.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Chang, W.

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
[Crossref]

Chen, S.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

Chen, Y. C.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Chen, Y. F.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Chen, Y. H.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Couny, F.

Dai, H. N.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Davidson, N.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

de Riedmatten, H.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

Deng, L.

L. Li, C. Zhu, L. Deng, and G. Huang, “Electromagnetically induced transparency and nonlinear pulse propagation in an atomic medium confined in a waveguide,” J. Opt. Soc. Am. B 30, 197 (2013).
[Crossref]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[Crossref]

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

Deng, Y. J.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Dewhurst, S. J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Du, S.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Dudin, Y. O.

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801(R) (2013).
[Crossref]

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
[Crossref]

Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
[Crossref]

Dutton, Z.

C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001).
[Crossref] [PubMed]

Eilam, A.

England, D. G.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Epple, G.

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
[Crossref] [PubMed]

Euser, T. G.

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
[Crossref] [PubMed]

Facão, M.

M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
[Crossref]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. 84, 5094 (2000).
[Crossref] [PubMed]

Friedmann, H.

Gaeta, A. L.

K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
[Crossref]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

A. R. Bhagwat and A. L. Gaeta, “Nonlinear optics in hollow-core photonic bandgap fibers,” Opt. Express 16, 5035 (2008).
[Crossref] [PubMed]

S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Garner, S. R.

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[Crossref]

Ghosh, S.

S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

Giroday, A. B.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Gisin, N.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

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I. Novikova, N. B. Phillips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78, 021802 (2008).
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Radnaev, A. G.

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
[Crossref]

Rarity, J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Riedmatten, H.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Roberts, P. J.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87 (2011).
[Crossref]

Rodrigues, S.

M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
[Crossref]

Rosenfeld, W.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Rui, J.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Russell, P. St. J.

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
[Crossref] [PubMed]

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
[Crossref]

G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St. J. Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express 15, 12680 (2007).
[Crossref] [PubMed]

F. Benabid, P. S. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13, 5694 (2005).
[Crossref] [PubMed]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358 (2003).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in Hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399 (2002).
[Crossref] [PubMed]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195 (2002).
[Crossref] [PubMed]

J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998).
[Crossref] [PubMed]

Saha, K.

K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
[Crossref]

Sanders, B. C.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706 (2009).
[Crossref]

Sangouard, N.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

Schnorrberger, U.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

Shields, A. J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Simeonov, L. S.

F. Blatt, L. S. Simeonov, T. Halfmann, and T. Peters, “Stationary light pulses and narrowband light storage in a laser-cooled ensemble loaded into a hollow-core fiber,” Phys. Rev. A. 94, 043833 (2016).
[Crossref]

Simon, C.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Skagold, N.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Slepkov, A. D.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

Sørensen, A. S.

I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98, 243602 (2007).
[Crossref] [PubMed]

Sprague, M. R.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Stace, T. M.

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012).
[Crossref]

Stevenson, R. M.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Thew, R.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Thompson, J. D.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706 (2009).
[Crossref]

Travers, J. C.

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
[Crossref]

Trotzky, S.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

Veit, C.

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

Venkataraman, V.

K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
[Crossref]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

Vuletic, V.

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Walmsley, I.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Walmsley, I. A.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Walsworth, R. L.

I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6, 333 (2012).
[Crossref]

I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98, 243602 (2007).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

Wang, I. C.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Weber, M.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Weinfurter, H.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Wheeler, N. V.

Wiederhecker, G. S.

Wilson Gordon, A. D.

Wrachtrup, J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Wu, Y.

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

Xiao, Y.

I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6, 333 (2012).
[Crossref]

Xu, J.

Yang, F.

F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011).
[Crossref]

Yang, S. J.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Young, R. J.

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

Yu, I. A.

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

Yuan, Z. S.

F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011).
[Crossref]

Zhang, H.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Zhang, R.

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[Crossref]

Zhao, B.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Zhao, R.

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
[Crossref]

Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
[Crossref]

Zhao, T. M.

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Zhu, C.

