Abstract

We investigate the light emission characteristics for single two level quantum dot (QD) in a realistic photonic crystal (PC) L3 cavity based upon the local coupling strength between the QD and cavity together with the Green’s function in which the propagation function related to the position of the detector is taken into account. We find for a PC cavity that the line shape of the propagation function in frequency domain is identical to that of the cavity and independent on the detector's position. We confirm that this identity is not influenced by the horizontal decay of the cavity. Furthermore, it is revealed that the vacuum fluorescence spectrum of the coupled system never give the triplet in strong coupling regime. Our work demonstrates that the experimental spectral-triplet in coupled system of single QD and PC cavity cannot be individually understood by vacuum Rabi splitting without including other physics mechanism.

© 2013 Optical Society of America

Cavity quantum electrodynamics (QED) [1,2] has been a hot topic that has been attracting sustaining interest for decades. It not only provides a test bed for quantum physics but also has important applications in quantum information science with atoms and photons [3,4]. By tailoring the light-matter interactions between the quantum dot (QD) and microcavity, various striking quantum phenomena have been revealed including vacuum Rabi splitting [59], quantum entanglement [1012], laser oscillation [13,14], single photon source with photon antibunching [15,16], blockade [17] and spontaneous emission control [18].

Since the first observation of the vacuum Rabi splitting (VRS) in a solid state system composing of QDs and photonic-crystal-cavity (PC cavity) [6], this system has been considered as a great candidate for realizing strong coupling between quantum dots and a microcavity. In the work of Hennessy et al. [8], an additional middle peak appeared along with the two VRS peaks under on-resonance conditions, forming a spectral triplet. This middle peak preserved exactly the wavelength, line width and polarization of the bare-cavity mode. This phenomenon has attracted intensive attentions and incurred controversial discussions. A view has been echoed that this phenomenon indicates a clear deviation from standard atomic cavity QED theories that treat a single QD as a two level artificial atom, and then a theoretical model was proposed for understanding this phenomenon based on both the exciton complexes in a QD and the quantum anti-Zeno effect caused by pure dephasing [1921]. In contrast, another theoretical model was proposed by Hughes et al. [22] in which the vacuum fluorescence spectrum is expressed as the product of a propagation function and the local dipole spectrum [23]. In this model, they assumed that the line width of the propagation function can be significantly smaller that the line width of the projected local density of states (PLDOS). This assumption is the key to produce a triple spectrum with VRS without considering other physics mechanism.

Motivated by the mentioned-above controversy about the triple spectrum in the coupled system of single two-level QD and a PC cavity, we investigate the vacuum fluorescence spectra for this coupled system based upon accurate numerical simulations of the propagation and local Green’s functions. Our results reveal that the propagation function determined by the related Green’s function with the position of the detector has the same line shape as that of the multiplication factor of the PLDOS related with local Green function, i.e., they have the identical central frequency and line width. This identity is independent on the position of the detector and not influenced by the horizontal decay of the cavity. As a consequence, the pure vacuum Rabi splitting effect only results in double fluorescence spectrum. The understanding of the experimental spectral-triplet in the coupled systems need to consider other physics mechanism.

We consider a QD as two level exciton placed in inhomogeneous dielectrics, the Hamiltonian of the system within the dipole approximation and rotating wave approach can be written as [24]

=ω0|ee|+λωλaλaλ+λgλ(r0)aλσ+gλ(r0)σ+aλ
where gλ(r0)=iω0(2ε0ωλ)1/2Eλ(r0)d is the coupling coefficient, σ=|ge| and σ+=|eg| are the Pauli operators of the two-level system, ω0 is the transition frequency of the bare emitter, r0 is the location of the QD, ωλand Eλ(r)are the frequency and electric field of the λ-th eigenmode in the nanostructure, and d=dd^ is the transition dipole moment between the two levels. The vacuum fluorescence spectrum is calculated by [22,23]
S(ω)=0dt10dt2eiω(t1t2)E()(r,t1)E(+)(r,t2).
It is straightforward to obtain that

S(ω)=f(rp,r0,ω)P(r0,ω)

Here

f(rp,r0,ω)=|K(rp,r0,ω)dε0|2

is the propagation function which describes the electric field intensity of at the probe point rp emitted by a classical dipole located at r0 with the transition frequency ω. The generalized-transverse Green function is introduced as [22,25]

