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Abstract
A quantum gas microscope plays an important role in cold-atom experiments, which provides a high-resolution imaging of the spatial distributions of cold atoms. Here we design, build and calibrate an integrated microscope for quantum gases with all the optical components fixed outside the vacuum chamber. It provides large numerical aperture (NA) of 0.75, as well as good optical access from side for atom loading in cold-atom experiments due to long working distance (7 mm fused silica+6 mm vacuum) of the microscope objective. We make a special design of the vacuum viewport with a T-shape window, to suppress the window flatness distortion introduced by the metal-glass binding process, and protect the high-resolution imaging from distortions due to unflattened window. The achieved Strehl ratio is 0.9204 using scanning-near-field microscopy (SNOM) fiber coupling incoherent light as point light source.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cold atoms in optical lattices provide a versatile platform to perform quantum simulations and investigate many-body quantum physics [1–3]. Usually, people measure the spatial or momentum profiles of atoms in optical lattices to understand the systems [3]. Among different measurement tools, the quantum gas microscope has been one of the most important breakthroughs in recent years, for it directly probes the in-situ particle occupation in optical lattice [4–11]. It is a powerful tool to probe and simulate phenomena such as phase transitions [12–15], artificial gauge fields [16–19], many-body dynamics [20–22], quantum transportation [23–26], and quantum entanglement [27–29]. It is also a helpful tool to manipulate and control atoms at the single particle level [30–33].
For these applications, a high NA objective compatible with a vacuum viewport is required to enhance the resolution and the fidelity of single atom manipulation. In most of these realizations, the method of solid immersion is required to boost NA in order to reach the single site resolution, which results in a limited optical access and a closer distance between atoms and vacuum viewports due to shorter working distance [34]. A limited optical access increases the difficulties of trapping and manipulating the atoms from side, and a closer distance between atoms and vacuum viewports results in a random trapping potential and shorter coherence time of the atomic ensemble due to the atoms deposited on the glass surfaces, mediated by van der Waals force. Besides these disadvantages, the solid immersion method also requires an immersion lens inside the vacuum chamber and decreases the flexibility of the system.
To overcome these disadvantages, we choose to design a solid-immersion-free quantum gas microscope with a large working distance. However, the major challenge for designing such a microscope system is that the window of the vacuum viewport introduces distortions and strongly deteriorates the imaging quality. The main reason is that the glass-metal binding of the viewport, sealing for the ultra-high vacuum (UHV), introduces plenties of tensions during the binding procedures. Particularly for a high NA objective with a larger working distance which requires a larger clear aperture, an unflattened window surface strongly deteriorates the imaging quality away from the diffraction limit. To solve this problem, one can either polish the distorted vacuum window surface with ion beam figuring technique, or use a thin sapphire window instead of the fused silica one. The former method costs high, and risks failure since the unevenly distributed tension in the window plate will release during the vacuum baking and distort the surface flatness of the already polished window. The latter method using thin sapphire plates introduces bifringes and changes the beam polarizations.
In this manuscript, we present a design for a quantum gas microscope integrated with our rubidium system which has a high NA of 0.75 without solid immersions, while the working distance is 13 mm (7 mm fused silica plus 6 mm vacuum) and provides large optical access from side to support in-situ preparation of condensates. To achieve such a microscope system, we design a vacuum viewport with a T-shape window, to avoid the surface distortions and achieve diffraction limited high NA imaging. We measure the point spread function of the image through the window and the microscope system, and confirm that our flexible and stable microscope system provides the diffraction limited imaging, which works compatibly with rubidium condensates as a quantum gas.
2. Design of the microscope system and the vacuum viewport
In our experiment, the microscope is designed to detect and control rubidium atoms with resolution on the single site level, which endows us with the ability to control the atoms one by one. Specifically, we plan to utilize 740 nm (850 nm) incoherent light source to project an arbitrary blue (red) detuned potential through the objective onto the optical lattice so that many-body physics such as many-body localization can be engineered [22]. Meanwhile, fluorescence imaging is used to detect the state of atoms. For these requirements, the microscope system needs to be diffraction limited for a wide spectrum range, including 740 nm $\sim$ 850 nm, and 532 nm for imaging and arbitrary potential projection.