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

P. S. Light, F. Benabid, G. J. Pearce, F. Couny, and D. M. Bird, “Electromagnetically induced transparency in acetylene molecules with counterpropagating beams in V and Λ schemes,” Appl. Phys. Lett. 94, 141103 (2009).
[Crossref]

Euro. Phys. J. D. (1)

C. Simon, M. Afzelius, J. Appe, A. B. Giroday, S. J. Dewhurst, N. Gisin, C. Hu, F. Jelezko, S. Krąğoll, J. Mąğuler, J. Nunn, E. Polzik, J. Rarity, H. Riedmatten, W. Rosenfeld, A. J. Shields, N. Skąğold, R. M. Stevenson, R. Thew, I. Walmsley, M. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Euro. Phys. J. D. 58, 1 (2010).
[Crossref]

J. Mod. Opt. (1)

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58, 87 (2011).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Am. B. (1)

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B. 28, A11 (2011)
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

C. Veit, G. Epple, H. Kübler, T. G. Euser, P. St. J. Russell, and R. Löw, “RF-dressed Rydberg atoms in hollow-core fibres,” J. Phys. B: At. Mol. Opt. Phys. 49, 134005 (2016).
[Crossref]

Laser Photon. Rev. (1)

I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6, 333 (2012).
[Crossref]

Nat. Commun. (1)

G. Epple, K. S. Kleinbach, T. G. Euser, N. Y. Joly, T. Pfau, P. St. J. Russell, and R. Löw, “Rydberg atoms in hollow-core photonic crystal fibres,” Nat. Commun. 5, 4132 (2014).
[Crossref] [PubMed]

Nat. Photon. (3)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3, 706 (2009).
[Crossref]

P. St. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278 (2014).
[Crossref]

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. St. J. Russell, and I. A. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photon. 8, 287 (2014).
[Crossref]

Nat. Phys. (2)

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbel, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100 (2009).
[Crossref]

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894 (2010).
[Crossref]

Nature (1)

C. Liu, Z. Dutton, C. Behroozi, and L. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490 (2001).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. A (8)

I. Novikova, N. B. Phillips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78, 021802 (2008).
[Crossref]

Y. O. Dudin, R. Zhao, T. A. B. Kennedy, and A. Kuzmich, “Light storage in a magnetically dressed optical lattice,” Phys. Rev. A 81, 041805(R) (2010).
[Crossref]

F. Yang, T. Mandel, C. Lutz, Z. S. Yuan, and J. W. Pan, “Transverse mode revival of a light-compensated quantum memory,” Phys. Rev. A 83, 063420 (2011).
[Crossref]

Y. Chen, Z. Bai, and G. Huang, “Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system,” Phys. Rev. A 89, 023835 (2014).
[Crossref]

M. Facão, S. Rodrigues, and M. I. Carvalho, “Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber,” Phys. Rev. A 91, 013828 (2015).
[Crossref]

K. Saha, V. Venkataraman, P. Londero, and A. L. Gaeta, “Enhanced two-photon absorption in a hollow-core photonic-band-gap fiber,” Phys. Rev. A 83, 033833 (2011).
[Crossref]

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801(R) (2013).
[Crossref]

M. Bajcsy, S. Hofferberth, T. Peyronel, V. Balic, Q. Liang, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Laser-cooled atoms inside a hollow-core photonic-crystal fiber,” Phys. Rev. A 83, 063830 (2011).
[Crossref]

Phys. Rev. A. (3)

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A. 85, 012518 (2012).
[Crossref]

M. Graf and E. Arimondo, “Doppler broadening and collisional relaxation effects in a lasing-without-inversion experiment,” Phys. Rev. A. 51, 4030 (1995).
[Crossref] [PubMed]

F. Blatt, L. S. Simeonov, T. Halfmann, and T. Peters, “Stationary light pulses and narrowband light storage in a laser-cooled ensemble loaded into a hollow-core fiber,” Phys. Rev. A. 94, 043833 (2016).
[Crossref]

Phys. Rev. E (1)

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[Crossref]

Phys. Rev. Lett (1)

T. Hong, “Spatial Weak-Light Solitons in an Electromagnetically Induced Nonlinear Waveguide,” Phys. Rev. Lett 90, 183901 (2003).
[Crossref] [PubMed]

Phys. Rev. Lett. (11)

M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. 84, 5094 (2000).
[Crossref] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[Crossref] [PubMed]

