Abstract

Creating strong coupling between quantum emitters and a high-fidelity photonic platform has been a central mission in the fields of quantum optics and quantum photonics. Here, we describe the design and fabrication of a scalable atom–light photonic interface based on a silicon nitride microring resonator on a transparent silicon dioxide-nitride multi-layer membrane. This new photonic platform is fully compatible with freespace cold atom laser cooling, stable trapping, and sorting at around 100 nm from the microring surface, permitting the formation of an organized, strongly interacting atom–photonic hybrid lattice. We demonstrate small radius (around 16 μm) microring and racetrack resonators with a high quality factor (Q) of 3.2×105, projecting a single atom cooperativity parameter (C) of 25 and a vacuum Rabi frequency (2g) of 2π×340MHz for trapped cesium atoms interacting with a microring resonator mode. We show that the quality factor is currently limited by the surface roughness of the multi-layer membrane, grown using low-pressure chemical vapor deposition processes. We discuss possible further improvements to a quality factor above 5×106, potentially achieving a single atom cooperativity parameter higher than 500 for strong single atom–photon coupling. Our microring platform may also find applications in on-chip solid-state quantum photonics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Creating efficient atom–light nanophotonic interfaces with stably trapped atoms in their optical near field can lead to a wide range of applications in quantum optics, quantum communications, and quantum many-body physics [13]. Optical nanofibers [48], photonic crystal waveguides [9], and cavities [10,11] are exemplary platforms that have recently demonstrated atom trapping and large atom–light interactions in the evanescent field of their guided modes. Key enabling features for enhanced coupling are sub-diffraction transverse confinement of guided photons and enhanced photonic density of states, achieved either through forming micro- or nano-scale Fabry–Perot cavities or through slow light effects in photonic crystal waveguides. They permit several far-off resonant optical trapping schemes [12] in the near field, such as two-color evanescent field traps [1315], side-illuminating optical traps [9,10,16], or a hybrid trap formed by Casimir–Polder vacuum force and a single-color optical potential in photonic crystal waveguides [17,18]. With near field (100nm) trapping above the dielectric surface, it is generally expected that tens to more than a hundred-fold increase in atom–photon coupling rate may be found for a trapped atom in a nanophotonic platform compared to those realized in mirror-based optical cavities and resonators.

On the other hand, achieving coherent quantum operations with high fidelity requires ultra-low optical loss in the host dielectric nanostructures [18,19], and has remained a challenge. In cavity quantum electrodynamics (QED), the figure of merit for quantum coherence is favored by a large single atom cooperativity parameter C=4g2/κγ1, requiring that the atom–photon coupling strength g is large compared to the geometric mean of the photonic loss rate (κ) and the atomic radiative decay rate into freespace (γ). For a perfect quantum emitter, g=3λ3ω0γ16π2Vm (assuming a spherical symmetric dipole), and C3λ34π2QVm depends solely on the ratio between the quality factor Q=ω0/κ of the photonic mode (of frequency ω0 and freespace wavelength λ) and the effective mode volume Vm, which is inversely proportional to the guided-mode photon energy density at the atomic trap location. State-of-the-art high-Q nanophotonic platforms have yet to achieve cooperativity parameters C10 due to limited Q/Vm, which stems mostly from fabrication imperfections. For example, Q104 and Vm/λ3100 are reported recently for a photonic crystal cavity [11] and an atom-induced cavity near the band edge of a photonic crystal waveguide [19,20] that are tailored for coupling with alkali atoms at resonant wavelengths ranging from λ780nm at rubidium D2-line to 894 nm at cesium D1-line. There are multiple schemes in existence for boosting Q/Vm in atom–nanophotonic platforms [3]. For comparison, monolithic micro-photonic resonators such as silica micro-toroids [21], bottles [22], and spheres [23] or silicon nitride micro-disks [24] are other photonic resonator structures with ultrahigh quality factors Q>106 but with large Vm/λ3>104 for transit atoms in time of flight. The prospect of direct laser cooling and atom trapping in their optical near field has remained elusive, partially due to geometrical constraints and limited optical access through the dielectric structures and their substrates [25], if present.

In this paper, we report a planar-type microring photonic structure and its racetrack-variant design capable of simultaneous realizations of strong confinement for large atom–photon coupling rate, experimentally accessible atom trapping and sorting schemes, and high Q/Vm, serving as a coherent, scalable atom–photon quantum interface. Our implementation is based on silicon nitride microring resonators that have recently achieved ultrahigh quality factors Q>107 in telecom optical wavelength band [26,27] and Q>3×106 close to Cs atomic spectroscopy bands [28]. We adapt the design to geometries tailored for cavity QED with neutral atoms and address major challenges that need to be overcome. We enable full optical access for laser cooling and trapping of alkali atoms, e.g., atomic cesium, directly on a microring by fabricating it on a transparent membrane substrate. Moreover, we investigate various trapping schemes including a two-color evanescent field trap and top-illuminating optical tweezers trap at tunable distances around 100 nm above a resonator waveguide, as well as the combination of both schemes for atom array sorting.

2. OVERVIEW OF THE PLATFORM

Figure 1 shows the schematics of our resonator platform. The microrings are fabricated on top of a suspended SiO2-Si3N4 multi-layer membrane, formed by a 2μm-thick SiO2 (silicon dioxide) layer and a 550-nm-thick Si3N4 (silicon nitride) bottom layer that can provide high tensile stress after being released from a silicon substrate to form a large window around an area of 2mm×8mm; see Fig. 2. The high tensile stress offered by the nitride bottom layer is necessary to preserve the optical flatness of the membrane. The transparent membrane allows laser beams to be sent from either top or bottom sides of the microring structure, allowing cold atoms to be directly laser cooled, trapped, and transported on the surface of a microring resonator [29].

 

Fig. 1. Interfacing single atoms with a microring structure on a membrane for strong atom–light interactions. (a) Schematics of a silicon nitride microring (radius R) on a dioxide-nitride membrane, with a single trapped atom (green sphere). Curved arrows depict single atom–photon coupling rate, g, to the resonator modes. Wavy arrows depict intrinsic resonator loss (at rate κi) and the atomic decay (at rate γ), respectively. A linear bus waveguide couples to and from the resonator modes at rates κc (depicted by crossed solid and dashed arrows). (b) Eeffective mode area Am of a microring of width W=1.1μm, height H=0.29μm, and radius R16μm; Am5.2μm2 at the depicted atom location (ρa,za)=(R,100nm). Shaded structures mark the microring waveguide (Si3N4) and supporting membrane (SiO2 and Si3N4 layers), respectively. (c) Atom–photon coupling strength g(z) along a vertical dashed line in (b); g(za)/2π=200MHz is marked by the dotted lines.

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Fig. 2. Fabricated small radius microring/racetrack resonators and optical quality measurements. (a) Optical image of an array of microrings (i) coupled to a linear waveguide bus (ii) for fiber edge coupling in a U-groove (iii). Membrane area is enclosed in a dashed box. (b) Overview of the optical chip. The membrane is suspended within a 2mm×8mm window. (c), (d) SEM of fabricated (c) microring and (d) racetrack resonators, both with width W=0.95μm and height H=0.36μm. (e) Scattering intensity measurements near the resonance of a racetrack resonator. Solid line is a fit, giving (κ,β,ω0)/2π=(1.01,0.655,334.792×103)GHz.