Hence, we customized a microscope objective with NA $=0.75$ and effective focal length of 9.98mm, with which we are able to suppress the focal shift to $0.3~\mathrm{\mu} \rm {m}$ and the lateral color shift to $0.08~\mathrm{\mu} \rm {m}$ for incoherent light source with 20 nm linewidth in the spectrum range of 740 nm $\sim$ 850 nm on the boundary of the field of view ($\pm 50~\mathrm{\mu} {\rm m}$), by alleviating chromatic aberration and reducing incident angle to preserve effective NA. Meanwhile, the working distance is 7 mm in fused silica plus 6 mm in vacuum. We compensated for the spatial and chromatic aberrations induced by light propagation in the flat-surfaced fused silica window in the design of the microscope objective.
In addition, the theoretical depth of field (DOF) for the microscope objective without adjusting the eyepiece or image plane is $\pm$0.3 $\mathrm{\mu}$m, estimated by
where $n$ is the refractive index of optical medium between atoms and first component of the microscope objective. This small value ensures that the imaging only measures one layer of atoms in optical lattices along the imaging direction.If the atoms are not exactly in the designed location, we can adjust the image plane to compensate. By adjusting the distance between the tube lens (focal length = 1308 mm and magnification $\times 130$) and the image plane, we are able to expand the depth of field (DOF) to theoretically $\pm 8$ $\mathrm{\mu}$m so that position requirements of atoms along optical axis are relaxed. This large DOF property is important for experiments in which atom positions cannot be controlled at will against thermal expansion. We also list the key properties of the objective in Table 1.
Table 1. Key properties of designed objective lens. Terms with * are characterized by criteria of Strehl ratio at $0.9$ with adjustable position of the tube lens.
In Fig. 1(a), we show the experimental setup to measure the performance of the microscope system. The objective vertically sits on a vacuum viewport, where this viewport seals the vacuum chamber for cold-atom experiments. The housing mount surrounding the objective is designed to provide a smooth and precise installation of the objective onto the vacuum viewport repeatable within 50 $\mathrm{\mu}$m precision in the plane of the window surface. The machining of the housing mount is controlled within 20 $\mathrm{\mu}$m so that the tilting error of the objective is within 0.02$^{\circ }$. The housing mount is made by 316 stainless steel assisted with 3D printing technology. Once the bottom of the objective touches the viewport window, we loose the touching points between the objective and the housing mount, then the objective sits firmly on the vacuum window against gravity. This design provides stability and robustness against the relative vibrations and drifts between the viewport and the objective. The inner surface of the viewport window is coated for high reflection at 1064 nm. Therefore, a vertical optical lattice with wavelength of 1064nm could hold the cold atoms at a stable relative position with respect to the objective.
Fig. 1. (a) Sketch of experiment setup. The objective is placed directly on the viewport with a specially designed mount. SNOM fiber coupled to an incoherent light source is used as the point-like emitter. (b) Configuration of the T-shape window. The viewport is made with a T-shape fused silica window bound to a titanium bucket-like mount. The inset shows the main components of the T-shape window.
A perfect objective does not guarantee high quality image though. One challenge of achieving diffraction limited imaging of such a microscope is the distortion from the unflattened window surface of the viewport. For a piece of fused silica substrate, usually it is easy to polish the surface to a flatness of $\lambda /10$ (around 50 nm). However, when the substrate is bound to the metal parts, the surface distortion is introduced due to the tensions between the substrate and the metal parts in the binding process. The surface distortions can be decomposed into different Zernike polynomial terms to facilitate the analysis [35]. In Table 2, we list the tolerance of the irregularities of the window surface required by our microscope, simulated by Zemax. As the binding process does not change the window thickness, and the tilting tolerance of the window with respect to the microscope objective is automatically fulfilled by our mechanical design, the first order surface distortion term becomes the defocus term. This term can be greatly compensated by adjusting the distance between the tube lens and the image plane, and has a peak-to-peak tolerance value of 800 nm in a surface region with the radius of 7 mm, which is determined by the light cone with NA = 0.75 emission angle and 6 mm propagation distance in vacuum. This tolerance is achievable with most vacuum viewports with window thickness of 7 mm.
The astigmatism term ($Z^{\pm 2}_2$ term in Zernike polynomial) in the surface distortion is the most dramatic term practically [36], and strongly limits the resolutions of a microscope. For a typical off-the-shelf viewport, the astigmatism term of the window surface is larger than the allowed tolerance (Table 2), usually with a peak-to-peak value of about 600 nm in a region with radius of 10.0 mm.
