Magneto-optical trapping using planar optics

Laser-cooled atoms are a key technology for many calibration-free measurement platforms—including clocks, gyroscopes, and gravimeters—and are a promising system for quantum networking and quantum computing. The optics and vacuum hardware required to prepare these gases are often bulky and not amenable to large-volume manufacturing, limiting the practical realization of devices benefiting from the properties of cold atoms. Planar, lithographically produced optics including photonic integrated circuits, optical metasurfaces (MSs), and gratings offer a pathway to develop chip-scale, manufacturable devices utilizing cold atoms. As a demonstration of this technology, we have realized laser cooling of atomic Rb in a grating-type magneto-optical trap (MOT) using planar optics for beam launching, beam shaping, and polarization control. Efficient use of available light is accomplished using MS-enabled beam shaping, and the performance of the planar optics MOT is competitive with Gaussian-beam illuminated grating MOTs.


Introduction
Measurements utilizing gases of laser-cooled atoms are presently confined to controlled laboratory environments due to the large optical assemblies required to prepare and manipulate cold gases. Methods for miniaturization, simplification, and integration of laser-cooling technology will impact applications including clocks [1][2][3][4], inertial sensors [5][6][7], magnetometers [8], vacuum sensors [9], quantum simulation [10], and quantum networking [11]. Preparing atoms into a magneto-optical trap (MOT) is a key step in these applications, and efforts to miniaturize MOT designs have centered around replacing conventional six-beam designs [12] with single-input-beam alternatives such as pyramid MOTs [13][14][15] and grating MOTs (GMOTs) [16,17]. While these methods provide significant simplification of the optical hardware required for laser cooling, it is desirable to achieve a laser-cooling platform composed of planar nanophotonic components which can be lithographically fabricated and integrated to form a portable, manufacturable package [18][19][20].
Advances in near-infrared and visible spectrum planar optics have enabled significant progress toward realizing a planar optics MOT [21]. Lithographically fabricated grating chips have broadened the scope of GMOT design [16,22] including the realization of integrated Zeeman-slowing [23], grating-based two-dimensional (2D) MOTs [24], and new methods for trapping alkaline earth atoms [25]. Photonic integrated circuits (PIC) fabricated on SiN x platforms have enabled chip-based interrogation of warm atomic vapors for clock applications [3,26] as well as accurately focused beams to interface with trapped ions for quantum information processing [27]. Recent works have demonstrated a beam-launching architecture for laser cooling using PIC-based large-area grating mode converters [28] and laser-cooling using a metasurface (MS) optic for beam splitting [29].
In this work, we demonstrate laser cooling using a collection of planar optical elements operating at 780 nm to form a GMOT of 87 Rb. We begin by coupling free-space light into a nanophotonic waveguide on a PIC (figure 1). The challenge in realizing this MOT is in efficiently converting the sub-micrometer waveguide mode in the PIC into a free-space mode of centimeter-scale, a change in mode area by a factor ≈10 10 . Beam expansion is necessary as magneto-optical trapping is inefficient with millimeter-scale or smaller laser beams due to the finite optical scattering forces present in laser cooling [12]. It is also necessary to increase the capture rate into the MOT, which scales strongly with the size of the laser cooling beams [22]. We employ a multi-stage approach to expand the waveguide mode using the combination of an extreme mode-converter (EMC) on the PIC and a transmissive, dielectric MS acting as an aspheric beam-shaper. The shaped free-space beam impinges on a segmented, reflective grating chip (figure 1(b)) which diffracts light into three additional beams to form a four-beam GMOT within a conventional glass vacuum chamber.

Design and characterization of planar optics
To form an MOT using planar optics, we manipulate the laser cooling light with a PIC, MS, and a grating chip as shown in figure 1. The PIC projects a linearly polarized Gaussian beam at ≈4 • from normal to the PIC surface (figure 1(f)), and a QWP converts the beam polarization to circular. The beam strikes the transmissive, dielectric MS at 4 • from normal. The MS phase profile causes the beam to deflect normal to the MS and to diverge such that a flat-top intensity profile is realized after expanding over ≈150 mm distance. At this distance, the beam is ≈20 mm in diameter and impinges on a three-segment diffraction grating chip. The grating chip (figure 1(b)) diffracts light at ≈51 • (the 1st diffraction order at normal incidence) at 780 nm. Three diffracted beams, one from each grating segment, overlap with the flat-top mode within a glass-walled vacuum chamber to form the laser-cooling volume of the GMOT. External electromagnets generate a quadrupole magnetic field whose center resides in the laser beam overlap volume. The arrangement of the overlapping beams and the quadrupole magnetic field provides confining forces both along the z-axis and in the radial (x-y) plane of the GMOT. The glass cell is attached to a chamber containing an ion pump and a Rb dispenser used to generate adjustable partial pressures of Rb.