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Due to its higher mode field intensity above the surface of the resonator waveguide (Supplement 1 Section 1.A), we utilize the fundamental transverse-magnetic (TM) mode for creating atom–light coupling. The cross section of the resonator waveguide is chosen for sufficient evanescent field strength above the waveguide surface while maintaining high Q. The small radius of the microring R=16μm ensures a moderately small mode volume Vm=AmL, where L=2πR is the circumference of the ring, and Am is the effective mode area defined as

Am(ρa,za)=ϵ(ρ,z)|E(ρ,z)|2dρdzϵ(ρa,za)|E(ρa,za)|2.
Here, (ρa,za) denotes the transverse atomic location in cylindrical coordinates, ϵ is the dielectric function of the microring structure, and E is the TM-mode electric field. Figure 1(b) plots the cross section of the effective mode area of a TM mode at cesium D1-line λD1=894nm. A moderately small mode area Am(R,za)5.2μm2 can be achieved when an atom is placed at around za100nm above the microring surface, projecting a mode volume of Vm523μm3, single-photon vacuum Rabi frequency 2g=2π×400MHz, and a cooperativity parameter C1×104Q. Achieving high Q>106 in such a small microring can thus make this platform well suited for on-chip cavity QED experiments with high fidelity.

A linear bus waveguide is fabricated next to an array of microrings to couple to the clockwise (CW) and counterclockwise (CCW) resonator modes. Away from the microring coupling region, the bus waveguide is tapered and extends all the way towards the edge of the transparent window where the waveguide is then embedded in a dioxide (or vacuum) top-cladding layer.

As shown in Fig. 2, a U-shaped fiber groove is fabricated for epoxy fixture of a lensed optical fiber, which is edge-coupled to the bus waveguide with 70% (or 50% with vacuum cladding) single-pass coupling efficiency as expected through our finite-difference-time-domain (FDTD) calculations [30]. We have currently achieved 30% coupling efficiency with vacuum cladding. The lensed fiber, the edge-coupled bus waveguide, and an array of coupled microrings form a complete package of high-fidelity atom–light nanophotonics interface; see Fig. 2.

3. FABRICATION OF MICRORING MEMBRANE CIRCUIT AND OPTICAL MEASUREMENTS

Figures 2(a)2(b) show the optical image of a fabricated membrane optical circuit (see [29] for fabrication procedures). Scanning electron micrographs (SEM) of microring and racetrack resonators on the membrane with coupling waveguide buses are shown in Figs. 2(c)2(d).

We characterize the quality factors near cesium D1-line by scanning the frequency ω of the coupled TM-mode and image the scattered light from individual rings on a charge-coupled-device (CCD) camera. The resonant frequency of the microring, ω0, has been thermally tuned by a freespace laser beam heating the silicon part of the optical circuit in vacuum [11]. Figure 2(d) shows a sample measurement. Double resonant peaks have been observed due to the coherent back-scattering effect from fabrication imperfections that mix the CW and CCW modes and create an energy splitting (see Supplement 1 Section 1.B). Our measured CCD counts can be well fitted by a coupled-mode model [31] that captures mode splitting and the peak asymmetry [see also Eq. (2) and Supplement 1 Section 1.B]. The fit gives total photon loss rate κ/2π=1.01GHz, corresponding to an under-coupled quality factor of Q3.2×105 due to waveguide coupling rate κc smaller than the intrinsic loss rate κi.

Using the measurement results and the fabricated geometry (W,H)=(0.95,0.36)μm, we project the single atom cooperativity parameter to be C25, calculated using (g,κ,γ)/2π(170,1010,4.6)MHz; under the same Q and the geometry presented in Fig. 1, we project C35 with g/2π=200MHz. We note that there is still much room for improvement. Below we discuss in detail the optical loss analysis and Q/Vm optimization for maximizing cooperativity C.

A. Current Fabrication Limit and Mitigation Methods

Currently, surface scattering dominates the photon loss in our fabricated microrings; see also Supplement 1 Section 3.A for fundamental limits of the microring platform regarding material absorption. We have characterized the surfaces of the multi-layer film using atomic force microscopy (AFM) and obtained the root-mean-squared roughness σt1.4nm and the correlation length Lt73nm for the top nitride layer. For the bottom surface roughness of the microring, we infer from the surface quality of the dioxide middle layer, which we measured (σb,Lb)(1.6,84)nm. We estimate the edge roughness and correlation length to be around (σ±,L±)(2,60)nm by employing a multipass e-beam writing technique [27,32] and optimized inductively coupled-plasma reactive-ion etching process with CHF3/O2 gas chemistry [27,32,33]. In Supplement 1 Section 3.B, we adopt a volume current method to model the scattering loss rate due to the measured surface roughness [34]. Our result indicates that Qsim3.5×105 is in reasonable agreement with our measured quality factor.

Due to the major roughness incurred in the low-pressure chemical vapor deposition (LPCVD)-deposited dioxide layer, we note that the surface roughness of the microring is around three times worse than a typical singlelayer nitride deposited on a silicon wafer or on a thermally grown dioxide film. Possible improvements can be made by using a chemical mechanical polishing (CMP) technique to reduce the surface roughness in the top nitride layer and the middle dioxide layer as well. It has been reported that the surface roughness and the correlation length of a nitride thin film can be greatly reduced down to σt,b0.1nm and Lt,b10nm from its original rough surface [27]. Alternatively, the edge roughness and correlation length may be reduced to σ±1.39nm and L±39nm by using a plasma-assisted resist reflow technique [35]. These immediate technological improvements permit a potential 10-fold increase in Q/Vm, as will be discussed below.

B. Q/Vm Optimization

Given the characteristics of the surface quality and edge roughness, we perform finite element method (FEM) analysis [36] to obtain a geometrical design that maximizes Q/Vm, concerning the dominant losses, including surface scattering loss and waveguide bending loss. By scanning the cross section and the radius of the microring, it is observed that the waveguide cross section cannot be reduced indefinitely due to the constraint of surface scattering. Similarly, the radius R of the ring is constrained to be above 10μm due to larger bending loss and scattering loss occurring at the sidewalls at larger bend curvature.

In Fig. 3, we plot the cooperativity parameter C as a result of the scan, assuming an atom is trapped at (ρa,za)=(R,100) nm. With the surface roughness at its current value, as in Fig. 3(a), C is maximized when the waveguide geometry tends towards a larger cross section (W, H), which reduces surface scattering, and smaller radius R, which reduces the mode volume. The best projection C46 uses a smaller ring R10μm than in our current design, and (W,H)=(0.8,0.36)μm. For reduced surface roughness, as in Fig. 3(b), a resonator geometry of (W,H,R)=(1.1,0.29,16)μm, as shown in Fig. 1, can achieve Q4.5×106. The projected cooperativity reaches C536, an almost 12 times improvement from our current optimal value. Similarly, a fundamental transverse-electric (TE) mode can also be optimized with a different geometry, giving higher Q8×106 but with a lower optimal C397 due to larger Vm.