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett. 93, 143904 (2004).
[Crossref] [PubMed]

S. Ghosh, A. R. Bhagwat, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with Rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[Crossref] [PubMed]

H. N. Dai, H. Zhang, S. J. Yang, T. M. Zhao, J. Rui, Y. J. Deng, L. Li, N. L. Liu, S. Chen, X. H. Bao, X. M. Jin, B. Zhao, and J. W. Pan, “Holographic Storage of Biphoton Entanglement,” Phys. Rev. Lett. 108, 210501 (2012).
[Crossref] [PubMed]

Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay,” Phys. Rev. Lett. 110, 083601 (2013).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. 86, 783 (2001).
[Crossref] [PubMed]

I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98, 243602 (2007).
[Crossref] [PubMed]

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103, 033003 (2009).
[Crossref] [PubMed]

R. Zhang, S. R. Garner, and L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103, 233602 (2009).
[Crossref]

Rev. Mod. Phys. (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33 (2011).
[Crossref]

Science (3)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in Hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399 (2002).
[Crossref] [PubMed]

J. C. Knight, I. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476 (1998).
[Crossref] [PubMed]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358 (2003).
[Crossref] [PubMed]

Other (8)

The spatial length of the signal pulse in the propagation direction is given by Ṽgτ0, which is about 2.5 mm according to the result (12) and the pulse duration τ0 = 1.0 × 10−7 s.

J. B. Khurgin and R. S. Tucker eds., Slow Light: Science and Applications (CRC, Taylor and Francis, Boca Raton, 2009).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Elsevier, 2008).

D. A. Steck, Cesium D Line Data, http://steck.us/alkalidata/ .

The frequency and wavenumber of the signal field are given by ωs + Δω and ks + K(Δω), respectively. Δω [K(Δω)] is the deviation of the signal-field frequency (wavenumber) when the atoms are present in the fiber core. Thus the point Δω = 0 corresponds to the center frequency of the signal field.

G. P. Agrawal, Nonlinear Fiber Optics (4th Edition) (Elsevier, 2007).

The Kerr nonlinearity in the HC-PCF in the absence of the atomic gas is many orders of magnitude smaller than the one obatined in the presence of the atomic gas via EIT given here, and hence can be neglected safely.

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, CA, 1992), Chap. 5.

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Figures (6)

Fig. 1
Fig. 1 (a) Kagome-structured HC-PCF with core radius r0 and pitch Λ0. (b) Atoms of a lambda-type three-level configuration are filled within the hollow core of the fiber, and initially prepared in the metastable |1〉 for suppressing four-wave mixing effect. (c) Numerical result of the electric-field distribution of the normalized fundamental-mode amplitude as a function of radius coordinate r in the HC-PCF made of silica when the atoms are absent. (d) Absorption spectrum Im(K) of the signal field as a function of Δω for different core radius r0. The red, blue and green lines are for r0 = 13 μm, 17 μm, and 100 μm, respectively. The other notations in the figure are explained in the text.
Fig. 2
Fig. 2 (a) The propagation of the ultraslow optical soliton, with |Ωs(z, τ)τ0| as a function of z/LD and t/τ0 (LD is dispersion length and τ0 is pulse duration). (b) The comparison of waveshapes between z = 0 (blue curve) and z = 2LD (red curve).
Fig. 3
Fig. 3 Numerical results on the storage and retrieval of an optical soliton pulse and a linear optical pulse for r0 = Λ0 = 13 μm. (a) [(b)] Evolution of the dimensionless half Rabi frequency |Ωsτ0| of the signal field (atomic coherence σ̃21) as a function of time t for different propagation distance z in the soliton regime. (c) [(d)] Evolution of the dimensionless half Rabi frequency |Ωsτ0| of the signal field (atomic coherence σ̃21) as a function of t for different z in the linear regime. In each panel, the black, red, green, yellow, sky blue, and blue solid lines are for z=0, 1, 2, 3, 4 and 5 cm, respectively; the purple solid line represents the dimensionless half Rabi frequency |Ωcτ0| of the control field.
Fig. 4
Fig. 4 Memory efficiency η of the optical soliton pulse as a function of the fiber length Lz. Solid lines are fitted curves based on numerical calculation. The blue, red and green solid lines are for the fiber core radius r0=13, 15 and 17 μm, respectively. Dashed-dotted lines for each core radius are the memory efficiencies when a microwave field is coupled to the two lower atomic levels [i.e. |1〉 and |2〉 in Fig. 1(b)].
Fig. 5
Fig. 5 (a) Storage and retrieval of the optical soliton pulse in the HC-PCF with core radius r0 = 50 μm and pitch Λ0 = 25 μm. The subplots from (i) to (v) give the intensity distribution |Es|2 of the soliton pulse in the (x, y) plane when propagating to the distance z = 0, 1, 2.5, 4, and 5 cm, respectively. t = 0, 3.5τ0, 15τ0, 25τ0, and 28.5τ0 shown respectively in (i) to (v) are the times when soliton’s peak arrives at the positions z = 0, 1, 2.5, 4, and 5 cm, respectively. (b) Storage and retrieval of a linear optical pulse in the same fiber.
Fig. 6
Fig. 6 Numerical result for the effective refractive index neff of the kagome-structured HC-PCF as a function of frequency ω with pitch Λ0 = 13 μm and three different core radius r0. The solid (dashed) line is for the fundamental (first higher-order) mode; the blue, red, and green colors are for r0 = 13 μm, r0 = 15 μm, r0 = 17 μm, respectively.