K(r,r,ω)=λωλ2Eλ(r)Eλ(r)ω2ωλ2=ω2c2G(r,r,ω)Iδ(rr)εr(r,ω),

where the dyadic Green’s function [26] satisfies the equation

[××εr(r,ω)ω2c2]G(r,r,ω)=Iδ(rr),

εr(r,ω) is the relative dielectric constant and c is the speed of light in vacuum. P(r0,ω)=[σ(ω)]σ(ω) with σ(ω)=0σ(t)eiωtdt is the local dipole or polarization spectrum. The conventional definition of the emission spectrum from a two-level exciton only consider P(r0,ω) [27,28]. Assuming that the exciton of the QD is initially at the excited state and the field is in vacuum state, P(r0,ω) can be obtained as

P(r0,ω)={|ωω0ω02d2ω2ε0d^K(r0,r0,ω)d^|2}1.
Equations (3), (4) and (7) indicate that the vacuum fluorescence spectrum depends on the Green function in two separate ways: one for propagation included in the propagation function, and one for the local field effect on the quantum dot included in the local dipole spectrum. According to Eq. (5), K(r,r,ω) is different from (ω/c)2G(r,r,ω)only when r=r, thus in Eq. (4) the calculation of Kfor the propagation function can be directly linked to the calculation of G. The direct calculation of K(r0,r0,ω) could be more difficult. In present work, the identity 1/(ωω+i0+)=[1/(ωω)]iπδ(ωω)is applied in Eq. (5), and then Eq. (7) can be rewritten as

P(r0,ω)={[ωω0Δ(r0,ω)]2+Γ(r0,ω)2/4}1,

where

Γ(r0,ω)=2πλ|gλ(r0)|2δ(ωωλ)=2ω02d2ω2ε0d^Im[K(r0,r0,ω)]d^

is the LCS and

Δ(r0,ω)=2π0Γ(r0,ω)ωωdω=ω02d2ω2ε0d^Re[K(r0,r0,ω)]d^

is the level shift [24]. Here the dielectrics is lossless and εr(r,ω) is real, according to Eq. (5) the imaginary part of K(r0,r0,ω)is identical to that of (ω/c)2G(r0,r0,ω), and then we have

Γ(r0,ω)=2ω02d2ε0c2d^Im[G(r0,r0,ω)]d=Γ0ωω0M(r0,ω,d^),

where Γ0 is the spontaneous emission rate of the QD in vacuum, M(r0,ω,d^) is the local multiplication factor of the PLDOS and can be obtained by the ab-initio mapping [29]. The level shift can be obtained by the principle value integral of the LCS in Eq. (10).

Finally, we have

S(ω)=f(rp,r0,ω){[ωω0Δ(r0,ω)]2+Γ(r0,ω)2/4}1,

where f(rp,r0,ω)=(ω2/c2ε0)2|G(rp,r0,ω)d|2.

We investigate single QD in Photonic Crystal L3 cavity following the design of [6], as depicted in Fig. 1(a). The base structure is composed of air holes in GaAs with refractive index n = 3.4. The spontaneous emission lifetime of the QD in GaAs is 1.82 ns.

 

Fig. 1 The schematic diagrams of the PC L3 cavity system. (a) Cross-section on central plane (z = 0 plane) of the PC L3 cavity. The location of the QD is r0 = (0, 0, 0) at the center of the cavity and the orientation d^ is along y direction. (b) The 3D schematic diagram with the locations of 15 probe points.

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The local multiplication factor of the PLDOS M(r0,ω,d^) is displayed in Fig. 2(a) for the PC slab L3 cavity with a = 300nm, r = 0.27a, s = 0.20a, the thickness d = 0.90a, and 31 air holes in the x-direction and 29 air holes in the y-direction. There is thus 14 layers of air holes that surround the defect. For convenience, this slab PC L3 cavity is denoted as Sample#1. We find that the M(r0,ω,d^) can be very well fitted by Lorentz function [29]

 

Fig. 2 (a) The multiplication factor of the PLDOS for the Sample#1. The propagation functions on probe points (b) A1 = (0, 0, 1.5) a, (c) B1 = (0, 0, 5.5) a and (d) C1 = (0, 0, 9.5) a.