 

Fig. 3. Cooperativity optimization via scanning the microring geometry, with the surface roughness parameters (σ±, L±, σt, Lt, σb, Lb)= (a) (2,60,1.4,73,1.6,84) nm and (b) (1.4,39,0.1,10,0.1,10) nm, respectively.

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4. ATOM TRAPPING IN THE OPTICAL NEAR FIELD OF THE MICRORING PLATFORM

We now discuss two schemes, both capable of creating tight far-off-resonant optical traps for cold atoms around zt=100nm above the top surface of the microring. While either scheme can function fully independently, we discuss the combination of both schemes for an atom array assembly on a microring (racetrack) resonator.

A. State-Insensitive Two-Color Evanescent Field Trap

The evanescent field-trapping scheme shares similarities with those realized in nano-fiber traps [13,15], and proposed in nanophotonic waveguides [37,38]. The trap is formed by two TM modes excited near the “magic” wavelengths λr=935.3nm and λb=793.5nm, so that they do not create differential light shifts in the laser cooling transition of cesium (Supplement 1 Section 2). Here, λb (frequency ωb) is blue-detuned from major optical transitions in the ground state, creating strongly repulsive optical force within a short range near the dielectric surface. λr (frequency ωr) is red-detuned, leading to an attractive force with longer decay length than that of the λb mode. The combination of both modes creates a stable trap above the waveguide surface; see Fig. 4.

 

Fig. 4. Two-color evanescent field trap. (a), (c) The coupling schemes are schematically shown in (a) for a microring and (c) for a racetrack resonator, where the injected lights are marked by red (ωr) and blue (ωb) arrows and the ± signs mark the direction of coupling. Sample total potential cross section Utot(ρ,0,z) in the near-field region above the resonators (enclosed by dashed boxes) are displayed accordingly, where the top surfaces of the resonator waveguides are centered at (ρ,z)=(ρw,0). Green spheres indicate the trap center and red spheres mark the positions of potential saddle points beyond which the trap opens. (b), (d) Trap depth ΔU (red curves) and the vertical trap position zt (black curves) can be adjusted by tuning the ratio of energy build-up factors Ir/Ib between the ωr and ωb modes; Ib = (b) 5.4×105 and (d) 8.0×104. For a microring trap (b), radial trap position |ρtρw| (blue curve) remains roughly unchanged until the trap completely opens; for a racetrack trap (d), ρt=ρw. (e), (f) Injected light frequencies and build-up factors I (black curves) around the microring resonances. In (e), ωr (red dashed line) is chosen to maximize the visibility V (red curve) and to eliminate the vector light shift (Supplement 1 Section 2). In (f), ωb modes (blue dashed line) are symmetrically excited around ω0,b to maximize Ib± and to eliminate potential corrugation and vector light shifts. Parameters used in (e), (f): (κ,κc,β)=2π×(1,0.5,0.6)GHz.

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Along the microring, coherent back-scattering mixes the CW and CCW counter-propagating modes and converts an otherwise smooth evanescent field intensity profile into a standing wave pattern just like an optical lattice (Supplement 1 Section 1.B). An optical lattice potential can provide strong longitudinal trap confinement along the microring. Exciting the resonator from either end of the coupling waveguide bus with power Pw and frequency ωb(r) near a resonance ω0,b(r) creates an electric field with a corrugated intensity profile:

|E(r)|2=I|E(ρ,z)|2[1±Vsin(2kl±ξ)],
where the ± sign is given by the direction of bus waveguide coupling that excites opposite mixtures of the resonator modes (Supplement 1 Section 1.D); the sign flip is necessary due to coherent back-scattering. Here, I=I(α) is a near-resonance energy build-up factor, with α=κ2+i[ωω0,b(r)] and a back-scattering rate β:
I(α)=κcPwω|α|2+β2|α2+β2|2.
|E(ρ,z)| is the normalized mode field amplitude, giving 2ϵ0ϵ(r)|E(r)|2dr=ωI, k is the propagation wavenumber, l is the arc length along the microring waveguide, and ξ=tan12(ωω0,b(r))/κ is a frequency-dependent phase shift. The visibility of the corrugation is given by
V(α)=2v|αβ|(|α|2+β2),
where the amplitude factor v0.2 for a TM mode (Supplement 1 Section 1.B). For the simplicity of discussion, we assume the waveguide parameters are equal for the two-color modes.

To form a homogeneous lattice trap along the resonator, we eliminate the standing wave pattern in the ωb mode to avoid incommensurate alignment between the blue-repulsive node and the red-attractive anti-node in the lattice potential. As shown in Fig. 4, we couple blue-detuned light from either end (+ and ) of the waveguide bus with symmetric detuning about ω0,b to completely cancel the potential corrugation (Eq. (2)) [39]. We note that a large detuning between the +/ modes is necessary to eliminate their interference contribution to the trap potential.

We calculate the two-color evanescent field trap potential using the incoherent sum of two-color potentials as

Uev(r)=αr(0)Ir|Er(ρ,z)|2[1+Vcos(2krl)]αb(0)Ib|Eb(ρ,z)|2,
where αr(0)3033 (a.u.; in atomic unit) and αb(0)2111 (a.u.) are atomic dynamic scalar polarizabilities at frequencies ωr and ωb, respectively. Similarly, Er,(b) are the excited mode fields, and Ir=Ir+ and Ib=Ib++Ib are energy build-up factors of the two-color modes [see Figs. 4(e) and 4(f)]; kr is the wave number of the red mode, and l=0 is shifted to center on a lattice site.

The two-color evanescent field trap can be made state-insensitive, i.e., independent of the Zeeman sublevels of cesium ground state atoms. We note that the vector light shift is completely canceled in the presented coupling scheme [15], as discussed in Supplement 1 Section 2.C. Thus, we include only the scalar light shift in Eq. (5).

Figure 4(a) shows sample potential cross sections in a transverse plane above the microring. Due to finite curvature of the microring waveguide that results in non-equal center shifts of the two-color modes, the trap center is shifted inwards by 160nm, and the trap axes are rotated. To avoid trap distortion, a racetrack resonator design [Fig. 4(c)] can be employed, where a symmetric trap can be found above the linear segments of the racetrack. The trap centers in Figs. 4(a) and 4(c) are (ρtρw,zt)(160,100)nm on a microring and (ρtρw,zt)(0,100)nm on a racetrack, respectively, where (ρ,z)=(ρw,0) is the top surface center of the microring (racetrack) waveguide.

To illustrate that the trap is strong enough against the atom-surface attraction, we have included in Fig. 4 the contribution of a Casimir–Polder potential Ucp(r)C4/z3(z+ƛ) for |ρρw|W/2, where C4/h=267Hz·μm4 is for cesium atom–Si3N4 surface coefficient, and ƛ=136nm is an effective wavelength [40]. The total trap potential

Utot(r)=Uev(r)+Ucp(r)
is dominated by Ucp only when z50nm. Here, the trap opens at potential saddle points near (ρs,zs)(300,60) nm for a ring and (±275,67) nm for a racetrack; Utot(ρs,0,zs)Utot(ρt,0,zt) defines the trap depth ΔU, which is ΔUkB×130μK in Figs. 4(a) and 4(c), and is 10 times larger than the typical temperature of laser-cooled cesium atoms.