Table 2. Tolerance of different irregularity terms of the vacuum viewport surface profile required by the microscope system and the value achieved with our T-shape vacuum viewport (peak-to-peak value in 7 mm radius). The tolerance values are obtained by Zemax simulation at the edge of the field of view with the criteria of diffraction limited imaging. And the measured data are measured by the home-made Fizeau interferometer. * the deviation of the thickness is supposed to be within $-7\ \mathrm{\mu} {\rm {m}}\sim +8\ \mathrm{\mu} \rm {m}$ with $7\ \rm {mm}$ the designed value.
To overcome this difficulty and make a vacuum viewport with flatness within the objective’s tolerance, we design a vacuum viewport with a T-shape window. In Fig. 1(b), we show the schematic of this viewport. The window is circularly shaped with a diameter of 50 mm. The central part (25 mm diameter) is a surface polished on both sides with a thickness of 7 mm, used for high NA microscope imaging. Meanwhile, the outer ring is polished only on the air side with 4 mm thickness, used to reduce the tension from the glass-metal binding procedure for the thick central part. To further reduce the tension and astigmatism, we use a titanium circle plate with thickness of 1.65 mm and outer diameter of 90 mm to connect the window and the titanium cylinder wall. Then, the titanium cylinder wall is connected to the metal part with conventional-viewport designs. Here, reducing the circle plate thickness helps us to further relieve the unwanted metal-glass tension and decrease the astigmatism term of the window surface profile.
We measure the surface profile of the T-shape viewport by a Fizeau-interferometry [37] with 505 nm incoherent light source [Thorlabs M505L4], and decompose the measured flatness into different Zernike polynomial terms. The measurement shows that the peak-to-peak astigmatism is 105 nm which is well below the objective required tolerance of 270 nm, and just one third of the astigmatism peak-to-peak value of the off-the-shelf bucket window viewports. This demonstrates that by using T-shape window and carefully designing the surrounding metal parts, one can eliminate the imaging distortion due to vacuum window for quantum gas microscope with large working distance and high numerical aperture.
3. Calibration of the microscope
To efficiently characterize the performance of the microscope system, we measure the point spread function (PSF) of the imaging for a point light source. To avoid the interference pattern from reflection of multiple surfaces, we use an incoherence light source with central wavelength at 760 nm and linewidth of 20 nm. We couple the light into a special fiber used for scanning- near-field optical microscopy (SNOM) [K-tek nanotechnology E50-780HP] [38]. SNOM fibers are special for their aluminum-coated tapered tiny tips drawing from melted silica, such that sub-micrometer fiber tip end and large emission NA can be obtained [39]. Since the diameter of the tip end is about 200 nm, smaller than the target resolution of our microscope system, and the emission angle is 4.52 steradian, which is twice as the NA = 0.75 collection angle (2.13 steradian) of the objective, we treat the tip end of the SNOM fiber as an ideal point emitter.
We mount the fiber tip on a 3-dimensional translation stage so that the position of the tip end can be tuned with a resolution of 1 $\mathrm{\mu}$m orthorgonal to the optical axis, and 0.5 $\mathrm{\mu}$m along the optical axis ($z$-direction) (Fig. 1(b)). We use a camera with a pixel size of 4.65 $\mathrm{\mu}$m $\times$ 4.65 $\mathrm{\mu}$m to monitor the PSF. As the magnification of the image system is 130, each pixel corresponds to a 35 nm $\times$ 35 nm square on the fiber tip. Fig. 2(a) shows the PSF pattern captured by the camera on the image plane. A self-developed program is utilized to capture and analyze pictures in real time when we optimize location of the fiber tip with respect to the microscope system. To quantify the PSF, this program fits real PSF to Airy disk with the same total intensity, characterizes radius of the PSF by the radius of the first zero point of the fitted Airy disk, and calculates the corresponding Strehl ratio [40].