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M(r0,ω,d^)=2|gc(r0)|2Γ0κ/2(ωωc)2+(κ/2)2

where ωc is the frequency of the cavity mode, gc(r0) is the g factor that characterizes the coupling strength between the QD and the cavity mode, κ=ωc/Q is the decay rate of the cavity mode and Q is the quality factor (Q factor). From Eq. (12) we can determine the characteristic parameters of the cavity QED system, the normalized frequency of cavity mode is found to be 0.2433232, the decay rate in the unit of normalized frequency is κ=1.74321×106, the Q factor is thus 139,583, and the g factor is g = 22.1GHz.

The propagation function in Eq. (4) is related to the electric dipole field determined by the Green’s function. Hughes et al. [22] proposed a simple analytical model of the generalized-transverse Green’s function Kfor planar PC cavities. They divided the decay rate of the cavity κ into two contributions κ=κv+κh, where κv and κh account for vertical and horizontal decay loss, respectively. They claimed that the local Green’s function has the form Klocal(r0,r0,ω)=ωc2|Ec(r0)|2/(ω2ωc2+iωκ), while the propagation Green’s function has the form Kprop(rp,r0,ω)=ωc2Ec(rp)Ec(r0)/(ω2ωc2+iωκv). For a planar PC cavity with high Q factor, Klocal(r0,r0,ω) and Kprop(rp,r0,ω) tend to zero very fast with increasing |ωωc|, then d^Im[Klocal(r0,r0,ω)]d^ and |Kprop(rp,r0,ω)d|2 have excellent Lorentz function. Comparing with our expression in Eq. (13), this equivalently assumes that the local multiplication factor M(r0,ω,d^) of the PLDOS has line width κ, while the propagation function f(rp,r0,ω) is of the line width κv. Moreover, it is assumed that there is considerable difference between κ and κv. Indeed, according to these assumptions we can also obtain the triple-peak spectrum from Eq. (12) if κ/κv>1.25as like in [22]. However, the above-mentioned assumption has not been justified by accurate numerical simulation.

We now simulate the propagation function f(rp,r0,ω) for the Sample#1 and determine its line width. 15 different probe points outside the cavity in air with different distances and angles to the QD are chosen, as shown in Fig. 1(b), and the propagation function f(rp,r0,ω) are obtained by the direct numerical simulations of the Green’s function. The propagation functions f(rp,r0,ω) for three probe points along the z axis, A1 = (0, 0, 1.5) a, B1 = (0, 0, 5.5) a and C1 = (0, 0, 9.5) a are also plotted in Figs. 2(b)-2(d). We can see that the propagation functions really have Lorentz line shape. Furthermore, the line widths κf of the propagation function f(rp,r0,ω) for these points are identical to the total decay rate κ of the cavity found from the M(r0,ω,d^), regardless how far these probe points are away from the surface of the PC L3 cavity in this direction.

By fitting the simulation data for all 15 probe points with the Lorentz function, we find that the central frequency in the propagation functions of every point remains unchanged as 0.2433232 identical to the cavity mode frequency. Table 1 lists the line width κf obtained by the fitting for all 15 probe points, and they are all identical to the total decay rate κ of the cavity. We note that the probe points have cover different vertical distances from the surface of the PC cavity and different azimuth angles, which should be enough to reflect the characteristics of the propagation functions for spatial locations in near, intermediate and far field. It is thus a reliable demonstration that, in a typical high Q PC L3 cavity structure, the line width of the propagation function is identical to that of the PLDOS, i.e., κf=κ, and that this identity is independent on the spatial location, or, in realistic experiments, the position of the detector.

Tables Icon

Table 1. κf factors obtained by fitting f(rp,r0,ω) in Eq. (13) on every probe point.