The energy build-up factors used to calculate the trap on the microring (racetrack) in Figs. 4(a) and 4(c) are Ir+=2.4×105 (4.2×104) for the ωr mode and Ib+=Ib=2.7×105 (4.0×104) for the ωb modes, respectively. Using the coupling scheme and parameters associated with Figs. 4(e) and 4(f), the required total power is Pr=320μW (56 μW) for ωr and Pb=740μW (110 μW) for ωb modes in a microring (racetrack), respectively.

We note that by adjusting the power ratio of the two-color modes, zt can be moved away from or pulled closer to the waveguide surface. In Figs. 4(b) and 4(d), we keep Pb fixed while tuning the ratio Ir/Ib (or Pr/Pb) and show that the trap center can be tuned from zt300nm to <100nm. Meanwhile, ρt remains fairly unchanged. This important feature would allow us to initiate atom trapping and sorting at zt>200nm and perform atom–light coupling at zt<100nm, discussed later.

Figure 5 shows the lattice potential along the axial position l of a microring and a racetrack, plotted using the cross sections of Utot in the planes of ρ=ρt and z=zt, respectively. The low visibility V<1 [Fig. 4(e)] in the attractive TM mode keeps the lattice potential nearly attractive everywhere along the resonator until very close to the resonator waveguide surface z<200nm. This feature allows atoms to traverse freely along the resonator without seeing strong potential barrier until they are cooled into individual lattice sites at zt100nm.

 

Fig. 5. Evanescent field lattice potential on (a) a microring and (b) racetrack resonator, respectively. Top panels show the potential cross sections Utot(ρt,l,z) while the bottom panels show Utot(ρ,l,zt). The lattice constant is d=290nm. Parameters used are identical to those in Figs. 4(a) and 4(c).

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Overall, the evanescent field trap provides three-dimensional tight confinement. For the example given in Figs. 4 and 5, the trap frequencies are (ωρ,ωl,ωz)=2π×(175,1500,1180)kHz for a microring trap, where ρ^ and z^ are along the tilted axes due to trap distortion, and (ωρ,ωl,ωz)=2π×(80,786,681)kHz for a racetrack trap.

B. Top-Illuminating Optical Potential

Illuminating the microring from the top surface using a red-detuned beam (wavelength λr) can also create a tight optical potential due to the top-illuminating beam interfering with its reflection from the microring structure (Fig. 6). The trap site closest to the dielectric surface, typically within a distance <λr/4, can be utilized for trapping atoms in the near-field region of the resonator mode. Once an atom is trapped, the top-illuminating beam can also be steered in the horizontal plane to transport and organize atoms along the microring. This simple scheme need not have trapping light guided by the resonator, and can be universally applied to any dielectric structures with finite surface reflectance. The strength and position of the first trap site can in principle be finely adjusted through geometrically tuning the phase shift of the reflected light. In fact, this method has been successfully implemented in a number of pioneering experiments trapping atoms on suspended nanostructures [9,10], although fully independent trap tuning cannot be achieved because the geometry of a nanostructure needs to be adjusted and its desired guided mode property is inevitably affected.

 

Fig. 6. Top-illuminating optical trap. (a) A tightly focused optical beam (an optical tweezers) creates a lattice of microtraps on top of the resonator waveguide. Inset shows the total potential cross-section Utot(ρ,z) of the nearest trap site above the surface. Green sphere marks the trap center at zt=150nm. Potential contours are KB×25μK, 50 μK, 75 μK, and 100 μK above Utot(ρw,zt)kB×1.57mK at the trap center. (b) Scanning the trap center zt by tuning the thickness of the dioxide layer and keeping the thickness of the bottom nitride layer fixed at 600 nm. Filled circle marks the geometry parameter for (a).

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For the microring (racetrack) platform, the trap condition in a top-illuminating potential can be finely adjusted independent of the waveguide properties, since multiple interfaces exist in the underlying membrane substrate. A desired trap condition can be realized simply by tuning the thickness of the dioxide or nitride layers in the membrane, as illustrated in Fig. 6.

Figure 6(a) shows a sample potential cross-section Utot(ρ,z)=Utw(ρ,z)+Ucp(ρ,z), where the optical potential Utw is calculated by using a FDTD method [30] with a tightly focused Gaussian beam (λr=935nm) of a 1/e2 beam waist w=1.2μm and a power of P=3.5mW projected from the top of the microring waveguide. The beam is polarized along ρ^, which is perpendicular to local waveguide orientation, to minimize reflection from the surface of the microring. In Fig. 6(b), we scan the thickness of the membrane and illustrate a configuration such that the closest trap site to the microring surface is centered around (ρtρw,zt)(0,150)nm, where zt is significantly smaller than λr/4234nm, and the trap depth of ΔUkB×105μK. With a tightly focused beam waist, the top-illuminating beam forms a tweezers-like optical potential, providing also strong transverse (along ρ^) and axial (along l^) confinements. The former is due to the waveguide width (Wλr), leading to a strong intensity variation in the transverse direction. The axial confinement, on the other hand, is ensured by the small beam waist of the tweezers beam. For the example given in Fig. 6(a), the trap frequencies are (ωρ,ωl,ωz)=2π×(43,89,332)kHz.

C. Trap Loading and Atom Sorting Along a Microring (Racetrack) Resonator

In [29], we have experimentally demonstrated that cold atoms can be directly laser cooled on a membrane optical circuit and loaded into a top-illuminating optical tweezers trap. We note that the presence of lattice potential along a tweezers trap likely reduces the probability for cold atoms to be cooled directly into the first site near the microring surface. Instead, multiple atoms may be randomly confined along the lattice of microtraps within a tweezers. An optical conveyor belt can be implemented to transport trapped atoms onto the microring surface [29]. By monitoring the transmission of a resonator mode tuned to atomic resonance, it is possible to transport trapped atoms onto the microring surface with deterministic control.

On the other hand, a two-color evanescent field trap provides a smooth transverse potential landscape (along z^), allowing a large number of laser-cooled atoms to be loaded uninterruptedly from freespace into the lattice potential at zt100nm above the microring, which has recently been demonstrated in nanofiber traps [1315]. Nonetheless, these trapped atoms should randomly fill the optical lattice without organization.

In Fig. 7, we illustrate how a tweezers trap can be used to sort trapped atoms in an evanescent field trap, similar to those in an optical lattice in freespace [41]. To begin with, one may utilize the two-color evanescent field trap for initial atom loading into Utot=Uev+Ucp at zt100200nm. Following laser cooling, fluorescence imaging [29] can be performed to determine the atomic distribution along the resonator. Once identifying the location of all trapped atoms, an optical tweezers trap Utw can be ramped on to draw an atom into a new vertical position zt200nm [Figs. 7(a)7(c)] and transport it along the resonator into a designated lattice site [Fig. 7(d)7(f); across multiple sites]. Following transport, the tweezers beam can then be adiabatically ramped off, releasing the trapped atom back to the evanescent field trap at zt. Atom sorting can be realized by reiterating the procedures to reorganize atoms in different trap sites.

