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The integration of photonic crystal waveguides with atom arrays in optical tweezers

Integrating nanophotonics and cold atoms has drawn increasing interest in recent years due to diverse applications in quantum information science and the exploration of quantum many-body physics. For example, dispersion-engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of ultracold neutral atoms via interactions with guided-mode light, but also the possibility to explore the physics of strong, photon-mediated interactions between atoms, as well as atom-mediated interactions between photons. While diverse theoretical opportunities involving atoms and photons in 1-D and 2-D nanophotonic lattices have been analyzed, a grand challenge remains the experimental integration of PCWs with ultracold atoms. Here we describe an advanced apparatus that overcomes several significant barriers to current experimental progress with the goal of achieving strong quantum interactions of light and matter by way of single-atom tweezer arrays strongly coupled to photons in 1-D and 2-D PCWs. Principal technical advances relate to efficient free-space coupling of light to and from guided modes of PCWs, silicate bonding of silicon chips within small glass vacuum cells, and deterministic, mechanical delivery of single-atom tweezer arrays to the near fields of photonic crystal waveguides.


I. INTRODUCTION
The research described in this manuscript attempts to create novel paradigms for strong quantum interactions of light and matter by way of single atoms and photons in nanoscopic dielectric lattices. Nanophotonic structures offer the intriguing possibility to control interactions between atoms and photons by engineering the medium properties through which they interact 1,2 . Opportunities beyond conventional Quantum Optics thereby emerge for unconventional quantum phases and phenomena for atoms and photons in one and twodimensional nanophotonic lattices [3][4][5] . The research is inherently multidisciplinary, spanning across nanophotonics, atomic physics, quantum optics, and condensed matter physics.
Beyond the advances reported here, this general area has diverse implementations for Quantum Information Science, including the realization of complex quantum networks 6 and the exploration of quantum many-body physics with atoms and photons 7 . Further avenues of interest are the investigation of quantum metrology and long distance quantum communication 8 combined with the integrated functionality of nanophotonics and atoms.
As a comparison, solid-state emitters coupled to nanophotonic structures 9-11 provide a complementary route to some of the physics described here. However, these systems exhibit inhomogeneous broadening which can make the coupling of even two such emitters in a single nanophotonic structure a challenging experimental task 12 and they are not, in their current form, designed to generate controllable interactions across a large system of emitters as has been demonstrated with numerous atomic physics platforms.
While exciting theoretical opportunities of atoms coupled to nanophotonics have emerged, this research only moves forward in the laboratory by advancing nanophotonic device fabrication and by integrating these novel devices into the realm of ultracold atoms. Important experimental milestones have been reached [13][14][15][16][17][18] , but generally laboratory progress has lagged theory in combining ultracold atoms and novel nanophotonic devices. As illustrated in Figure 1, a grand challenge for experiments in this new field is the realization of atomic arrays with high fractional filling of single atoms into unit cells of 1D and 2D lattices 1,2 . In this manuscript we describe an apparatus that provides several significant advances relative to prior technical capabilities, that are summarized as follows: 1. Silicate bonding -We have previously used large manipulators inside conventional stainless steel chambers for mounting our Silicon chips illustrated in Figure 2a. This method respectively. In both cases the Silicon Nitride structures (gray) are suspended above an underlying Silicon substrate (dark background). Green spheres represent the yet to be achieved single atoms trapped by optical forces within unit cells of the photonic crystal structures 20,21 posed several limitations in our previous experiments 15,16,21 , including mechanical and thermal instability, complexity in fiber alignment and assembly, and limitations on baking temperature and out-gasing due to various epoxy resins and bonding agents used for "gluing" optical fibers to Silicon chips and chips to vacuum mounting hardware. Following discussions with Jun Ye and John Hall at JILA, we have developed a new platform to mount our chips in vacuum. As shown in Figure 2b and also described in details in Section II, we now bond a Si chip to an SiO 2 substrate by way of silicate bonding that we have developed in our group (with significant input from a LIGO research team at Caltech). This bonding technique has extremely low out-gassing properties compared to our previous chip mounting configurations and enables high temperature baking of our vacuum cell for ultra-high vacuum (UHV) operation.

