Membrane MOT: Trapping Dense Cold Atoms in a Sub-Millimeter Diameter Hole of a Microfabricated Membrane Device

We present a demonstration of keeping a cold-atom ensemble within a sub-millimeter diameter hole in a transparent membrane. Based on the effective beam diameter of the magneto-optical trap (MOT) given by the hole diameter (d = 400 um), we measure an atom number that is 10^5 times higher than the predicted value using the conventional d^6 scaling rule. Atoms trapped by the membrane MOT are cooled down to 10 mK with sub-Doppler cooling. Such a device can be potentially coupled to the photonic/electronic integrated circuits that can be fabricated in the membrane device representing a step toward the atom trap integrated platform.


Introduction
The past two decades have witnessed remarkable advances in computing and sensing demonstrations that leverage coherence and entanglement in systems well-described by quantum mechanics 1,2 . Concurrently, the advent of microfabrication techniques promises to buttress the exploration of new frontiers in quantum applications [3][4][5] through atom-light interactions [6][7][8][9][10][11][12][13][14][15][16] in addition to incorporating compact MOTs 17-25 on atom chips [26][27][28][29][30][31][32][33] and superconducting circuits [34][35][36][37][38] . Already, quantum engineering for integrated quantum systems has seen the development of compact and scalable laser systems using hybrid integrated photonic circuits 39,40 with silicon photonics, III-V photonics and nonlinear optics. Such techniques are poised to expand reliable operation of cold-atom positioning, navigation and timing (PNT) sensors 41 in new and challenging environments. Engineering of quantum systems has also enabled integrated, on-chip quantum computing platforms capable of individual spin addressing, spin-spin entanglement and spin readout. Quantum processers with more than 50 qubits have been demonstrated with superconducting circuits possible in the near future 42,43 . Likewise, new efforts are exploring novel surface ion-trap platforms 44 combining microfabricated surface electrodes and integrated photonics on the same chip. These quantum engineering efforts seek to inaugurate a quantum-to-classical interface 45 to realize a true quantum device.
We demonstrate membrane MOT devices compatible with PIC technology 46 , which can pave the way toward atom trap integrated platforms (ATIP) for neutral atoms. In this architecture, the suspended membrane waveguide can be used to trap and probe neutral atoms through the evanescent field of optical waveguide modes, and the heat generated at the waveguide can be dissipated through the membrane attached to the substrate, which can deliver sufficient guided optical powers in vacuum for evanescent-field optical traps. Thanks to the heat dissipation capability, there may be no need for the fabrication of optical waveguides on the substrate [10][11][12] . Photonic ATIPs will be crucial for enabling future neutral atom quantum applications. Atomic spins positioned near the waveguide surface offer an interface between spin information and the guided optical mode which can be processed in the PIC. Compared to artificial counterparats 47,48 , neutral atoms offer powerful and compelling advantages in terms of homogeneous physical properties and long coherence and life times due to being well-isolated from noisy materials. Compared to trapped ion approaches, neutral atoms offer near-term scaling advantages, larger atomic ensembles and wide-ranging sensing modalities.
In this paper, we demonstrate a foundational technique for laser cooling atoms directly in the vicinity of an optical information bus. This approach is advantageous in terms of technical simplicity and efficacy. In particular, efficient atom loading nearby the nanostructure is crucial for positioning and coupling many atoms, not a single atom, to the evanescent field of the guided mode. In so doing, we can connect the success efficient two-color evanescent-field atom trapping with nanofibers [49][50][51][52] to the unique features and possibilities of the photonic ATIP. Underpinning our approach is our introduction of a MOT produced in a sub-millimeter diameter hole on a microfabricated transparent membrane. The membrane itself can support an optical waveguide that traverses the hole allows the optical field to interact with the atomic spins via the evanescent tail extending into the vacuum. In our demonstration, we imitate such a waveguide with a mock, micron-width beam fabricated from the membrane material, allowing us to test the atom loading dynamics around such a structure.
It is well known that the number of atoms accumulated in a MOT scales unfavorably with MOT beam diameter (d), especially below 2 mm where the scaling converts from 1/d 3.6 to 1/d 6 53 . In our system 54 , we reimagine the interface between a MOT and a membrane MOT device with a transparent membrane that divides the MOT loading volume in two and provides a small membrane hole for cold atoms to collect. This is enabled by the overdamped harmonic motion of an atom that enters the loading volume. Through the laser cooling dynamics, atoms can quite often dissipate kinetic energy and relax into the center of the trap without entering the other hemisphere. Thus, many atoms eventually accumulate at the center of the membrane hole. This requires the diameter of the membrane hole to be larger than the diameter of the MOT cloud which can readily sub-mm, whereas the size of the membrane itself can be orders of magnitude larger and define a generous loading volume. The efficacy of this approach can be clearly shown by comparison with the achievable atom number in a MOT specified by cooling beam diameters limited by the diameter of the membrane hole. A MOT beam diameter limited by the 400 µm-hole diameter would yield a number of trapped atoms 10 5 times smaller than what we observe. Using the membrane MOT with the 400 µm-hole diameter, we achieved about 10 5 atoms, but the extrapolated atom number (d 6 scaling) from the open space MOT is less than one with the 400 µm beam diameter. Furthermore, this geometry is compatible with sub-Doppler cooling mechanisms [55][56][57][58] and allows temperature so 10 µK to be reached in our setup. Our membrane MOT approach offers a convenient means for positioning a large number of trapped atoms within 300 µm of a microfabricated structure in the plane of an ATIP.