With the simulation data of the PLDOS and the propagation function, we are able to calculate the vacuum fluorescence spectrum S(ω) in Eq. (12). We tune the transition wavelength of the QD across the resonant wavelength of the high Q PC L3 cavity, the detuning between these two wavelengths is set to be −0.06 nm, 0 nm and 0.06 nm, respectively. Figure 3(a) shows that, when the transition wavelength of the QD is resonant with the cavity mode, a symmetric Rabi splitting appears in the local dipole spectrum P(r0,ω), the space of the splitting is 44.1GHz. When the transition frequency of the QD is detuned with the cavity mode, the spectra exhibit asymmetric vacuum Rabi splitting. The space of the splitting shows a typical anti-crossing. These all indicate that the strong coupling between the QD and the cavity mode is achieved. From the above fact that the line shape of the propagation function is independence on the spatial location of the probe point in this structure, we can choose a certain probe point to calculate the vacuum fluorescence spectrum S(ω) that represents the result for arbitrary detector location, here we choose the point C1 = (0, 0, 9.5) a. It can be seen clearly in Fig. 3(b) that the vacuum fluorescence spectrum is still double under on-resonance condition, the spectral triplet observed in [8] doesn’t appear. Furthermore, the frequencies of the two peaks in the vacuum fluorescence spectra remain nearly the same as those in the dipole spectra, and the vacuum Rabi splitting obtained under the on-resonance condition also remains 44.1GHz, the only difference is that the relative heights of the Rabi splitting peaks in the detuned cases are changed slightly. These results demonstrate that the VRS only yields double peaks in vacuum fluorescence spectra.

 

Fig. 3 (a) The local dipole spectra P(r0,ω) of the Sample#1. (b) The vacuum fluorescence spectra S(ω)for the probe point C1 = (0, 0, 9.5)a. The wavelength detuning between transition wavelength of the QD and the resonant wavelength of the cavity (1232.92 nm) increases from −0.06 nm to 0.06 nm (from top to bottom).

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Although our results in Figs. 2 and 3 support κf=κ, this high Q L3 cavity may be a special structure with horizontal decay κh=0 so that it also satisfies κf=κv. In order to make a further justification, we then consider reducing the number of air hole layers surrounding the defect in Sample#1 to increase the horizontal decay.

Figure 4 displays the decay rate κ obtained from the multiplication factor M(r0,ω,d^), and the corresponding Q factor for L3 cavities with different number of air hole layers surrounding the defect. The sample with 14 layers of air holes is the original Sample#1. When the number of air hole layers decreases from 14 to 9, the decay rate κ only increases slightly, the Q factor is still above 120,000; while if the number of air hole layers is decreased further, the decay rate κ is dramatically increased and the Q factor is reduced. This varying of the Q factor is similar with the one in early work by O. Painter et al. [30], in which they found that the horizontal decay κh decreases exponentially with the number of the air hole layers and the vertical decay κv stays relatively constant. For a L3 cavity with number of surrounding air hole layers less than 7, the total decay is dominated by the in-plane losses. When the number of the surrounding air hole layers increases, the horizontal decay κh is decreased well below κv, and the total decay rate κ asymptotically approaches κv.

 

Fig. 4 The decay rate κfrom the multiplication factor M(r0,ω,d^) with the corresponding Q factor, and the line width κf of the propagation functions f(rp,r0,ω), for different numbers of air hole layers in the L3 cavity.

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The line width κf of the propagation functions f(rp,r0,ω) for each L3 cavity with different number of surrounding air hole layers is also displayed in Fig. 4. For L3 cavities with number of surrounding air hole layers less than 7, our simulation results indicate that κf is still in excellent agreement with κ rather than κv. These results confirm that a remarkable horizontal decay does not influence the identity between the line width of M(r0,ω,d^) and that of f(rp,r0,ω) in the PC L3 cavity structures, and the key assumption proposed in [22] that supports the triple-peak spectrum is invalid.

Figure 5 displays the local dipole spectra and the vacuum fluorescence spectra for L3 cavities with number of surrounding air hole layers less than 7. For PC L3 cavities with 5 or 6 surrounding air hole layers, the vacuum fluorescence spectra remain as doublet with two broad peaks. Comparing corresponding curves in Figs. 5(a) and 5(b), it can be seen that the valleys in the vacuum fluorescence spectra become shallow than those in the local dipole spectra, and the splitting spaces of the peak become slightly narrower. When the number of surrounding air hole layers is decreased to 4, the Q factor of the cavity is too low to achieve the strong coupling between the quantum dot and the cavity mode, and both the local dipole and vacuum fluorescence spectra become singlet.

 

Fig. 5 (a) The local dipole spectra P(r0,ω)and (b) vacuum fluorescence spectra S(ω) for the L3 cavities with less than 7 layers of air holes surrounding the defect. The transition wavelength of the QD is resonant with the resonant wavelength λc of each cavity.