Equations (40)

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E = l = s , c e l R r 0 J 1 ( k r 0 ) l ( z , t ) q l ( x , y ) e i [ β l z ω t ] + c . c . .
i ( t + Γ ) σ = [ H ^ int , σ ] ,
i ( z + n 2 c n eff t ) Ω s + κ 13 σ ˜ 31 = 0 ,
K = Δ ω c n 2 n eff + κ 13 ( Δ ω + d 21 ) | ζ ( x , y ) Ω c | 2 ( Δ ω + d 21 ) ( Δ ω + d 31 ) ,
Ω s ( 1 ) = F exp ( i θ ) ,
σ j 1 ( 1 ) = δ j 3 ( Δ ω + d 21 ) δ j 2 ζ * ( x , y ) Ω c * | ζ ( x , y ) Ω c | 2 ( Δ ω + d 21 ) ( Δ ω + d 31 ) ζ ( x , y ) F e i θ , ( j = 2 , 3 )
V g = { 1 c n 2 n eff + κ 13 ( Δ ω + d 21 ) 2 + | ζ ( x , y ) Ω c | 2 [ | ζ ( x , y ) Ω c | 2 ( Δ ω + d 21 ) ( Δ ω + d 31 ) ] 2 } 1 .
W = κ 13 ζ ( x , y ) Ω c a 32 * ( 2 ) + ( Δ ω + d 21 ) ( 2 a 11 ( 2 ) + a 22 ( 2 ) ) | ζ ( x , y ) Ω c | 2 ( Δ ω + d 21 ) ( Δ ω + d 31 )
i U z K 2 2 2 U τ 2 W | U | 2 U = i a U ,
χ ( 3 ) = 2 c ω s | p 13 | 2 2 W .
E s = τ 0 | p 13 | K ˜ W ˜ R r 0 J 1 ( k r 0 ) J 0 ( 2.405 r r 0 ) sech [ 1 τ 0 ( t z V ˜ g ) ] × exp [ i ( K ˜ 0 1 2 L D ) z i ( ω s + Δ ω ) t ] + c . c . ,
L N = 2.9 cm ,
V ˜ g = Re ( V g ) = 8.17 × 10 4 c ,
P max = 0.82 × 10 9 W ,
Ω c = Ω c 0 { 1 1 2 tanh [ t T c off T s ] + 1 2 tanh [ t T c on T s ] } ,
η = T c on d t r r 0 d x d y | E s out ( x , y , t ) | 2 T c off d t r r 0 d x d y | E s in ( x , y , t ) | 2 ,
J 2 = | T c off d t r r 0 d x d y E s out ( x , y , t + Δ T ) E s in ( x , y , t ) | 2 T c off d t r r 0 d x d y | E s in ( x , y , t ) | 2 T c on d t r r 0 d x d y | E s out ( x , y , t ) | 2 ,
E = α ω e α ( ω ) α ( ω ) q α ( x , y ) e i [ β α ( ω ) z ω t ] + c . c . ,
( 2 x 2 + 2 y 2 ) q α ( x , y ) + n 2 ( x , y ) ω 2 c 2 q α ( x , y ) = β α 2 ( ω ) q α ( x , y ) .