The SiN x -based PIC (figure 1(c)), which launches the Gaussian beam into free space, is composed of a waveguide and an EMC similar to the design described in references [30,31]. The PIC is fabricated from a 250 nm thick layer of nominally stoichiometric silicon nitride (SiN x ) clad from both sides in 3 μm of silicon dioxide (SiO 2 ) with photonic structures defined using electron-beam lithography followed by reactive-ion etching. Light is edge-coupled into the fundamental TE 0 mode of a waveguide of 250 nm × 300 nm cross-section, aided by an inverse taper at the edge of the chip that adiabatically expands the optical mode to increase coupling efficiency of free-space light into the waveguide. Light is guided ≈5 mm across the chip to the EMC where it is evanescently coupled into a SiN x slab mode and then scattered into free-space using an apodized grating structure where it forms a circular, collimated Gaussian beam with an 1/e 2 radius of ≈ 140 μm at an angle of ≈4 • from the surface normal (along the negative-y axis). In the EMC, both the slab-mode coupling and the apodized grating scattering rate are spatially varied to project the desired collimated, 2D Gaussian intensity profile, increasing the mode area by a factor of ≈10 5 . The total power efficiency of the PIC from input to output beam is ≈9% with input and output coupling losses of ≈6.5 dB and ≈3 dB, respectively. The free-space linearly polarized beam from the PIC is converted to circular polarization using a conventional QWP (figure 1).
The Pancharatnam-Berry (PB) type MS [32], composed of dielectric Si pillars (figure 1(d)), converts the PIC-launched Gaussian beam into a diverging beam with half angle of 3.8 • , such that a flat-top intensity profile is realized at a distance d ≈ 150 mm, and redirects the beam normal to the MS optic with a deflection angle of 4 • , as shown in figure 1(f). The divergence enables the beam to fill a circular region of radius R ≈ 10 mm, matching the ruled region of the grating chip (figure 2), after expanding over the 150 mm distance. The flat-top intensity realized at the grating surface provides uniform illumination of the grating chip, such that the generated optical forces from the incident and diffracted beam are approximately balanced across the laser-cooling volume. The 4 • deflection allows spatial separation from the 0th order transmission and ensures a uniform polarization state of the expanding beam.
The MS, similar to the work described in reference [33], is constructed from rectangular, polycrystalline Si nanopillars supported by a fused-silica substrate. The pillars reside on a square grid with 280 nm spacing covering an area of 300 μm × 300 μm. The pillars (figure 2(d)) have nominal in-plane dimensions of 92 nm × 176 nm and a constant height of 660 nm. The geometry of Si pillars which compose the MS have shape-birefringence such that each pillar acts as a half-wave retarding element for 780 nm light (the wavelength of the Rb cooling transitions). Circularly polarized light incident on these structures has its polarization handedness reversed and receives a local geometrical phase shift set by the pillars' in-plane rotational orientation. The pillar-orientation-dependent phase shift is used to generate the desired phase profile. The MS is mounted above the QWP and spatially centered on the PIC-launched beam.
The phase profile encoded on the MS is the planar equivalent to a prism followed by a non-spherical, negative focal length lens. The phase profile is determined using a ray optics approach assuming that the local phase gradients φ in the planar optic will deflect normally incident light at an angle θ z from normal as sin (θ z ) = λ 2πn φ , where λ is the vacuum wavelength of light and n is the effective index of the propagating medium. The radially symmetric phase gradient, which maps the power in an ideal Gaussian beam of 1/e 2 radius w uniformly into a circle of radius R at a distance d from the MS, can be expressed as: (1) This phase profile is not stationary in propagation, and the flat-top intensity is realized in a region around the design distance d away from the MS which includes the GMOT capture volume. The 4 • deflection is achieved using an additional linear phase ramp along the y-axis of the MS and spatially separates the flat-top mode from the undesired 0th order transmission at the grating location. The composite phase profile exiting the MS is plotted in figure 2(c). The intensity profile of the flat-top beam is measured at the location of the diffraction grating (figure 2(a)). The flat-top mode achieves the desired 10 mm radius at 150 mm expansion distance and achieves high uniformity over the mode area (figure 2(c)). Root-mean-squared (RMS) intensity variations are observed at ≈7% in the central 20% of the mode area and <20% over the central 80% of the mode area. Two lobes with peak intensities ≈2.5 × the central mode intensity are formed on the periphery of the flat-top mode due to the ≈4 • incidence angle of the PIC-launched beam with the MS. These lobes likely alter the total GMOT capture rate. The balance of forces at the location of the trapped atoms is minimally impacted by these lobes as they do not significantly overlap within this volume. Ripples in the mode profile arise both from diffractive effects during beam propagation as well as spatially varying diffraction efficiency and optical absorption across the MS, primarily at the location of phase discontinuities. Separation between the flat-top mode and the 0th order beam is necessary as the peak intensity of the unshaped, 0th order beam is ≈ 100 × higher than that of the flat-top mode at this location. The intense, 0th order beam would distort or destroy the GMOT if they were to significantly overlap. High-order diffraction is seen in the 0th order beam due to clipping of the Gaussian profile in the EMC.