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In order to further confirm the irrationality of the assumption in [22], we consider a classical dipole source

Pex(r,t)=dd^δ(t)δ(rr0),

located inside the cavity. The electric field induced by this dipole can be calculated by the Green’s function as

Ed(r,t)=d2πε0c20ω2G(r,r0,ω)d^eiωtdω+c.c.=d2πε00K(r,r0,ω)d^eiωtdω+c.c.Pex(r,t)ε0εr(r0)
According to the assumption in [22], for r inside the cavity the Green’s function should take the form of Klocal, for r outside the cavity we should use Kprop. The electric field inside the cavity can be obtained as

Elocal(r,t>0)=E0(r)exp(iωctκ2t)+c.c.,

where

E0(r)=iωcd2ε0Ec(r)Ec*(r0)·d^,

and the electric field outside the cavity can be written as

Eprop(r,t>0)=E0(r)exp(iωctκv2t)+c.c.

On the boundary surface of the cavity, the electromagnetic boundary condition requires that both electric fields inside and outside the surface have the same time dependence. It can be seen in Eqs. (16)-(18) that this boundary condition is broken under the assumption in [22].

On the other hand, we can also consider the exponential decay of the energy stored in the cavity mode

U(t)=U(0)exp(κt)=U(0)exp(ωcQt),

the total power loss of the cavity is defined by energy lost per time as

P(t)=dU(t)dt=κU(t).

This power can be separated into two vertical and horizontal parts as P(t)=Pv(t)+Ph(t), the decay rate can also be written as κ=κv+κh, and the power lost in the vertical direction can thus be written as [30]

Pv(t)=κvU(t)=κvU(0)exp(κt).

Equation (21) demonstrates that the vertical decay rate κv is defined to represent the amount of vertical loss power Pv(t) . More importantly, it is shown clearly that Pv(t) decays exponentially at the total decay rate κ rather than κv. Therefore, the vertical decay rate κv should not be used to characterize the time dependence of the cavity energy and the electric field. It is thus unreasonable to assume that the line width of the propagation function is κv.

Our simulation results indicate that the line width κfof the propagation function f(rp,r0,ω) is independent on rp. We further confirm that κf is identical to the total decay rate κrather than the vertical decay rate κv. Moreover, Eq. (21) is valid regardless of what leads to the horizontal decay κh. Therefore, the identity κf=κis still valid when the horizontal decay κh is caused by other imperfection in realistic fabrications, such as the material losses or the disorder of the photonic crystal. We can thus conclude that, the pure VRS of the coupled system of the two-level QD and PC L3 cavity do not produce triple spectrum in strong coupling regime.

In summary, we have studied the vacuum fluorescence spectrum from the coupled system of a single two-level QD and PC L3 cavity based on accurate numerical simulations of the propagation and local Green’s functions. It is found that the propagation function related to the position of the detector has a Lorentz line shape, whose central frequency and line width are identical to those of the PLDOS. Moreover, this identity is independent on the position of the detector outside the slab of the PC cavity, and is not influenced by the horizontal decay κh. Based on the simulation results and brief theoretical analysis, we have confirmed that the assumption proposed in [22] about the propagation and local optical Green’s function is invalid. Therefore, the pure VRS leads to only double peaks rather than triplet in the vacuum fluorescence spectrum in strong coupling regime. In order to understand the spectral triplet observed in the experiments, it is necessary to consider other physics mechanism beyond the VRS. Our work should stimulate further research interest on this topic.

Acknowledgments

We thank Dr. Chao Li for useful discussions. This work was financially supported by the National Basic Research Program of China (2010CB923200), the National Natural Science Foundation of China (Grant U0934002), and the Ministry of Education of China (Grant V200801).