2.
A new generation of PCWs -We have developed optical chips that eliminate fiber optics within the vacuum chamber, achieve more efficient coupling of light into and out of our PCWs, increase power handling capabilities by twenty fold to facilitate long-lived guided-mode optical traps 20 , and enable high-temperature baking for improved atom trapping times 22 . All of these goals have been met by way of the design and fabrication of devices that utilize free-space optical coupling whereby input laser light is coupled from outside the vacuum chamber directly into individual PCWs. As described in Section III, we have removed the need for in-vacuum fibers by designing and fabricating a new Y-coupler at the terminating ends. The Silicon chip also has a significantly reduced footprint necessitated by having the terminating Y-couplers much closer to the edges of the Silicon chip to allow free-space coupling for numerical apertures (N.A.) ∼ 0.1 − 0.2 of the new Y-couplers 22 .

3.
A new laboratory -Free-space coupling and silicate bounding have enabled the construction of a new laboratory in the Quantum Optics Group at Caltech, which is built around a vacuum envelope reduced in size by approximately a factor of 10 2 to reach a volume ∼ 10 cm 3 with unprecedented optical access relative to our prior chambers, as shown in Figure 2c.
We aim to achieve nanoscopic lattices of atoms that are assembled deterministically with arrays of single-atom tweezers and that are coupled to guided modes (GMs) of PCWs for efficient atom-photon coupling along the PCW and of GM photons to and from free-space.
As described in Section IV, our experiment is in the spirit of recent worldwide advances with free-space tweezer arrays 23-26 but adds the significant complexity of assembling such atomic arrays near the surfaces of 1D and 2D PCWs.
A general summary of our advances is provided by Figure 2, which shows our 'old' 22,27,29 4 and 'new' 28 systems side by side. Of course, small glass cells with volume ∼ 1 cm 3 for various optical trapping schemes have been employed by various groups for many years 30 .
But to our knowledge, no group has succeeded to implement a compact setup as in Figure   2(b, c) when the difficult constraints of localization of atoms near PCWs have been part of the setup 28 . In previous atom-nanophotonic experiments [15][16][17]21 in the Quantum Optics Group at Caltech, the nanophotonic chips were held inside a stainless vacuum chamber by a long mechanic manipulator (∼ 10 cm) with input-output fibers pre-aligned and glued in the V-groove on  Figure   4(e). It should be noted that the rectangular prism table is AR-coated on its outer side (i.e., facing into the glass cell), while the glass cell is AR-coated on its outer surface but not inner.

