Demonstration of a MOT in a sub-millimeter membrane hole

We demonstrate the generation of a cold-atom ensemble within a sub-millimeter diameter hole in a transparent membrane, a so-called “membrane MOT”. With a sub-Doppler cooling process, the atoms trapped by the membrane MOT are cooled down to 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μK. The atom number inside the unbridged/bridged membrane hole is about \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^4$$\end{document}104 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^5$$\end{document}105, and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/e^2$$\end{document}1/e2-diameter of the MOT cloud is about 180 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μm for a 400 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μm-diameter membrane hole. Such a membrane device can, in principle, efficiently load cold atoms into the evanescent-field optical trap generated by the suspended membrane waveguide for strong atom-light interaction and provide the capability of sufficient heat dissipation at the waveguide. This represents a key step toward the photonic atom trap integrated platform (ATIP).

Membrane MOT devices compatible with photonic integrated circuits (PIC) technology 49 can pave the way toward atom trap integrated platforms (ATIP) 50 for neutral atoms. In this architecture, the suspended membrane waveguide can be used to trap and probe neutral atoms through the evanescent fields of optical waveguide modes, which is capable of delivering sufficient optical powers in vacuum while the membrane structure attached to the silicon substrate dissipates the heat generated from optical absorption in the waveguide. This heat dissipation capability could eliminate the need for the fabrication of optical waveguides on the substrate [11][12][13] . 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 counterparts 51,52 , 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 noise sources. Compared to trapped ion approaches, neutral atoms offer near-term scaling advantages, larger atomic ensembles and a wide range of sensing modalities.
In this paper, we demonstrate a foundational technique for laser cooling atoms directly in the vicinity of an optical waveguide that can act as an information bus. This approach is advantageous in terms of technical simplicity and efficacy. In particular, efficient atom loading near the suspended membrane waveguide is crucial for positioning and coupling many atoms to the evanescent-field guided mode. In doing so, we can bring the success of evanescent-field optical traps around a nanofiber [53][54][55][56] to the photonic ATIP with unique features and new possibilities. 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, allowing the optical field to interact with the atomic spins via the evanescent field extending into the vacuum. In our demonstration, we imitate such a waveguide with a three-micrometer-width mechanical beam fabricated from the membrane material, allowing us to test the atom loading dynamics around such a structure.
In our system 57 , we reimagine the interface between a MOT and a device with a transparent membrane that divides the MOT loading volume in two and collects cold atoms in a sub-millimeter hole in the membrane.

Experimental setup and membrane fabrication
In the experiment, 133 Cs atoms were used for the free-space and membrane MOTs with cooling and repump beams (852 nm, D2 transition) and an absorption probe (895 nm, D1 transition). The vacuum setup was configured with a glass chamber (40 mm × 40 mm × 100 mm), a mini-cube and a 5 L/s ion pump, resulting in a pressure of 10 −8 mbar. The entire chamber, and hence the samples, were moved with a 1D lab-jack and a 2D translation stage and aligned to the free-space MOT. Six intensity-balanced collimated MOT beams ( < 4 mm 1/e 2 diameter) pass through the transparent membrane (5 mm × 5 mm) and can be precisely aligned to the membrane hole, i.e., the MOT loading zone, using multiple 2D translation stages. As shown in Fig. 1b, 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. 1a and loads MOT atoms into the sub-millimeter membrane hole. Two rods support the aluminum membrane sample holder with ∼ 40 degree angle, allowing the MOT beams to pass through the membrane without being occluded by the silicon substrate. The symmetry axis of quadrupole MOT coils is aligned to the vertical axis, i.e., the gravity direction. We checked Doppler-cooling and sub-Doppler cooling of the free-space MOT and the membrane MOT with and without a dummy waveguide at the center hole.
We used two membranes made of AlN (aluminum nitride) and SiN (silicon nitride) for the experiments. Importantly, the thermal conductivity of AlN is 10 times higher than SiN, which can be advantageous in terms of heat dissipation of a suspended waveguide. The absorption loss of membrane ridge waveguides (Fig. 1c) 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 57 is shown in Fig. 2. Tensile SiN/AlN films were deposited on the front side of a silicon wafer. Front-side SiN was deposited via low pressure chemical vapor deposition