Experimental setup and membrane fabrication
In the experiment, the 133 Cs atoms were used for the open space and membrane MOTs with the cooling and repump beams (852 nm, D2 transition) and the absorption probe (895 nm, D1 transition). The vacuum setup is configured with a glass chamber (40 mm×40 mm×100 mm), a mini-cube (Kimball Physics) and a 5 l/s ion pump. All the chamber platform can be moved with a 1D lab-jack and a 2D translation stage and be aligned to the MOT under the vacuum of 10 −8 mbar. Six intensity balanced MOT beams are collimated with fiber-port collimators, and the small MOT beams (< 4 mm diameter) pass through the transparent membrane (5 mm × 5mm) and can be precisely aligned to the membrane hole, i.e., the MOT loading zone, using multiple 2D translation stages. Four horizontal laser cooling beams cool atoms in the horizontal plane, and two vertical laser cooling beams cool atoms along the vertical axis, i.e., the gravity direction. The transparent membrane captures atoms with two large hemispherical capture volumes as shown in Fig. 1 (a) and loads MOT atoms into the sub-millimeter membrane hole. An adapter with a groove-grabber between a mini-flanged cube and 2-3/4" CF flanged glass chamber firmly hold two stainless steel rods into the glass cell. The two rods support the aluminum membrane sample holder with ∼ 40 degree angle, which allows the MOT beams can capture atoms without blocking MOT beams as shown in Fig. 1 (b). The axis of quadruple MOT coils is aligned to the vertical axis, i.e., the gravity direction. The MOT and X, Y, Z bias coils are prepared with 3D printed ULTEM mount, which can be aligned with the 2D translation stage. We checked Doppler-cooling and sub-Doppler cooling of free-space MOT and membrane MOT with/without a dummy waveguide at the center hole.
We have used two membranes made of AlN (Aluminum nitride) and SiN (Silicon nitride) for the experiments. Especially, the thermal conductivity of AlN is 10 times higher than SiN, which can be advantageous in terms of heat dissipation in vacuum. The absorption loss of membrane rib waveguides needs to be considered because it is the main cause of heat generation at the suspended waveguide section. The fabrication process of the membrane MOT devices 54

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leaving approximately 50 µm of Si below the patterned membrane region. Final membrane release is accomplished by a KOH wet etch for SiN membranes, and XeF2 dry release for AlN membranes. Depending on the shape of membrane holes, an arbitrary shaped MOT can be prepared at the proximity of the membrane MOT devices for interfacing atoms through integrated photonics/electronics.