The MS has an experimentally measured conversion efficiency into the flat-top mode of ≈71%. The efficiency is limited by several factors including Fresnel reflection, optical absorption in Si due to above-bandgap operation, fabrication imperfections, and lithographic limits on the number of sub-wavelength elements that can be placed within an optical wavelength. Other MS types, including designs based on propagation phase [33], could be used to generate the desired circular polarization and phase profile simultaneously without requiring the QWP. Variations in absorption and diffraction, including the effect of phase discontinuities, exist in all MS types and lead to spatial structure in the output beam intensity. For the divergent beam we are creating, undesired spatial structure in the beam's intensity formed at the MS will persist as the beam propagates due to the beam's significant divergence. Such non-ideal intensity variations are detrimental to the GMOT performance, however the PB-type MS utilized here offers acceptable variation in absorption and diffraction across the surface of the device [34]. We note that while we have chosen to use separate elements for the EMC and MS, direct integration of MSs with the EMC is possible and has been demonstrated in reference [33].
The grating-chip is composed of three, 120 • oriented one-dimensional diffraction gratings ( figure 1(e)). First order diffraction from the gratings opposes the incident beam to provide both axial and radial confining forces, realizing a four-beam geometry GMOT [35]. The grating chip is fabricated from Al-coated Si as described in reference [23] with periodic square grooves arranged with a nominal pitch of 1 μm and trench width of 500 nm. The ruled grating pattern fills a circular region with diameter of 22 mm. A triangular opening with an inscribed circular diameter of 3 mm is etched through the center of the grating chip to eliminate reflected light along the beam axis. First order diffraction for normally incident light at 780 nm occurs at ≈51.3 • with a diffraction efficiency of ≈33%. The diffraction angle is chosen to provide a balance between axial and radial confining forces, providing a nearly spherical GMOT as shown in figure 3. The optimal diffraction efficiency of 1/3 is approximated by controlling the etch depth and duty cycle of the grating as described in reference [16]. The grating is mounted ex vacuo parallel to the wall of the vacuum cell and normal to the diverging flat-top laser beam. The GMOT forms ≈5 mm away (negative z-direction) from the inside surface of the glass chamber wall ( figure 1(f)). The overlap of the incident and diffracted beams forms a GMOT trapping volume V trap ≈ 0.34 cm 3 , partially restricted by the 4 mm wall thickness of the vacuum chamber.
The GMOT is formed using the D 2 transitions in 87 Rb. Laser cooling light is prepared using standard methods to address the 5S 1/2 −→ 5P 3/2 , F = 2 −→ F' = 3 (trapping) and F = 1 −→ F' = 2 (repumping) transitions near 780.24 nm [12]. The laser-cooling beams are combined and coupled into the PIC waveguide using fiber and free-space optics to match the ≈0.93 μm 1/e 2 mode radius at the waveguide facet. The transitions (separated by ≈6.6 GHz) have natural linewidths Γ of ≈ 2π × 6.1 MHz and the trapping light has a saturation intensity I sat ≈ 3.6 mW cm −2 . Imaging of the GMOT is performed along an optical path orthogonal to the flat-top beam axis (x-direction in figure 1). The loading rate of the GMOT is measured using fluorescence imaging while atom number and temperature are measured using absorption imaging in TOF. Absorption imaging measures the optical depth of the gas, proportional to the atomic column density, as the natural logarithm of the ratio of incident to transmitted optical intensity. During TOF expansion and imaging, the GMOT electromagnets and MOT optical fields are switched off. A permanent magnet creates an ≈50 μT field along the x-direction to serve as a spin quantization axis for imaging.