i t σ 11 i Γ 13 σ 33 + ζ * ( x , y ) Ω s * σ 31 ζ ( x , y ) Ω s σ 31 * = 0 ,
i t σ 22 i Γ 23 σ 33 + ζ * ( x , y ) Ω c * σ 32 ζ ( x , y ) Ω c σ 32 * = 0 ,
i t σ 33 + i Γ 13 σ 33 + ζ * ( x , y ) Ω s * σ 31 + ζ ( x , y ) Ω s σ 31 * ζ * ( x , y ) Ω c * σ 32 + ζ ( x , y ) Ω c σ 32 * = 0 ,
( i t + d 21 ) σ 21 ζ ( x , y ) Ω s σ 32 * + ζ * ( x , y ) Ω c * σ 31 = 0 ,
( i t + d 31 ) σ 31 ζ ( x , y ) Ω s ( σ 33 σ 11 ) + ζ ( x , y ) Ω c σ 21 = 0 ,
( i t + d 32 ) σ 32 ζ ( x , y ) Ω c ( σ 33 σ 22 ) + ζ ( x , y ) Ω s σ 21 * = 0 ,
i ζ ( x , y ) ( z + n 2 c n eff t ) Ω s + κ 13 σ 31 = 0 ,
a 11 ( 2 ) = P 2 P 1 i Γ 13 | ζ ( x , y ) Ω c | 2 ( 1 d 32 * 1 32 ) | ζ ( x , y ) | 2 ,
a 22 ( 2 ) = G | ζ ( x , y ) | 2 i Γ 13 a 11 ( 2 ) i Γ 13 ,
a 21 ( 2 ) = ζ * ( x , y ) Ω c * ( 2 Δ ω + d 21 + d 31 ) D 2 ζ ( x , y ) ,
a 31 ( 2 ) = ( Δ ω + d 21 ) 2 + | ζ ( x , y ) Ω c | 2 D 2 ζ ( x , y ) ,
a 32 ( 2 ) = ζ ( x , y ) Ω c d 32 [ | ζ ( x , y ) | 2 D * ( a 11 ( 2 ) + 2 a 22 ( 2 ) ) ] ,
σ ˜ j j ( z , t ) = d x d y | ζ ( x , y ) | 2 σ j j ( x , y , z , t ) d x d y | ζ ( x , y ) | 2 , ( j = 1 , 2 , 3 )
σ ˜ 21 ( z , t ) = d x d y | ζ ( x , y ) | 2 σ 21 ( x , y , z , t ) d x d y | ζ ( x , y ) | 2 ,
σ ˜ 31 ( 32 ) ( z , t ) ζ ( x , y ) = σ 31 ( 32 ) ( x , y , z , t ) ,
i t σ ˜ 11 i Γ 13 σ ˜ 33 + ρ Ω s * σ ˜ 31 ρ Ω s σ ˜ 31 * = 0 ,
i t σ ˜ 22 i Γ 23 σ ˜ 33 + ρ Ω c * σ ˜ 32 ρ Ω c σ ˜ 32 * = 0 ,
i t σ ˜ 33 + i Γ 3 σ ˜ 33 ρ Ω s * σ ˜ 31 + ρ Ω s σ ˜ 31 * ρ Ω c * σ ˜ 32 + ρ Ω c σ ˜ 32 * = 0 ,
( i t + d 21 ) σ ˜ 21 ρ Ω s σ ˜ 32 * + ρ Ω c * σ ˜ 31 = 0 ,
( i t + d 31 ) σ ˜ 31 Ω s ( σ ˜ 33 σ ˜ 11 ) + Ω c σ ˜ 21 = 0 ,
( i t + d 32 ) σ ˜ 32 Ω c ( σ ˜ 33 σ ˜ 22 ) + Ω s σ ˜ 21 * = 0 ,

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