Fig. 2. Results of the image calibration. SNOM fiber coupling incoherent light source is used as a point emitter. (a) Image of the PSF through microscope system. The maximum intensity is normalized to unity. (b) Azimuthal averaged PSF versus fitted Airy disk. Blue triangles represent the averaged PSF intensity while red solid line describes the distribution of Airy disk along radial direction. (c) Difference of the PSF and the fitted Airy disk. It is shown that the residual is within $8\%$. (d) Strehl ratio versus off-axis distance of the point emitter. Blue dots plot the Strehl ratio measured at different points and the error bar characterizes standard deviation from three images. The orange line is the Strehl ratio simulated by Zemax. Vertical dashed line and horizontal dashed line represent the designed field of view and Strehl ratio = 0.9 criteria respectively.
By scanning the fiber tip in $x-y$ plane for different z positions iteratively, we obtain a PSF with the Strehl ratio of $0.9204$, radius of $677.01\ \rm {nm}$ (the Rayleigh criteria is $618.13\ \rm {nm}$ for $\rm {NA}=0.75$ microscope system for $760\ \rm {nm}$ light source), and main peak power of $0.8161$ (0.84 for the ideal case), which is above the criteria of diffraction limit of imaging (shown in Fig. 2(a-c)). As a comparison, the Zemax simulation of the designed microscope system has a Strehl ratio of 0.9980 at the center of field of view. We attribute this discrepancy to three factors: irregularities of the vacuum window (by measuring the vacuum window through an interferometer, it is guaranteed that those irregularities are acceptable with a Strehl ratio above 0.9), residual misalignment of the fiber position which is limited by the precision of our translation stage, and the imperfection of the alignment of optical components in the microscope objective. Furthermore, we measured Strehl ratio of the image through the microscope system for point light source at different positions within the designed field of view. The measured Strehl ratio are all above 0.85, as shown in Fig. 2(d). With the measured PSF, we also simulate the image quality of a square lattice with lattice spacing of $532\ \rm {nm}$, taking into account the quantum efficiency and noises induced by the camera (Andor iXon Ultra 888). In the simulation, we granulate the PSF distribution with a 5 $\times$ 5 matrix which maps to the pixel array corresponding to one site in the lattice and assume that photon number collected by each pixel obeys Poisson distribution, where the average number of photons emitted is proportional to local PSF intensity. Furthermore, we take into account the noises introduced by dark current, readout noises of the camera, and photon collection efficiency of the objective. It turns out that for each atom, 2000 photon-induced electrons on CCD are sufficient to generate an image with good signal-to-noise ratio to measure the parity of atom number in each lattice site with a fidelity of $99.993\%$. Thus, for $D_2$ line of rubidium 87 with a $2.13\ \rm {sr}$ collecting angle, a $80\%$ transmission of the objective and a quantum efficiency of $95\%$ for the camera, the exposure time approximates 500 ms when the imaging light intensity is around 0.002 saturation intensity to prevent heating, which is less than the life time of single atom trapped in deep optical lattices with cooling [41,42]. Simulation results are shown in Fig. 3, which demonstrates that for a $532\ \rm {nm}$ lattice, our microscope system is able to achieve an in-situ image with single site and single atom resolution.
Fig. 3. Simulation of image of atoms in $532~\rm {nm}$ lattice. (a) Demonstration of a $3\times 3$ array of lattice sites with one or none atom in each site. Each lattice site is mapped to a $5\times 5$ pixel array on the camera. (b) Simulated histogram of the fluorescence count for the center trap imaging. The blue (orange) histogram corresponds to the photon number collected by the center vacant (occupied) site while each of the eight neighbour sites is occupied by one atom, which demonstrates that the influence of surrounding sites can be neglected.
4. Conclusion
In conclusion, we realize an integrated and robust $\rm {NA}=0.75$ quantum gas microscope with long working distance and large field of view. The T-shape vacuum viewport helps us to reduce the surface distortion of the vacuum window to satisfy the tolerance requirement of the microscope objective. The test result demonstrates the capability of the microscope system to accomplish in-situ image of atom array at single site resolution, which endows us the ability to study many body physics with 532 nm lattice spacing. We believe that its robustness and flexibility will simplify the installation and adjustment process. Meanwhile with the single site resolution and large field of view, it provides convenience to explore the fundamental principles of quantum many body system.
Funding
National Key Research and Development Program of China (2021YFA1400904, 2021YFA0718303); National Natural Science Foundation of China (92165203, 61975092, 11974202).
Disclosures
The authors declare no competing interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon request.
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