 

Fig. 7. Atom transport in an evanescent field lattice trap. (a)–(c) Illustration of tweezers trap transfer. Potential cross-sections Utot=Uev+Utw+Ucp are shown with a tweezers trap centered at l=d=290nm, and with increasing tweezers power, Ptw= (a) 2 mW, (b) 4 mW, and (c) 6 mW. (d)–(f) Trapped atom transport from l=d to l=0. Potential cross-sections Utot are shown with a fixed tweezers power Ptw=6mW and shifted tweezers trap center at l/d= (d) -0.5, (e) -0.44, and (f) -0.37. Vertical arrows indicate the center of the tweezers trap. Filled circles mark the position of trapped atoms in the target site center, which is enclosed by potential contours that are KB×25μK, 50 μK, and 100 μK, respectively, above the local potential minimum at zt200nm.

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5. CONCLUSION AND OUTLOOK

In this paper, we have demonstrated that microring and racetrack resonator platforms can be fabricated to be completely compatible with laser cooling and trapping with cold atoms and with reasonably high cooperativity parameters C2546. This number can be further boosted by more than 10-fold with further fabrication improvements, thus holding great promises as an on-chip atom cavity QED platform. We have discussed two viable optical trapping schemes, both using magic wavelengths of atomic cesium, for localizing atoms around zt=75150nm above the dielectric surface of a resonator waveguide structure. The combination of both schemes permits controlled atom transport along a resonator, allowing for the formation of an organized atom–nanophotonic hybrid lattice useful for collective quantum optics and many-body physics [3,42].

Last, we note that although our emphasis is on coupling with cold-trapped atoms, these microrings may also be adapted for coupling with solid-state quantum emitters [4345], or with atomic thermal vapors [46,47]. For emitters on the surface of a resonator waveguide and considering only radiative losses, the effective mode volume Vm63(λ/n)3 and C360n3 using our current fabricated structures, where n is the host refractive index for embedded quantum emitters. Improving to Q4.5×106 would lead to a projected C5000n3 that may be potentially useful for on-chip solid-state quantum photonics.

Funding

Air Force Office of Scientific Research (FA9550-17-1-0298); Office of Naval Research (N00014-17-1-2289).

Acknowledgment

We acknowledge discussions from H. J. Kimble, S.-P. Yu, S. Bhave, M. Hosseini, S. Caliga, Y. Xuan, and B.-L. Yu.

 

See Supplement 1 for supporting content.

REFERENCES AND NOTES

1. J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009). [CrossRef]  

2. J. I. Cirac and H. J. Kimble, “Quantum optics, what next?” Nat. Photonics 11, 18–20 (2017). [CrossRef]  

3. D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018). [CrossRef]  

4. E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010). [CrossRef]  

5. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012). [CrossRef]  

6. S. Kato and T. Aoki, “Strong coupling between a trapped single atom and an all-fiber cavity,” Phys. Rev. Lett. 115, 093603 (2015). [CrossRef]  

7. H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016). [CrossRef]  

8. N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016). [CrossRef]  

9. A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015). [CrossRef]  

10. J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013). [CrossRef]  

11. T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014). [CrossRef]  

12. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” in Advances in Atomic, Molecular, and Optical Physics (Elsevier, 2000), Vol. 42, pp. 95–170.

13. F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004). [CrossRef]  

14. V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004). [CrossRef]  

15. C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012). [CrossRef]  

16. J. Pérez-Ríos, M. E. Kim, and C.-L. Hung, “Ultracold molecule assembly with photonic crystals,” New J. Phys. 19, 123035 (2017). [CrossRef]  

17. C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, “Trapped atoms in one-dimensional photonic crystals,” New J. Phys. 15, 083026 (2013). [CrossRef]  

18. A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015). [CrossRef]  

19. J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015). [CrossRef]  

20. J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

21. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006). [CrossRef]  

22. D. O’shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601(2013). [CrossRef]  

23. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014). [CrossRef]  

24. P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006). [CrossRef]  

25. D. J. Alton, “Interacting single atoms with nanophotonics for chip-integrated quantum networks,” Ph.D. thesis (California Institute of Technology, 2013).

26. Y. Xuan, Y. Liu, L. T. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. Jaramillo-Villegas, A. A. Noman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. Wang, D. E. Leaird, A. M. Weiner, and M. Qi, “High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation,” Optica 3, 1171–1180 (2016). [CrossRef]  

27. X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017). [CrossRef]  

28. P. Kaufmann, X. Ji, K. Luke, M. Lipson, and S. Ramelow, “Characterization of ultra-high-q Si3N4 micro-ring resonators with high-precision temperature control,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), p. JTu2A.72.

29. M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019). [CrossRef]  

30. https://www.lumerical.com.

31. K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007). [CrossRef]  

32. S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), p. SM3K.6.

33. C. J. Krückel, A. Fülöp, T. Klintberg, J. Bengtsson, P. A. Andrekson, and V. Torres-Company, “Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides,” Opt. Express 23, 25827–25837 (2015). [CrossRef]  

34. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef]  

35. G. A. Porkolab, P. Apiratikul, B. Wang, S. H. Guo, and C. J. K. Richardson, “Low propagation loss algaas waveguides fabricated with plasma-assisted photoresist reflow,” Opt. Express 22, 7733–7743 (2014). [CrossRef]  

36. https://www.comsol.com.

37. Y. Meng, J. Lee, M. Dagenais, and S. Rolston, “A nanowaveguide platform for collective atom-light interaction,” Appl. Phys. Lett. 107, 091110 (2015). [CrossRef]  

38. T. H. Stievater, D. A. Kozak, M. W. Pruessner, R. Mahon, D. Park, W. S. Rabinovich, and F. K. Fatemi, “Modal characterization of nanophotonic waveguides for atom trapping,” Opt. Mater. Express 6, 3826–3837 (2016). [CrossRef]  

39. Alternatively, one may also excite the blue-detuned mode via single end of the waveguide bus using a laser of finite line width δνβ (β<2π×0.6GHz) so that no coherent back-scattering can establish within the microring.

40. N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011). [CrossRef]  

41. D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016). [CrossRef]  

42. C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016). [CrossRef]  

43. G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015). [CrossRef]  

44. S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019). [CrossRef]  

45. A. Nandi, X. Jiang, D. Pak, D. Perry, K. Han, E. S. Bielejec, Y. Xuan, and M. Hosseini, “Anomalous emission from a one-dimensional lattice of ions in silicon photonics,” arXiv:1902.08898 (2019).