Trapping and sub-Doppler cooling of atoms in a sub-millimeter membrane hole
We characterized three different MOT configurations as follows: (1) free space, (2) unbridged membrane hole (see Fig. 1d: Left), and (3) bridged membrane hole (see Fig. 1d: Middle, Right). Membrane MOT devices can trap atoms in sub-millimeter diameter holes and we compared steady-state atom number, loading rate, lifetime and sub-Doppler cooled atom temperature to the free-space MOT. The same laser cooling beams, i.e., MOT beams, (852 nm, Cs D2 transition) were used for all the MOT measurements with and without the membrane geometry affecting those characterization results. The localization of membrane MOT atoms is determined by the geometry of the membrane hole and the transparent membrane. The transparent membrane ( 5 mm × 5 mm ) effectively provides a larger loading zone (i.e., MOT beams) compared to the membrane hole diameter but restricts atom trajectories. Therefore, most of the membrane MOT atoms are accumulated at the membrane hole ( d Hole ≤ 1 mm).
The measured steady-state atom number is shown in Fig. 3. The MOT atom number at the membrane hole decreased by about 5-to-10 times compared to the free-space MOT ( d MOT = 3.8 mm ), which may result from lower atom loading rate near the membrane device (see Fig. 4a). Bridged membrane MOT devices with a comparable loading rate to the unbridged membrane devices show lower atom numbers than that of the membrane MOT devices at the membrane hole due to a lower 1/β MOT lifetime (see Fig. 4b). The atom number was not strongly affected by the type of membrane (AlN or SiN). The transmittance of membranes should be maximized for a target wavelength, e.g., a laser cooling beam. Using 200 nm-thick AlN and SiN membranes, the transmittance at 852nm wavelengths is greater than 95%, effectively providing two complete hemispherical capture volumes for Cs atoms. The transmittance depends on the thickness and refractive index of the membrane and the light wavelength. In addition, the membrane thickness and the height of the membrane ridge can affect the evanescent-field mode of the suspended membrane ridge waveguides 49 .
The optical intensity of Gaussian beams is defined as I(r, z) = 2P/(πw(z) 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) ≈ 3.8 mm in free space. Therefore, the free-space intensity of the MOT beam is I = (41.7 ± 3.2) I sat , where I sat = 1.1 mW/cm 2 and Ŵ = 2π · 5.2 MHz (FWHM) for the 133 Cs D2 transition at 852 nm. The detuning of MOT beams is δ = −2Ŵ and the magnetic field gradient of the MOT coils is dB/dz ≈ 13.6 G/cm . Using an absorption probe (895 nm, Cs D1 transition), we measure 6. www.nature.com/scientificreports/ the number of atoms accumulated in a MOT scales unfavorably with MOT beam diameter 62-64 , especially below 2 mm where the scaling converts from 1/d 3.6 to 1/d 6 . Hence, attempting to make a free-space MOT with a submillimeter 1/e 2 -diameter Gaussian beam results in a negligible number of atoms. The efficacy of the membrane MOT approach can be shown in a higher atom number localized within a membrane hole compared to the atom number in the free-space MOT specified by a MOT beam diameter which can localize atoms within the same size of the membrane hole. The membrane MOT is better at trapping atoms in a small volume compared to shrinking down the free-space MOT beams. Based on the loading rate and lifetime measurement of the membrane and free-space MOTs, we found that the vacuum limited lifetime is the same near and far from the membrane in the case of no waveguide bridge, shown in Fig. 4. The loading rate drops by about four near the membrane hole leading to the smaller atom number. The loading rate is affected by the capture velocity, v c , of the MOT 63 , and v c is a function of intensity, optical detuning, and diameter of the MOT beams, magnetic-field gradient, and the physical structure at the    www.nature.com/scientificreports/ MOT. It is fair to assume that the membrane structure further limits v c and therefore reduce the loading rate as shown in Fig. 4a. In addition, the Cs vapor density in our experimental vacuum chamber is much lower than the saturation vapor pressure at room temperature. Under this condition, Cs vapor continuously deposit onto the membrane surface, which causes low near surface vapor density 65 . The MOT lifetime limited by collisions with background Cs atoms is therefore a bit longer, as shown in Fig. 4b. The bridged membrane hole decreases the MOT lifetime (see Fig. 4b) due to the collision between cold atoms and the dummy waveguide, leading to a smaller steady-state atom number. The usual MOT loading equation 66 is N(t) = α β (1 − e −βt ) , where α is loading rate (atoms/ms) and 1/β is MOT lifetime (ms). The steady-state MOT atom number, α/β , is determined by loading rate α and loss rate β. Similar to a reference 67 , the atom number in the MOT is affected by the position of MOT atoms relative to the surface. When the MOT atoms approach the surface within ~ 100-μm distance, the MOT atom number significantly decreases because of atomic collisions with 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 µ m for d Hole = 0.4, 0.6, 1.0 mm (photolithography mask pattern). As shown in Fig. 4a, loading rates of MOT atoms decrease by a factor of four near the membrane due to the reduced capture velocity compared to the free-space MOT, which leads to the smaller steady-state atom number. In addition, the MOT lifetime of the bridged membrane MOT device (red triangle) is significantly lower than other cases, and other membrane MOT devices (blue square) have similar MOT lifetimes to the free-space MOT ( d MOT = 3.8 mm ) MOT as shown in Fig. 4b. Collisions of atoms with the waveguide surface is a likely contributing factor in the higher loss rate. Other possibilities include a reduced effective capture volume (partially blocked MOT beams; reduced intensity and impure polarization of MOT beams to pass through the membrane, 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 sequence ( ∼ 1 − 2 ms ) is performed with intensity lowering and frequency ramping while keeping the quadrupole magnetic field on. We measured atom temperature with time-of-flight measurement after sub-Doppler cooling. The temperatures of the free-space MOT atoms ( d MOT = 3.8 mm ), membrane MOT atoms ( d Hole = 0.4, 0.6, 1.0 mm ), and bridged membrane MOT atoms ( d Hole = 1.0 mm ) are similar. The bridged section of the membrane MOT device imitates a 3-µm-width membrane ridge waveguide across the membrane hole. The horizontal temperature ( T H ) corresponds 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. 1b. Both horizontal and vertical 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 in estimating the temperature inside the membrane. The temperature of membrane MOTs (blue square) shows a bit lower temperature than the free-space MOT (black circle). This could be due to hotter atoms colliding with the membrane and disappearing before the time-of-flight detection. The total atom number decreases, but we can achieve a colder cloud inside the hole. The lowest cloud temperature of the membrane MOT devices ( d Hole = 0.4 mm , blue square) is 5.3 µ K. The lowest measurable cloud temperature of the bridged membrane MOT devices ( d Hole = 1.0 mm , red triangle) is 9.7 µ K. In the temperature measurement www.nature.com/scientificreports/ 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. 4b) would not limit the atom number on the time scale (1-to-5 ms) of the time-of-flight, temperature measurement. In particular, the MOT lifetime of the bridged membrane was lower than that of other membranes. This will require further study in future investigations.

Conclusion
We developed membrane MOT devices capable of capturing 10 5 cold atoms in a sub-millimeter diameter center hole of a transparent membrane. Sub-Doppler cooling in the membrane MOT was demonstrated with the temperature of 10 µ K. This membrane device can accumulate many atoms at the center of the membrane hole during the laser cooling process, and atoms can dissipate kinetic energy and relax into the center hole without entering the other hemisphere atom loading zone. This device was designed to improve the localization of cold atoms onto the suspended membrane ridge waveguide. By implementing the membrane hole, we achieve efficient atom loading around the suspended waveguide by leveraging two large hemispherical MOT capture volumes. This device can enable photonic atom trap integrated platforms (ATIP) 50 with neutral atoms providing scalability, homogeneous physical properties, long coherence and lifetimes, and room-temperature operability. Membrane MOT devices with integrated photonics can utilize the guided, evanescent-field modes to trap and interface atoms. In addition, integrated photonics/electronics can be fabricated on the membrane device to enable advanced integration required for quantum applications. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2021