Characterization of planar optics GMOT
We have realized a GMOT using the D 2 transitions in 87 Rb and the planar optics described above. Capture into the GMOT is maximized when the trapping light detuning is ≈ −1.5 Γ and the axial gradient of the magnetic quadrupole field is ≈ 0.11 T m −1 , consistent with values reported in reference [22]. Repumping light, copropagating with the trapping light, is resonant to the repumping transition and has a central intensity of 25 μW cm −2 for all measurements. In the low intensity limit, the trapped gas has an approximately Gaussian shape with 1/e 2 radii (w MOT ) of 270 μm axially and 390 μm radially. The dimensions of the gas increase with I trap as the total GMOT population grows, and the radial-to-axial aspect ratio saturates to 2 at high trapping light intensity.
At the maximum trapping light intensity I trap ≈ 1.8 mW cm −2 (≈0.5 I sat ), the GMOT loading rate measured using fluorescence imaging is ≈10 7 s −1 with a trapping lifetime of ≈0.25 s, consistent with a background Rb partial pressure of 8 × 10 −7 Pa [36]. The gas temperature measured using TOF absorption imaging is (176 ± 5) μK in the axial direction and (219 ± 7) μK in the radial direction ( figure 3). Here, uncertainties are the standard uncertainty of the mean. The measured temperature is close to the 87 Rb D 2 Doppler cooling limit of 146 μK [37], and the axis-dependent temperature is a consequence of the force balance set by the diffraction angle of the grating chip [38]. Lower temperatures would be achievable using additional cooling stages including polarization-gradient cooling [39] or Λ-enhanced gray molasses [40]. Inset shows the same data over a larger intensity range. Extrapolated population using GMOT performance and volume scaling in reference [22] is plotted for V trap ≈ 0.34 cm 3 (black star).
The steady-state population of the GMOT (N MOT ) is characterized at varying trapping laser intensities. We observe that N MOT grows in an approximately linear fashion starting from near 0 population at I trap ≈ 0.45 mW cm −2 and reaches a population of ≈ 2.8 × 10 6 at I trap ≈ 1.8 mW cm −2 (figure 4). The GMOT population below I trap = 0.5 mW cm −2 is minimal due to a combination of decreased scattering forces and increased trap loss at low I trap [41,42]. Linear growth of atom number with I trap is typical at low saturation of the atomic transition, and maximum steady-state GMOT populations are typically observed at I trap I sat For comparison, N MOT in reference [22] was observed to peak at 6 × 10 7 using I trap ≈ 50 mW cm −2 (≈14 I sat ) in V trap ≈ 1 cm 3 . The same work demonstrated a volume scaling N MOT ∼ V trap 1.2 , predicting an equivalent maximum N MOT of 1.8 × 10 7 atoms in our system (V trap = 0.34 cm 3 , star point in figure 4 inset). The volume-scaled population is consistent with our observed GMOT population trend.

Comparison to Gaussian-illuminated GMOT
We compare the performance of the planar-optics, flat-top illuminated GMOT to traditional, Gaussian-beam illuminated GMOTs. A bulk-optics assembly is used to prepare collimated, circularly polarized Gaussian beams normally incident to the grating chip. Two beam waists (intensity 1/e 2 radii) of w ≈ 16 mm and ≈24 mm are tested. Each Gaussian beam impinges at normal incidence on the segmented grating chip and is apodized within a 20 mm diameter circle to match the boundary size of the 20 mm diameter flat-top beam. The concomitant beam overlap volume approximates that of the flat-top beam GMOT and enables a fair comparison of their relative performance. GMOTs are prepared using the same nominal laser frequencies, quadrupole field gradient, and Rb partial pressure used in the flat-top illuminated GMOT. The intensity of the trapping light is varied (quoted using the Gaussian beam's central intensity), and atom number and temperature measurements are made using TOF imaging. Measured temperatures and in-trap sizes are consistent with the flat-top illuminated GMOT values.
The Gaussian-illuminated GMOT population is lower than that observed with flat-top illumination as shown in figure 4. For Gaussian illumination, the onset of appreciable capture is also observed at non-zero laser intensity and N MOT also increases approximately linearly in the low-saturation regime. Reduced capture rate for Gaussian illumination is expected due to decreased optical forces at the periphery of the capture volume and to imperfect balancing of laser-cooling forces arising from the Gaussian intensity profile [38]. Accordingly, the onset intensity of the linear population trends also shifts to higher intensity for smaller w. Zero N MOT intercept values of I trap ≈ 0.48 mW cm −2 , I trap ≈ 0.61 mW cm −2 , and I trap ≈ 0.88 mW cm −2 are observed for the flat-top, w ≈ 24 mm and w ≈ 16 mm beams, respectively. The shift to capture beginning at higher central beam intensity corresponds roughly to equal intensities averaged over the trapping volume. Mean intensities over the trapping volume are calculated to be ≈110%, ≈84.7%, and ≈77% of I trap for the flat-top, w = 24 mm, and w = 16 mm beams, respectively. The population reduction with Gaussian illumination is most pronounced in the low saturation regime in which optical forces are linearly related to intensity. At high values of I trap , the observed N MOT trends for flat-top and Gaussian illumination begin to converge due to saturation of the atomic transition as shown in figure 4 inset.