46. R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016). [CrossRef]  

47. R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

References

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  1. J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
    [Crossref]
  2. J. I. Cirac and H. J. Kimble, “Quantum optics, what next?” Nat. Photonics 11, 18–20 (2017).
    [Crossref]
  3. D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
    [Crossref]
  4. E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
    [Crossref]
  5. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
    [Crossref]
  6. S. Kato and T. Aoki, “Strong coupling between a trapped single atom and an all-fiber cavity,” Phys. Rev. Lett. 115, 093603 (2015).
    [Crossref]
  7. H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
    [Crossref]
  8. N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
    [Crossref]
  9. A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
    [Crossref]
  10. J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
    [Crossref]
  11. T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
    [Crossref]
  12. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” in Advances in Atomic, Molecular, and Optical Physics (Elsevier, 2000), Vol. 42, pp. 95–170.
  13. F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004).
    [Crossref]
  14. V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
    [Crossref]
  15. C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
    [Crossref]
  16. J. Pérez-Ríos, M. E. Kim, and C.-L. Hung, “Ultracold molecule assembly with photonic crystals,” New J. Phys. 19, 123035 (2017).
    [Crossref]
  17. C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, “Trapped atoms in one-dimensional photonic crystals,” New J. Phys. 15, 083026 (2013).
    [Crossref]
  18. A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
    [Crossref]
  19. J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
    [Crossref]
  20. J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).
  21. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
    [Crossref]
  22. D. O’shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601(2013).
    [Crossref]
  23. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
    [Crossref]
  24. P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006).
    [Crossref]
  25. D. J. Alton, “Interacting single atoms with nanophotonics for chip-integrated quantum networks,” Ph.D. thesis (California Institute of Technology, 2013).
  26. Y. Xuan, Y. Liu, L. T. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. Jaramillo-Villegas, A. A. Noman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. Wang, D. E. Leaird, A. M. Weiner, and M. Qi, “High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation,” Optica 3, 1171–1180 (2016).
    [Crossref]
  27. X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
    [Crossref]
  28. P. Kaufmann, X. Ji, K. Luke, M. Lipson, and S. Ramelow, “Characterization of ultra-high-q Si3N4 micro-ring resonators with high-precision temperature control,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), p. JTu2A.72.
  29. M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
    [Crossref]
  30. https://www.lumerical.com .
  31. K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
    [Crossref]
  32. S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), p. SM3K.6.
  33. C. J. Krückel, A. Fülöp, T. Klintberg, J. Bengtsson, P. A. Andrekson, and V. Torres-Company, “Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides,” Opt. Express 23, 25827–25837 (2015).
    [Crossref]
  34. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005).
    [Crossref]
  35. G. A. Porkolab, P. Apiratikul, B. Wang, S. H. Guo, and C. J. K. Richardson, “Low propagation loss algaas waveguides fabricated with plasma-assisted photoresist reflow,” Opt. Express 22, 7733–7743 (2014).
    [Crossref]
  36. https://www.comsol.com .
  37. Y. Meng, J. Lee, M. Dagenais, and S. Rolston, “A nanowaveguide platform for collective atom-light interaction,” Appl. Phys. Lett. 107, 091110 (2015).
    [Crossref]
  38. T. H. Stievater, D. A. Kozak, M. W. Pruessner, R. Mahon, D. Park, W. S. Rabinovich, and F. K. Fatemi, “Modal characterization of nanophotonic waveguides for atom trapping,” Opt. Mater. Express 6, 3826–3837 (2016).
    [Crossref]
  39. Alternatively, one may also excite the blue-detuned mode via single end of the waveguide bus using a laser of finite line width δν≫β (β<2π×0.6  GHz) so that no coherent back-scattering can establish within the microring.
  40. N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011).
    [Crossref]
  41. D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
    [Crossref]
  42. C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016).
    [Crossref]
  43. G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
    [Crossref]
  44. S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
    [Crossref]
  45. A. Nandi, X. Jiang, D. Pak, D. Perry, K. Han, E. S. Bielejec, Y. Xuan, and M. Hosseini, “Anomalous emission from a one-dimensional lattice of ions in silicon photonics,” arXiv:1902.08898 (2019).
  46. R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
    [Crossref]
  47. R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

2019 (2)

M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
[Crossref]

S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
[Crossref]

2018 (2)

R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
[Crossref]

2017 (3)

X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
[Crossref]

J. I. Cirac and H. J. Kimble, “Quantum optics, what next?” Nat. Photonics 11, 18–20 (2017).
[Crossref]

J. Pérez-Ríos, M. E. Kim, and C.-L. Hung, “Ultracold molecule assembly with photonic crystals,” New J. Phys. 19, 123035 (2017).
[Crossref]

2016 (8)

Y. Xuan, Y. Liu, L. T. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. Jaramillo-Villegas, A. A. Noman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. Wang, D. E. Leaird, A. M. Weiner, and M. Qi, “High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation,” Optica 3, 1171–1180 (2016).
[Crossref]

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
[Crossref]

D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref]

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

T. H. Stievater, D. A. Kozak, M. W. Pruessner, R. Mahon, D. Park, W. S. Rabinovich, and F. K. Fatemi, “Modal characterization of nanophotonic waveguides for atom trapping,” Opt. Mater. Express 6, 3826–3837 (2016).
[Crossref]

C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016).
[Crossref]

R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
[Crossref]

2015 (7)

S. Kato and T. Aoki, “Strong coupling between a trapped single atom and an all-fiber cavity,” Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
[Crossref]

Y. Meng, J. Lee, M. Dagenais, and S. Rolston, “A nanowaveguide platform for collective atom-light interaction,” Appl. Phys. Lett. 107, 091110 (2015).
[Crossref]

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

C. J. Krückel, A. Fülöp, T. Klintberg, J. Bengtsson, P. A. Andrekson, and V. Torres-Company, “Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides,” Opt. Express 23, 25827–25837 (2015).
[Crossref]

2014 (3)

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

G. A. Porkolab, P. Apiratikul, B. Wang, S. H. Guo, and C. J. K. Richardson, “Low propagation loss algaas waveguides fabricated with plasma-assisted photoresist reflow,” Opt. Express 22, 7733–7743 (2014).
[Crossref]

2013 (3)

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, “Trapped atoms in one-dimensional photonic crystals,” New J. Phys. 15, 083026 (2013).
[Crossref]

D. O’shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601(2013).
[Crossref]

2012 (2)

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

2011 (1)

N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011).
[Crossref]

2010 (1)

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

2009 (1)

J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

2007 (1)

K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
[Crossref]

2006 (2)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006).
[Crossref]

2005 (1)

2004 (2)

F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004).
[Crossref]

V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[Crossref]

Akimov, A. V.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Alton, D.

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

Alton, D. J.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011).
[Crossref]

D. J. Alton, “Interacting single atoms with nanophotonics for chip-integrated quantum networks,” Ph.D. thesis (California Institute of Technology, 2013).

Andrekson, P. A.

Aoki, T.

S. Kato and T. Aoki, “Strong coupling between a trapped single atom and an all-fiber cavity,” Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Apiratikul, P.

Appel, J.

H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
[Crossref]

Asenjo-Garcia, A.

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

Balykin, V.

V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[Crossref]

Balykin, V. I.

F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004).
[Crossref]

Barbosa, F. A. S.

Barclay, P. E.

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006).
[Crossref]

Barredo, D.

D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref]

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Beguin, J.-B.

H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
[Crossref]

Bengtsson, J.

Bielejec, E. S.

A. Nandi, X. Jiang, D. Pak, D. Perry, K. Han, E. S. Bielejec, Y. Xuan, and M. Hosseini, “Anomalous emission from a one-dimensional lattice of ions in silicon photonics,” arXiv:1902.08898 (2019).

Borselli, M.

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Browaeys, A.

D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref]

Bryant, A.