II. SILICATE BONDING
We In order to mode-match the guided mode of a photonic waveguide to a Gaussian beam, we taper the waveguide width to 130 nm, before terminating the waveguide and launching the mode. The terminated end of the suspended waveguide is affixed to the substrate through two ≤ 100 nm wide tethers. Conventionally, the tethers are simply arranged perpendicular to the waveguide 19 , as shown in the SEM image in Figure 5a (i). Two issues arise from such tethering design. First, the tether pair is polarized by the guided mode light, creating scattering and back-reflection that are undesirable. Second, the tethers are perpendicular to the waveguide, therefore releasing the tensile stress on the waveguide, potentially making the tapered section of the waveguide mechanically pliable. At high optical power, the waveguide-tether junction is observed to produce fluctuating scattering intensity prior to mechanical failure, which we attribute to thermally-induced stress distributions causing physical movements of the junction. These pose a significant constraint for achieving guided mode traps at magic wavelengths for Cs with a typical power handling ∼ 10 mW, well beyond the ∼ 0.5 mW limit found for conventional couplers in Refs. 19 and 38. To overcome this limitation, an unconventional Y-shaped termination of the free-standing end of the waveguide was designed in joint consideration of mechanical and optical properties, as shown in Figure 5a (ii). The termination ends of the suspended waveguide need to be mechanically affixed to the substrate with tethers. By tilting the tethers away from the tapered waveguide, a controllable weak tensile stress can be maintained on the waveguide and tethers to make them mechanically robust. Optically, the tethers are tilted away from the electric field vector of the incoming mode, reducing the polarizability of each tether.
This effect, in addition to the partial cancellation of the polarization vectors of the two tethers, reduce the total polarizability of the junction, therefore reducing the scattering 9 loss due to the tethers, as shown in Figure 5b (i) and (ii) with vectorial illustrations for conventional coupler with 90 • tethers and the Y-coupler, respectively. In practice, a tilt angle of 60 • from perpendicular was chosen from FDTD optimization 39 . The simulated field pattern of a Gaussian beam incident on the junction from below is shown in Figure 5c.
Coupling efficiencies of a 1/e 2 waist w 0 ∼ 2.5 µm beam with different input polarizations to different couplers are calculated from FDTD simulations and are summarized in Table I. It suggests that, the Y-coupler has a better performance than conventional couplers in terms of Gaussian-beam-to-waveguide transmission (87% vs. conventional 79%) and reflection (< 0.1% vs. conventional 2.7%) for input polarization along y direction (TE), which is critical for quantum correlation measurements in nanophotonics 15 . In experiment, we have measured a coupling efficiency up to 80% for TE input using the Y-coupler design 28 . In Figure 6, we show measurement data asserting the power handling capability of the devices with the free-space coupling and Y-coupler design strategy. Figure 6a  and will be discussed in Section V.
After transport of the 1D trapped atoms array to the target position ∼ 10 µm from the PCW, the single atom 1D array will be further transferred into reflective traps near the dielectric surface of the PCW for strong atom-light interactions 13,21,45 . Here, we numerically investigate a protocol for atom assembly on the PCW inspired by Refs. 13 and 25, now within the setting of the APCW. As illustrated in Figure 9a, moving the entire tweezer array vertically along the y direction is achieved by sweeping the RF drive frequency for a second AOD with axis along y orthogonal to that of the first AOD forming the original tweezer array along x. Figure 9b shows a typical atom trajectory (white curve) from numerical simulation being successfully transferred into the so-called z 1 trap close to the upper surface of the APCW trap with the largest coupling rate to TE mode of the APCW 16,17 . Here, the free-space initial position of the tweezer waist is located at (x, y, z) = (0, −2.5, −1) µm with the atom initial temperature ∼ 50 µK. For the APCW as well as more complicated structures such as 2D photonic crystals in Figure 1b, we have recently proposed a quite different scheme for direct delivery with high efficiency of single atoms from free-space tweezer traps into z 1 traps at the surfaces of nanophotonic structures 47 . In this work, we exploit the rapid spatial variation of the Gouy phase for optical tweezers formed by radial Laguerre-Gauss beams to reduce the trap size in the axial direction.  Further atom trapping near PCWs in tweezer arrays focused by high resolution objectives is a work under progress.

VI. SUMMARY AND OUTLOOK
We have presented an advanced apparatus for the integration of atoms and nanophotonics with several significant advances, including 1) efficient free-space coupling of light to and from guided modes of PCWs with greatly improved power handling capabilities relative to our previous work [15][16][17]  The advanced atom-nanophotonic platform that we have described can provide a foundation for realizing nanoscopic atomic lattices in 1D and 2D as envisioned in Figure 1  With a broad set of such objectives in mind, we have developed the advanced apparatus described in this manuscript. In terms of an outlook for closing the aforementioned gap described in the introduction between experiment and theory (e.g., Ref. 1), there are two issues to address. The first is the development of an apparatus suited to the laboratory realization of the current cartoon depicted in Figure 1 for dense filling of 1D and 2D PCWs with single atoms, which our advanced apparatus should be capable of achieving. However, the second challenge is that the PCW should excel beyond the current APCW in terms of coupling strength between single atoms and photons within a guided mode of the PCW. For a 1D PCW, the still current state-of-the-art is the experiment in Ref. 17. This experiment and its possible improvements are reviewed in Ref. 52. For previous experiments with the APCW 16,17 , the ratio of the waveguide coupling rate Γ max 1D (ν 1 ) for an atom trapped within the vacuum gap to the rate Γ of atomic spontaneous decay to all other modes is P = Γ max 1D (ν 1 )/Γ 1.4. Here the notation is as described in Ref. 17 The motor technology for the PI stage (voice coil) produces both DC and AC magnetic fields. The DC magnetic field in three directions is measured by a magnetometer as shown in Figure 11. The measured total magnetic field produced by the PI stage is around 250 mG at a distance of 6 cm from atoms in the science cell. The magnetic field is zeroed near the PGC cloud position by three pairs of Helmholtz coils and further suppression of magnetic field by a factor of ∼ 10 is also achieved by shielding the PI stage with a mu-metal box, as shown in dashed lines in Figure 11.