References and links

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References

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  1. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
    [CrossRef] [PubMed]
  2. K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
    [CrossRef] [PubMed]
  3. C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002).
    [CrossRef] [PubMed]
  4. J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
    [CrossRef]
  5. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
    [CrossRef] [PubMed]
  6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
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  7. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
    [CrossRef] [PubMed]
  8. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
    [CrossRef] [PubMed]
  9. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
    [CrossRef] [PubMed]
  10. J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
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  11. R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
    [CrossRef] [PubMed]
  12. R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
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  13. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
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  14. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
    [CrossRef]
  15. W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
    [CrossRef] [PubMed]
  16. D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
    [CrossRef] [PubMed]
  17. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
    [CrossRef]
  18. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
    [CrossRef]
  19. M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
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  20. M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
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  21. M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
    [CrossRef] [PubMed]
  22. S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express17(5), 3322–3330 (2009).
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  24. X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
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  25. M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
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  26. C. T. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1993).
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  28. L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
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  29. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
    [CrossRef]
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2013 (1)

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

2012 (1)

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

2010 (1)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

2009 (5)

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[CrossRef]

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express17(5), 3322–3330 (2009).
[CrossRef] [PubMed]

2008 (3)

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

2007 (4)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

2006 (2)

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006).
[CrossRef]

2005 (1)

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

2004 (3)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
[CrossRef]

2003 (2)

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

2002 (2)

C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002).
[CrossRef] [PubMed]

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

2001 (1)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

1999 (2)

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999).
[CrossRef]

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

1989 (1)

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

Arakawa, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

Asano, T.

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Badolato, A.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Brecha, R. J.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

Carmichael, H. J.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Chang, H.-S.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chang, W.-H.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chen, G.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Chen, W.-Y.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chyi, J.-I.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

del Valle, E.

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[CrossRef]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Doherty, A. C.

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Englund, D.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Faraon, A.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Forchel, A.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Furusawa, A.

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Fushman, I.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Gérard, J. M.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Gérard, J.-M.

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Gippius, N. A.

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Götzinger, S.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

Gu, B.-Y.

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Hennessy, K. J.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

Hofmann, C.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Hours, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Hsieh, T.-P.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
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Hsu, T.-M.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Hu, E. L.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Huang, Y.-G.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Hughes, S.

Imamoglu, A.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Inoue, J.-i.

T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006).
[CrossRef]

Iwamoto, S.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

Jiang, H.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Jin, C.-J.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Johne, R.

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Kamp, M.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
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H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Kojima, K.

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kumagai, N.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

Lagendijk, A.

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
[CrossRef]

Laussy, F. P.

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[CrossRef]

Lemaître, A.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Liu, J.-F.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Löffler, A.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
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H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
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Malpuech, G.

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Martrou, D.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Monroe, C.

C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002).
[CrossRef] [PubMed]

Noda, S.

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Nomura, M.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

O'Brien, J. L.

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Ochiai, T.

T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006).
[CrossRef]

Ota, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

Painter, O.

Panzarini, G.

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

Pavlovic, G.

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Peter, E.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Petroff, P.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Press, D.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
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J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
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Raizen, M. G.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Reinecke, T. L.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Rice, P. R.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Sakoda, K.

T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006).
[CrossRef]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999).
[CrossRef]

Sek, G.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Senellart, P.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Shelykh, I. A.

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Solnyshkov, D. D.

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Stoltz, N.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Suttorp, L. G.

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
[CrossRef]

Tejedor, C.

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[CrossRef]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999).
[CrossRef]

Wang, R.

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Wang, X.-H.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Winger, M.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Wubs, M.

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
[CrossRef]

Xu, H.-Q.

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Yamaguchi, M.

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

Yamamoto, Y.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett.98(11), 117402 (2007).
[CrossRef] [PubMed]

Yao, P.

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Yu, Y.-C.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Zhuo, X.-L.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

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

Nat. Photonics (2)

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Nat. Phys. (2)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

Nature (6)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002).
[CrossRef] [PubMed]

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Opt. Express (1)

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Figures (5)

Fig. 1
Fig. 1

The schematic diagrams of the PC L3 cavity system. (a) Cross-section on central plane (z = 0 plane) of the PC L3 cavity. The location of the QD is r0 = (0, 0, 0) at the center of the cavity and the orientation d ^ is along y direction. (b) The 3D schematic diagram with the locations of 15 probe points.

Fig. 2
Fig. 2

(a) The multiplication factor of the PLDOS for the Sample#1. The propagation functions on probe points (b) A1 = (0, 0, 1.5) a, (c) B1 = (0, 0, 5.5) a and (d) C1 = (0, 0, 9.5) a.