Discussion
Use of the MS-generated flat-top beam allows for efficient use of the available optical power in illuminating the grating chip. Uniform illumination in a GMOT ensures that diffracted light from the grating segments can balance the forces created from the incident beam. In Gaussian-beam illuminated GMOTs, this is typically accomplished using beam waists of similar or larger dimension than the clear aperture of the grating [9,43]. Light falling outside of the grating aperture is wasted-for the w ≈ 24 mm beam used here, ≈30% of the light strikes the ruled grating area and ≈2.5 times the optical power is required to observe the onset of trapping (accounting for the ≈71% efficiency of the MS). Similarly, ≈2.5 times more optical power is required for the w ≈ 24 mm beam to trap 10 6 atoms relative to the flat-top beam. Further improvements in power efficiency could be obtained through more complex MS-enabled beam shaping.
The absolute power efficiency of the planar optics in generating the divergent flat-top beam from a fiber-launched Gaussian beam is ≈6.4 % (≈12 dB loss). Coupling light into and projecting light from the PIC is the largest source of loss at ≈10.5 dB due to a combination of insertion loss into the PIC, waveguide loss, and scattering into the PIC substrate in the EMC. Similar devices have demonstrated losses as low as 7.5 dB ± 0.5 dB using fiber edge coupling [30], and significant improvement in the mode coupler efficiencies are possible with more complex designs. The MS efficiency corresponds to ≈1.5 dB loss and is competitive with other high-performance designs [44]. The grating design is also a source of lost optical power as, by design, only 1/3 of the incident light is diffracted toward the capture volume. Schemes using large area MSs or PIC-based beam launching for all required beams provide paths to potentially higher power efficiency at the expense of greater experimental complexity.
Physical size is also a limitation of the planar optics GMOT presented here for the realization of small, cold atom-based devices. Within the GMOT geometry, reduction of the beam expansion distances (increasing the beam divergence) introduces several effects that complicate the balancing of optical forces in the GMOT including round-trip expansion of the beam, spatial variation in diffraction efficiency across the grating chip, and non-uniform geometrical compression of the diffracted beams. Incident-angle dependence of the diffracted polarization state can also arise, though this is measured to be minimal for our grating chip. For the 3.8 • half-divergence angle (150 mm expansion distance) used here, the divergent mode sufficiently approximates a collimated beam at the grating to allow for use of uniform-pitch grating chip and formation of the GMOT. Steeper divergence angles could be accommodated using gratings with spatially-varying pitch and curvature designed to compensate for the angle-dependent effects, enabling the possibility of millimeter-scale separation between the MS and the grating chip in such designs. The finite forces available in laser cooling limit miniaturization beyond the millimeter scale.

Conclusion
We have demonstrated a GMOT of Rb using planar optical elements including a PIC, MS, and grating chip to launch and manipulate light for laser cooling. Bridging the gap between the sub-micrometer-scale guided mode on the PIC and the centimeter-scale beam needed for laser cooling, a magnification of the mode area by ≈10 10 , is accomplished using an on-chip EMC to launch a Gaussian mode into free space as well as a beam-shaping, polarization-dependent MS to generate an expanding, flat-top mode laser beam. The flat-top beam efficiently illuminates a grating chip to realize a four-beam GMOT with capture rates demonstrated as high as ≈10 7 s −1 and gas temperatures below 200 μK. Steady-state GMOT populations were demonstrated at ≈2.8 × 10 6 , consistent with published volume and intensity scaling for GMOT performance [22]. Comparisons to equivalent Gaussian-beam-illuminated GMOTs demonstrate the power efficiency of the flat-top beam profile relative to conventional Gaussian-illumination.
The GMOT geometry and planar optics demonstrated here offer a natural pathway toward realizing calibration-free measurement platforms and other quantum devices utilizing laser-cooled atoms. The demonstrated architecture is compatible with further integration with on-chip light sources, solid-state alkali dispensers [45], MEMS-based vacuum hardware [46,47], and on-chip methods for imaging. improvements in near-infrared and visible spectrum PIC will make these devices more power efficienct and expand the scope of addressable atoms. We hope that the small physical size and robustness of planar optics GMOT designs will enable new compact atomic clocks, expand the emerging role of cold atom interferometry in space, and contribute to the widespread quantum networking.