Trapping atoms in sub-millimeter holes and sub-Doppler cooled atoms
We characterized three different MOT configurations based on location as follows: (1) open space, (2) membrane hole, and (3) pierced membrane hole. Membrane MOT devices can trap atoms in sub-millimeter holes, by measuring steady-state atom number, loading rate, lifetime and sub-Doppler cooled atom temperature compared to the open space MOT atoms. We shared the same laser cooling beams (852 nm, Cs D2 transition) for all the MOT measurements, and the effective MOT beam diameter or the membrane geometry affects those characterization results. Since the atom loading zone is defined by the geometry of membrane holes and the transparent membrane blocks atom trajectory, we regard the membrane hole diameter d Hole as the effective beam diameter d. We found that the membrane MOT (d ≤ 1 mm, membrane area of 5 mm × 5 mm) can significantly enhance the number of trapped atoms at the membrane hole due to two large hemi-spherical capture volumes. We measured the steady-state atom number as shown as Fig. 3. The MOT atom number at the membrane hole decreased by about 5-to-10 times compared to the open space MOT (d = 3.8 mm), which may results from lower atom loading rate nearby the membrane device (see Fig. 4 (a)). The pierced membrane MOT devices with a comparable loading rate to the membrane device show even lower atom numbers than that of the membrane MOT devices at the membrane hole due to a lower 1/β MOT lifetime (see Fig. 4 (b)). The atom number was not much changed depending on a type of membrane (AlN or SiN). The transmittance of membranes should be maximized for a target wavelength, e.g., a laser cooling beam. Using 200nm-thickness AlN and SiN memranes, the transmisstance at 852nm wavelengths is greater than 95% and two complete hemispherical capture volumes can be consituted for Cs atoms. The transmittance depends on the thickness and refractive index of the membrane and the light wavelength. In addition, the mebrane thickness and the height of the membrane rib can affect the evanescent-field mode of the suspended membrane rib waveguides 46 .
The optical intensity of Gaussian beams is defined as I(r, z) = P/(πw(z) 2 /2) exp(−2r 2 /w(z) 2 ), and the beam radius w(z) is the distance from the maximum intensity where the intensity drops to 1/e 2 (≈ 13.5%). The optical power of each MOT beam is P = 2.6 ± 0.2 mW, and the beam diameter of the MOT beam is d MOT = 2w(z) ≈ 3. The usual MOT loading equation 59 is where α is loading rate (atoms/ms) and 1/β is MOT lifetime (ms); β is loss rate. The steady state atom number of the membrane MOT, α/β , is determined by loading rate and loss rate. Based on reference 60 , the atom number in the MOT is significantly changed depending on the position of MOT atoms from the surface. Additional atom loss increases when the MOT approaches the surface because of atomic collisions with the surface. This attenuates the MOT atom number when the cloud comes less than 300 µm of the surface. For this case, the loading rate (α) is constant (the loading rate probably also decreases when it is getting closer to the surface), whereas the loss rate (β ) exhibits a dramatic increase nearby the surface.
The membrane MOT is always centered inside the hole. The distance to the cloud from the membrane hole edge is a half of the hole diameter such as 200, 300, 500 µm for d Hole = 0.4, 0.6, 1.0 mm (photolithography mask pattern). As shown in Fig. 4 (a) Fig. 4 (b). There may exist atomic collisions on waveguide surface resulting in a higher loss rate. Other possibilities include a reduced effective capture volume (partially blocked MOT beams; reduced intensity and impure polarization of cooling beams, surface scattered photons with different k-vectors) and additional waveguide scattered photons with different k-vectors.
We obtained sub-Doppler cooled temperatures of membrane MOT atoms as shown in Fig. 5, which means the membrane MOT will be practical for real-world applications. Starting from steady-state MOTs, polarization gradient (PG) cooling process (1 ∼ 2 ms) with intensity lowering and frequency ramping is started while keeping the quadrupole magnetic field on. We measured atom temperature with time-of-flight measurement after sub-Doppler cooling. The temperatures of the open space MOT atoms (d MOT = 3.8 mm), membrane MOT atoms (d Hole = 0.4, 0.6, 1.0 mm), and pierced membrane MOT atoms (d Hole = 1.0 mm) are similar. The pierced section of the membrane MOT devices imitates a 3-µm-width membrane rib waveguide across the membrane hole. We estimate the temperatures with 2D time-of-flight images. The horizontal temperature (T H ) coresponds to the temperature of atoms on the plane of four horizontal laser cooling beams, and the vertical temperature (T V ) corresponds to the temperature of atoms along the gravity axis of two vertical laser cooling beams as shown in Fig. 1 (b). Both horizontal and vetical temperature follow the trend of the time of flight (TOF) measurements even though the membrane MOT devices affect the expansion of atoms and there is some uncertainty of estimating the temperature inside the membrane. The temperature of membrane MOTs (blue square) shows a bit lower temperature than the open space MOT (black circle). Probably, hotter atoms during the sub-Doppler cooling process have more chance to hit the membrane and disappear quickly, so we cannot detect those atoms to determine the temperature. The total atom number decreases, but we can achieve colder cloud inside the hole. The lowest cloud temperature of the membrane MOT devices (d Hole = 0.4 mm, blue square) is 5.3 µK. The lowest measurable cloud temperature of the pierced membrane MOT devices (d Hole = 1.0 mm, red triangle) is 9.7 µK. In the temperature measurement of the sub-Doppler cooled membrane-MOT atoms, the atom number at the membrane hole appears to drop off with drop time as the MOT atoms expand and approach to the membrane. However, the 1/β MOT lifetime measurement of the Doppler cooled membrane-MOT atoms (Fig. 4(b)) would not limit the atom number for the time scale (1-to-5 ms) of the time-of-flight, temperature, measurement. In particular, the MOT lifetime of the pierced membrane was lower than that of other membranes. We need to study and understand these further for the next step.

Conclusion
We developed membrane MOT devices capable of holding 10 5 cold atoms in a sub-millimeter diameter center hole of the membrane. Sub-Doppler cooling of membrane MOT has been demonstrated as 10 µK. Two large hemispherical MOT capture volumes of the membrane MOT devices are generated by six laser-cooled beams through a transparent membrane. This membrane device can accumulate many atoms at the center of the membrane hole during the laser cooling process through the overdamped harmonic motion of an atom, and atoms can dissipate kinetic energy and relax into the center hole without entering the other hemisphere atom loading zone. Based on the effective MOT beam diameter, 400 µm-hole diameter, we measured 10 5 times higher atom number with d 6 scaling. This device was designed to overcome the limited atom-position accessibility onto the membrane rib waveguide by implementing the membrane hole which leads to efficient atom loading around the suspended waveguide across the hole levereged by two large hemispherical MOT capture volumes. Key enabling technology with the membrane device is to achieve photonic atom trap integrated platforms (ATIP) with neutral atoms having scalability, homogeneous physical properties, long coherence and life times, and room-temperature operability. This membrane MOT devices with integrated photonics can utilize the guided, evanescent-field modes to trap and interface atoms. Integrated photonics/electronics can be additionally fabricated on the membrane device for fulfilling advanced engineering capability required for quantum applications.