Fig. 3
Fig. 3

(a) The local dipole spectra P( r 0 ,ω ) of the Sample#1. (b) The vacuum fluorescence spectra S( ω ) for the probe point C1 = (0, 0, 9.5)a. The wavelength detuning between transition wavelength of the QD and the resonant wavelength of the cavity (1232.92 nm) increases from −0.06 nm to 0.06 nm (from top to bottom).

Fig. 4
Fig. 4

The decay rate κfrom the multiplication factor M( r 0 ,ω, d ^ ) with the corresponding Q factor, and the line width κ f of the propagation functions f( r p , r 0 ,ω ) , for different numbers of air hole layers in the L3 cavity.

Fig. 5
Fig. 5

(a) The local dipole spectra P( r 0 ,ω ) and (b) vacuum fluorescence spectra S( ω ) for the L3 cavities with less than 7 layers of air holes surrounding the defect. The transition wavelength of the QD is resonant with the resonant wavelength λ c of each cavity.

Tables (1)

Tables Icon

Table 1 κ f factors obtained by fitting f( r p , r 0 ,ω ) in Eq. (13) on every probe point.

Equations (21)

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= ω 0 |ee|+ λ ω λ a λ a λ + λ g λ ( r 0 ) a λ σ + g λ ( r 0 ) σ + a λ
S( ω )= 0 d t 1 0 d t 2 e iω( t 1 t 2 ) E ( ) ( r, t 1 ) E ( + ) ( r, t 2 ) .
S( ω )=f( r p , r 0 ,ω )P( r 0 ,ω )
f( r p , r 0 ,ω )= | K( r p , r 0 ,ω )d ε 0 | 2
K( r, r ,ω )= λ ω λ 2 E λ ( r ) E λ ( r ) ω 2 ω λ 2 = ω 2 c 2 G( r, r ,ω ) Iδ( r r ) ε r ( r,ω ) ,
[ ×× ε r ( r,ω ) ω 2 c 2 ]G( r, r ,ω )=Iδ( r r ),
P( r 0 ,ω )= { | ω ω 0 ω 0 2 d 2 ω 2 ε 0 d ^ K( r 0 , r 0 ,ω ) d ^ | 2 } 1 .
P( r 0 ,ω )= { [ ω ω 0 Δ( r 0 ,ω ) ] 2 +Γ ( r 0 ,ω ) 2 /4 } 1 ,
Γ( r 0 ,ω )=2π λ | g λ ( r 0 ) | 2 δ( ω ω λ ) = 2 ω 0 2 d 2 ω 2 ε 0 d ^ Im[ K( r 0 , r 0 ,ω ) ] d ^
Δ( r 0 ,ω )= 2π 0 Γ( r 0 , ω ) ω ω d ω = ω 0 2 d 2 ω 2 ε 0 d ^ Re[ K( r 0 , r 0 ,ω ) ] d ^
Γ( r 0 ,ω )= 2 ω 0 2 d 2 ε 0 c 2 d ^ Im[ G( r 0 , r 0 ,ω ) ]d= Γ 0 ω ω 0 M( r 0 ,ω, d ^ ),
S( ω )=f( r p , r 0 ,ω ) { [ ω ω 0 Δ( r 0 ,ω ) ] 2 +Γ ( r 0 ,ω ) 2 /4 } 1 ,
M( r 0 ,ω, d ^ )= 2 | g c ( r 0 ) | 2 Γ 0 κ/2 ( ω ω c ) 2 + ( κ/2 ) 2
P ex ( r,t )=d d ^ δ( t )δ( r r 0 ),
E d ( r,t )= d 2π ε 0 c 2 0 ω 2 G( r, r 0 ,ω ) d ^ e iωt dω +c.c. = d 2π ε 0 0 K( r, r 0 ,ω ) d ^ e iωt dω +c.c. P ex ( r,t ) ε 0 ε r ( r 0 )
E local ( r,t>0 )= E 0 ( r )exp( i ω c t κ 2 t )+c.c.,
E 0 ( r )= i ω c d 2 ε 0 E c ( r ) E c * ( r 0 )· d ^ ,
E prop ( r,t>0 )= E 0 ( r )exp( i ω c t κ v 2 t )+c.c.
U( t )=U( 0 )exp( κt )=U( 0 )exp( ω c Q t ),
P( t )= dU( t ) dt =κU( t ).
P v ( t )= κ v U( t )= κ v U( 0 )exp( κt ).

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