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 () of , projecting a single atom cooperativity parameter () of 25 and a vacuum Rabi frequency () of 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 , 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
CorrectionsTzu-Han Chang, Brian M. Fields, May E. Kim, and Chen-Lung Hung, "Microring resonators on a suspended membrane circuit for atom-light interactions: erratum," Optica 8, 759-759 (2021)
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 [1–3]. Optical nanofibers [4–8], photonic crystal waveguides , 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  in the near field, such as two-color evanescent field traps [13–15], 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 () 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 , requiring that the atom–photon coupling strength is large compared to the geometric mean of the photonic loss rate () and the atomic radiative decay rate into freespace (). For a perfect quantum emitter, (assuming a spherical symmetric dipole), and depends solely on the ratio between the quality factor of the photonic mode (of frequency and freespace wavelength ) and the effective mode volume , which is inversely proportional to the guided-mode photon energy density at the atomic trap location. State-of-the-art high- nanophotonic platforms have yet to achieve cooperativity parameters due to limited , which stems mostly from fabrication imperfections. For example, and are reported recently for a photonic crystal cavity  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 at rubidium D2-line to 894 nm at cesium D1-line. There are multiple schemes in existence for boosting in atom–nanophotonic platforms . For comparison, monolithic micro-photonic resonators such as silica micro-toroids , bottles , and spheres  or silicon nitride micro-disks  are other photonic resonator structures with ultrahigh quality factors but with large 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 , 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 , 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 in telecom optical wavelength band [26,27] and close to Cs atomic spectroscopy bands . 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 multi-layer membrane, formed by a -thick (silicon dioxide) layer and a -nm-thick (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 ; 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 .
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 . The small radius of the microring ensures a moderately small mode volume , where is the circumference of the ring, and is the effective mode area defined as1(b) plots the cross section of the effective mode area of a TM mode at cesium D1-line . A moderately small mode area can be achieved when an atom is placed at around above the microring surface, projecting a mode volume of , single-photon vacuum Rabi frequency , and a cooperativity parameter . Achieving high 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 (or 50% with vacuum cladding) single-pass coupling efficiency as expected through our finite-difference-time-domain (FDTD) calculations . We have currently achieved 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  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 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, , has been thermally tuned by a freespace laser beam heating the silicon part of the optical circuit in vacuum . 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  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 , corresponding to an under-coupled quality factor of due to waveguide coupling rate smaller than the intrinsic loss rate .
Using the measurement results and the fabricated geometry , we project the single atom cooperativity parameter to be , calculated using ; under the same and the geometry presented in Fig. 1, we project with . We note that there is still much room for improvement. Below we discuss in detail the optical loss analysis and optimization for maximizing cooperativity .
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 and the correlation length 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 . We estimate the edge roughness and correlation length to be around by employing a multipass e-beam writing technique [27,32] and optimized inductively coupled-plasma reactive-ion etching process with 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 . Our result indicates that 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 and from its original rough surface . Alternatively, the edge roughness and correlation length may be reduced to and by using a plasma-assisted resist reflow technique . These immediate technological improvements permit a potential 10-fold increase in , as will be discussed below.
Given the characteristics of the surface quality and edge roughness, we perform finite element method (FEM) analysis  to obtain a geometrical design that maximizes , 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 of the ring is constrained to be above due to larger bending loss and scattering loss occurring at the sidewalls at larger bend curvature.
In Fig. 3, we plot the cooperativity parameter as a result of the scan, assuming an atom is trapped at nm. With the surface roughness at its current value, as in Fig. 3(a), is maximized when the waveguide geometry tends towards a larger cross section (, ), which reduces surface scattering, and smaller radius , which reduces the mode volume. The best projection uses a smaller ring than in our current design, and . For reduced surface roughness, as in Fig. 3(b), a resonator geometry of , as shown in Fig. 1, can achieve . The projected cooperativity reaches , 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 but with a lower optimal due to larger .
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 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 and , so that they do not create differential light shifts in the laser cooling transition of cesium (Supplement 1 Section 2). Here, (frequency ) is blue-detuned from major optical transitions in the ground state, creating strongly repulsive optical force within a short range near the dielectric surface. (frequency ) is red-detuned, leading to an attractive force with longer decay length than that of the mode. The combination of both modes creates a stable trap above the waveguide surface; see Fig. 4.
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 and frequency near a resonance creates an electric field with a corrugated intensity profile:Supplement 1 Section 1.D); the sign flip is necessary due to coherent back-scattering. Here, is a near-resonance energy build-up factor, with and a back-scattering rate : 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 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 to completely cancel the potential corrugation (Eq. (2)) . 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 as4(e) and 4(f)]; is the wave number of the red mode, and 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 , 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 , 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 on a microring and on a racetrack, respectively, where 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 for , where is for cesium atom– surface coefficient, and is an effective wavelength . The total trap potential4(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 () for the mode and () for the modes, respectively. Using the coupling scheme and parameters associated with Figs. 4(e) and 4(f), the required total power is (56 μW) for and (110 μW) for modes in a microring (racetrack), respectively.
We note that by adjusting the power ratio of the two-color modes, can be moved away from or pulled closer to the waveguide surface. In Figs. 4(b) and 4(d), we keep fixed while tuning the ratio (or ) and show that the trap center can be tuned from to . Meanwhile, remains fairly unchanged. This important feature would allow us to initiate atom trapping and sorting at and perform atom–light coupling at , discussed later.
Figure 5 shows the lattice potential along the axial position of a microring and a racetrack, plotted using the cross sections of in the planes of and , respectively. The low visibility [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 . This feature allows atoms to traverse freely along the resonator without seeing strong potential barrier until they are cooled into individual lattice sites at .
Overall, the evanescent field trap provides three-dimensional tight confinement. For the example given in Figs. 4 and 5, the trap frequencies are for a microring trap, where and are along the tilted axes due to trap distortion, and for a racetrack trap.
B. Top-Illuminating Optical Potential
Illuminating the microring from the top surface using a red-detuned beam (wavelength ) 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 , 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.
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 , where the optical potential is calculated by using a FDTD method  with a tightly focused Gaussian beam () of a beam waist and a power of projected from the top of the microring waveguide. The beam is polarized along , 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 , where is significantly smaller than , and the trap depth of . With a tightly focused beam waist, the top-illuminating beam forms a tweezers-like optical potential, providing also strong transverse (along ) and axial (along ) confinements. The former is due to the waveguide width (), 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 .
C. Trap Loading and Atom Sorting Along a Microring (Racetrack) Resonator
In , 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 . 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 ), allowing a large number of laser-cooled atoms to be loaded uninterruptedly from freespace into the lattice potential at above the microring, which has recently been demonstrated in nanofiber traps [13–15]. 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 . To begin with, one may utilize the two-color evanescent field trap for initial atom loading into at . Following laser cooling, fluorescence imaging  can be performed to determine the atomic distribution along the resonator. Once identifying the location of all trapped atoms, an optical tweezers trap can be ramped on to draw an atom into a new vertical position [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 . Atom sorting can be realized by reiterating the procedures to reorganize atoms in different trap sites.
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 . 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 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 [43–45], 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 and using our current fabricated structures, where is the host refractive index for embedded quantum emitters. Improving to would lead to a projected that may be potentially useful for on-chip solid-state quantum photonics.
Air Force Office of Scientific Research (FA9550-17-1-0298); Office of Naval Research (N00014-17-1-2289).
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.
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