X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
[Crossref]

S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), p. SM3K.6.

Cardenas, J.

X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
[Crossref]

S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), p. SM3K.6.

Chandra, A.

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

Chang, D. E.

D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
[Crossref]

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
[Crossref]

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, “Trapped atoms in one-dimensional photonic crystals,” New J. Phys. 15, 083026 (2013).
[Crossref]

Chang, T.-H.

M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
[Crossref]

Chen, C.-A.

M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
[Crossref]

Choi, K.

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

Choi, K. S.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Cirac, J. I.

J. I. Cirac and H. J. Kimble, “Quantum optics, what next?” Nat. Photonics 11, 18–20 (2017).
[Crossref]

C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016).
[Crossref]

A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
[Crossref]

Corzo, N. V.

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

Czaplewski, D. A.

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

Dagenais, M.

Y. Meng, J. Lee, M. Dagenais, and S. Rolston, “A nanowaveguide platform for collective atom-light interaction,” Appl. Phys. Lett. 107, 091110 (2015).
[Crossref]

Dawkins, S. T.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Dayan, B.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

de Leon, N. P.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Ding, D.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

Dobbertin, H.

R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

Douglas, J. S.

D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
[Crossref]

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

Dutt, A.

Fan, L.

Fatemi, F. K.

Feist, J.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Fields, B. M.

M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
[Crossref]

Fülöp, A.

Furusawa, A.

J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Gaeta, A. L.

Goban, A.

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

Gonzalez-Tudela, A.

A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
[Crossref]

González-Tudela, A.

D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
[Crossref]

C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016).
[Crossref]

Gorshkov, A.

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

Gouraud, B.

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

Grimm, R.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” in Advances in Atomic, Molecular, and Optical Physics (Elsevier, 2000), Vol. 42, pp. 95–170.

Grinkemeyer, B.

S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
[Crossref]

Gruhler, N.

R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
[Crossref]

Guendelman, G.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Gullans, M.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Guo, S. H.

Habibian, H.

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

Hakuta, K.

F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004).
[Crossref]

V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[Crossref]

Han, K.

Hood, J.

A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Hood, J. D.

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

Hosseini, M.

A. Nandi, X. Jiang, D. Pak, D. Perry, K. Han, E. S. Bielejec, Y. Xuan, and M. Hosseini, “Anomalous emission from a one-dimensional lattice of ions in silicon photonics,” arXiv:1902.08898 (2019).

Hung, C.-L.

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H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
[Crossref]

Srinivasan, K.

K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
[Crossref]

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006).
[Crossref]

Stanev, T. K.

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

Stern, N.

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

Stern, N. P.

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011).
[Crossref]

Stievater, T. H.

Teng, M.

Thiele, T.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Thompson, J. D.

S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Tiecke, T. G.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Torres-Company, V.

Vahala, K.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Varghese, L. T.

Vetsch, E.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Volz, J.

D. O’shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601(2013).
[Crossref]

Vuckovic, J.

J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

Vuletic, V.

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Wang, B.

Wang, C.

Wang, J.

Wang, P.-H.

Wei, G.

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

Weidemüller, M.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” in Advances in Atomic, Molecular, and Optical Physics (Elsevier, 2000), Vol. 42, pp. 95–170.

Weiner, A. M.

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

Wilson, J.

S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
[Crossref]

Xuan, Y.

Xue, X.

Yu, S.-P.

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Zibrov, A. S.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

Appl. Phys. Lett. (3)

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-QSiNx microdisks with atom chips,” Appl. Phys. Lett. 89, 131108 (2006).
[Crossref]

Y. Meng, J. Lee, M. Dagenais, and S. Rolston, “A nanowaveguide platform for collective atom-light interaction,” Appl. Phys. Lett. 107, 091110 (2015).
[Crossref]

G. Wei, T. K. Stanev, D. A. Czaplewski, I. W. Jung, and N. P. Stern, “Silicon-nitride photonic circuits interfaced with monolayer MoS2,” Appl. Phys. Lett. 107, 091112 (2015).
[Crossref]

Nat. Commun. (1)

M. E. Kim, T.-H. Chang, B. M. Fields, C.-A. Chen, and C.-L. Hung, “Trapping single atoms on a nanophotonic circuit with configurable tweezer lattices,” Nat. Commun. 10, 1647 (2019).
[Crossref]

Nat. Photonics (4)

J. L. O’brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

J. I. Cirac and H. J. Kimble, “Quantum optics, what next?” Nat. Photonics 11, 18–20 (2017).
[Crossref]

A. Gonzalez-Tudela, C.-L. Hung, D. E. Chang, J. I. Cirac, and H. J. Kimble, “Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals,” Nat. Photonics 9, 320–325 (2015).
[Crossref]

J. S. Douglas, H. Habibian, C.-L. Hung, A. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Photonics 9, 326–331 (2015).
[Crossref]

Nature (2)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (2014).
[Crossref]

New J. Phys. (5)

C. Lacroûte, K. Choi, A. Goban, D. Alton, D. Ding, N. Stern, and H. Kimble, “A state-insensitive, compensated nanofiber trap,” New J. Phys. 14, 023056 (2012).
[Crossref]

J. Pérez-Ríos, M. E. Kim, and C.-L. Hung, “Ultracold molecule assembly with photonic crystals,” New J. Phys. 19, 123035 (2017).
[Crossref]

C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, “Trapped atoms in one-dimensional photonic crystals,” New J. Phys. 15, 083026 (2013).
[Crossref]

N. P. Stern, D. J. Alton, and H. J. Kimble, “Simulations of atomic trajectories near a dielectric surface,” New J. Phys. 13, 085004 (2011).
[Crossref]

R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
[Crossref]

Opt. Express (3)

Opt. Mater. Express (1)

Optica (2)

Phys. Rev. A (3)

K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007).
[Crossref]

F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004).
[Crossref]

V. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[Crossref]

Phys. Rev. Lett. (8)

D. O’shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601(2013).
[Crossref]

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

S. Kato and T. Aoki, “Strong coupling between a trapped single atom and an all-fiber cavity,” Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

H. Sorensen, J.-B. Beguin, K. Kluge, I. Iakoupov, A. Sorensen, J. Muller, E. Polzik, and J. Appel, “Coherent backscattering of light off one-dimensional atomic strings,” Phys. Rev. Lett. 117, 133604 (2016).
[Crossref]

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref]

A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

S. Saskin, J. Wilson, B. Grinkemeyer, and J. D. Thompson, “Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array,” Phys. Rev. Lett. 122, 143002 (2019).
[Crossref]

Phys. Rev. X (1)

R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to slot waveguides,” Phys. Rev. X 8, 021032 (2018).

Proc. Natl. Acad. Sci. USA (2)

C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proc. Natl. Acad. Sci. USA 113, E4946–E4955 (2016).
[Crossref]

J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. Kimble, “Atom–atom interactions around the band edge of a photonic crystal waveguide,” Proc. Natl. Acad. Sci. USA 113, 10507–10512 (2016).

Rev. Mod. Phys. (1)

D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, “Colloquium: quantum matter built from nanoscopic lattices of atoms and photons,” Rev. Mod. Phys. 90, 031002 (2018).
[Crossref]

Science (3)

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Coupling a single trapped atom to a nanoscale optical cavity,” Science 340, 1202–1205 (2013).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

D. Barredo, S. D. Leseleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref]

Other (8)

Alternatively, one may also excite the blue-detuned mode via single end of the waveguide bus using a laser of finite line width δν≫β (β<2π×0.6  GHz) so that no coherent back-scattering can establish within the microring.

https://www.comsol.com .

S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), p. SM3K.6.

https://www.lumerical.com .

P. Kaufmann, X. Ji, K. Luke, M. Lipson, and S. Ramelow, “Characterization of ultra-high-q Si3N4 micro-ring resonators with high-precision temperature control,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), p. JTu2A.72.

D. J. Alton, “Interacting single atoms with nanophotonics for chip-integrated quantum networks,” Ph.D. thesis (California Institute of Technology, 2013).

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” in Advances in Atomic, Molecular, and Optical Physics (Elsevier, 2000), Vol. 42, pp. 95–170.

A. Nandi, X. Jiang, D. Pak, D. Perry, K. Han, E. S. Bielejec, Y. Xuan, and M. Hosseini, “Anomalous emission from a one-dimensional lattice of ions in silicon photonics,” arXiv:1902.08898 (2019).

Supplementary Material (1)

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» Supplement 1       Supplemental document

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Figures (7)

Fig. 1.
Fig. 1. Interfacing single atoms with a microring structure on a membrane for strong atom–light interactions. (a) Schematics of a silicon nitride microring (radius R) on a dioxide-nitride membrane, with a single trapped atom (green sphere). Curved arrows depict single atom–photon coupling rate, g, to the resonator modes. Wavy arrows depict intrinsic resonator loss (at rate κi) and the atomic decay (at rate γ), respectively. A linear bus waveguide couples to and from the resonator modes at rates κc (depicted by crossed solid and dashed arrows). (b) Eeffective mode area Am of a microring of width W=1.1μm, height H=0.29μm, and radius R16μm; Am5.2μm2 at the depicted atom location (ρa,za)=(R,100nm). Shaded structures mark the microring waveguide (Si3N4) and supporting membrane (SiO2 and Si3N4 layers), respectively. (c) Atom–photon coupling strength g(z) along a vertical dashed line in (b); g(za)/2π=200MHz is marked by the dotted lines.
Fig. 2.
Fig. 2. Fabricated small radius microring/racetrack resonators and optical quality measurements. (a) Optical image of an array of microrings (i) coupled to a linear waveguide bus (ii) for fiber edge coupling in a U-groove (iii). Membrane area is enclosed in a dashed box. (b) Overview of the optical chip. The membrane is suspended within a 2mm×8mm window. (c), (d) SEM of fabricated (c) microring and (d) racetrack resonators, both with width W=0.95μm and height H=0.36μm. (e) Scattering intensity measurements near the resonance of a racetrack resonator. Solid line is a fit, giving (κ,β,ω0)/2π=(1.01,0.655,334.792×103)GHz.
Fig. 3.
Fig. 3. Cooperativity optimization via scanning the microring geometry, with the surface roughness parameters (σ±, L±, σt, Lt, σb, Lb)= (a) (2,60,1.4,73,1.6,84) nm and (b) (1.4,39,0.1,10,0.1,10) nm, respectively.
Fig. 4.
Fig. 4. Two-color evanescent field trap. (a), (c) The coupling schemes are schematically shown in (a) for a microring and (c) for a racetrack resonator, where the injected lights are marked by red (ωr) and blue (ωb) arrows and the ± signs mark the direction of coupling. Sample total potential cross section Utot(ρ,0,z) in the near-field region above the resonators (enclosed by dashed boxes) are displayed accordingly, where the top surfaces of the resonator waveguides are centered at (ρ,z)=(ρw,0). Green spheres indicate the trap center and red spheres mark the positions of potential saddle points beyond which the trap opens. (b), (d) Trap depth ΔU (red curves) and the vertical trap position zt (black curves) can be adjusted by tuning the ratio of energy build-up factors Ir/Ib between the ωr and ωb modes; Ib = (b) 5.4×105 and (d) 8.0×104. For a microring trap (b), radial trap position |ρtρw| (blue curve) remains roughly unchanged until the trap completely opens; for a racetrack trap (d), ρt=ρw. (e), (f) Injected light frequencies and build-up factors I (black curves) around the microring resonances. In (e), ωr (red dashed line) is chosen to maximize the visibility V (red curve) and to eliminate the vector light shift (Supplement 1 Section 2). In (f), ωb modes (blue dashed line) are symmetrically excited around ω0,b to maximize Ib± and to eliminate potential corrugation and vector light shifts. Parameters used in (e), (f): (κ,κc,β)=2π×(1,0.5,0.6)GHz.
Fig. 5.
Fig. 5. Evanescent field lattice potential on (a) a microring and (b) racetrack resonator, respectively. Top panels show the potential cross sections Utot(ρt,l,z) while the bottom panels show Utot(ρ,l,zt). The lattice constant is d=290nm. Parameters used are identical to those in Figs. 4(a) and 4(c).
Fig. 6.
Fig. 6. Top-illuminating optical trap. (a) A tightly focused optical beam (an optical tweezers) creates a lattice of microtraps on top of the resonator waveguide. Inset shows the total potential cross-section Utot(ρ,z) of the nearest trap site above the surface. Green sphere marks the trap center at zt=150nm. Potential contours are KB×25μK, 50 μK, 75 μK, and 100 μK above Utot(ρw,zt)kB×1.57mK at the trap center. (b) Scanning the trap center zt by tuning the thickness of the dioxide layer and keeping the thickness of the bottom nitride layer fixed at 600 nm. Filled circle marks the geometry parameter for (a).
Fig. 7.
Fig. 7. Atom transport in an evanescent field lattice trap. (a)–(c) Illustration of tweezers trap transfer. Potential cross-sections Utot=Uev+Utw+Ucp are shown with a tweezers trap centered at l=d=290nm, and with increasing tweezers power, Ptw= (a) 2 mW, (b) 4 mW, and (c) 6 mW. (d)–(f) Trapped atom transport from l=d to l=0. Potential cross-sections Utot are shown with a fixed tweezers power Ptw=6mW and shifted tweezers trap center at l/d= (d) -0.5, (e) -0.44, and (f) -0.37. Vertical arrows indicate the center of the tweezers trap. Filled circles mark the position of trapped atoms in the target site center, which is enclosed by potential contours that are KB×25μK, 50 μK, and 100 μK, respectively, above the local potential minimum at zt200nm.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Am(ρa,za)=ϵ(ρ,z)|E(ρ,z)|2dρdzϵ(ρa,za)|E(ρa,za)|2.
|E(r)|2=I|E(ρ,z)|2[1±Vsin(2kl±ξ)],
I(α)=κcPwω|α|2+β2|α2+β2|2.
V(α)=2v|αβ|(|α|2+β2),
Uev(r)=αr(0)Ir|Er(ρ,z)|2[1+Vcos(2krl)]αb(0)Ib|Eb(ρ,z)|2,
Utot(r)=Uev(r)+Ucp(r)

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