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arXiv:2108.07106 · Physical Review Research

Self-Bayesian aberration removal via constraints for ultracold atom microscopy

Emine Altuntaş, Ian B. Spielman

Published Oct 29, 2021• 9 citations
arXivHTMLPDF

Abstract

High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements, each of which contributes to loss and light scattering, making them unsuitable for quantum backaction limited ``weak'' measurements. We employ a low-cost high NA aspheric lens as an objective for a practical and economical---although aberrated---high-resolution microscope to image $^{87}\mathrm{Rb}$ Bose-Einstein condensates. Here, we present a methodology for digitally eliminating the resulting aberrations that is applicable to a wide range of imaging strategies and requires no additional hardware. We recover nearly the full NA of our objective, thereby demonstrating a simple and powerful digital aberration correction method for achieving optimal microscopy of quantum objects. This reconstruction relies on a high-quality measure of our imaging system's even-order aberrations from density-density correlations measured with differing degrees of defocus. We demonstrate our aberration compensation technique using phase-contrast imaging, a dispersive imaging technique directly applicable to quantum backaction limited measurements. Furthermore, we show that our digital correction technique reduces the contribution of photon shot noise to density-density correlation measurements which would otherwise contaminate the desired quantum projection noise signal in weak measurements.

DOI
10.1103/physrevresearch.3.043087

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High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements, each of which contributes to loss and light scattering, making them unsuitable for quantum backaction limited ``weak'' measurements. We employ a low-cost high NA aspheric lens as an objective for a practical and economical---although aberrated---high-resolution microscope to image 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensates. Here, we present a methodology for digitally eliminating the resulting aberrations that is applicable to a wide range of imaging strategies and requires no additional hardware. We recover nearly the full NA of our objective, thereby demonstrating a simple and powerful digital aberration correction method for achieving optimal microscopy of quantum objects. This reconstruction relies on a high-quality measure of our imaging system's even-order aberrations from density-density correlations measured with differing degrees of defocus. We demonstrate our aberration compensation technique using phase-contrast imaging, a dispersive imaging technique directly applicable to quantum backaction limited measurements. Furthermore, we show that our digital correction technique reduces the contribution of photon shot noise to density-density correlation measurements which would otherwise contaminate the desired quantum projection noise signal in weak measurements.
We present a high-resolution, simple, and versatile system for imaging ultracold Rydberg atoms in optical lattices. The imaging objective is a single aspheric lens [with a working distance of 20.6 mm and a numerical aperture (NA) of 0.51] placed inside the vacuum chamber. Adopting a large-working-distance lens leaves room for electrodes and electrostatic shields to control electric fields around Rydberg atoms. With this setup, we achieve a Rayleigh resolution of 1.10 μm or 1.41λ (λ = 780 nm), limited by the NA of the aspheric lens. For systems of highly excited Rydberg states with blockade radii greater than a few μm, the resolution achieved is sufficient for studying many physical processes of interest.
In cold atom experiments, high resolution imaging systems have been used to extract in-situ density information when studying quantum gases, which is one of the hot topics in this field. Such a system is usually called “quantum-gas microscope”. In order to achieve a long working distance and large magnification, high resolution imaging of cold atoms through a vacuum window usually requires a long distance between the atoms and the camera. However, due to space limitation caused by a large number of nearby optical elements, it may be difficult to realize a long imaging system, which is a common case in cold atom experiments. Herein we present an imaging system that can achieve a short distance between the atoms and the image plane with diffraction-limited 1 μm resolution and 50 magnification. The telephoto lens design is adopted to reduce the back focal length and enhance the pointing stability of the imaging lens. The system is optimized at an operating wavelength of 767 nm and corrects aberrations induced by a 5-mm-thick silica vacuum window. At a working distance of 32 mm, a diffraction-limited field of view of 408 μm is obtained. The simulation result shows that by changing the air space between lenses, our design operates across a wide range of window thicknesses (0–15 mm), which makes it robust enough to be used in typical laboratories. This compact imaging system is made from commercial on-shelf Φ2 in (1 in = 2.54 cm) singlets and consists of two components: a microscope objective with a numerical aperture of 0.47 and a telephoto objective with a long effective focal length of 1826 mm. Both are infinitely corrected, allowing the distance between them to be adjusted to insert optical elements for irradiating atoms with laser beams of different wavelengths without affecting the imaging resolution. Taking the manufacturing and assembling tolerances into consideration, the Monte Carlo analyses show that more than 95% of the random samples are diffraction-limited within the field of view. This high success rate ensures that these two objectives can be achieved easily in the experiment. Combined with its performance with other wavelengths (470–1064 nm), this imaging system can be used for imaging different atom species, such as sodium, lithium, and cesium.
Adaptive optics (AO) is central to high-resolution microscopy, yet conventional implementations often require repeated correction-and-measurement cycles whose number increases with aberration complexity. This measurement burden can become prohibitive when the available temporal window for correction is short or when photon budgets are constrained. Here, we demonstrate an AO strategy that exploits the spatial correlations of entangled photon pairs to retrieve aberrations directly. By using the second-order correlation function as an aberration-sensitive metric, the required correction can be determined with only a few measurements, without relying on image-based feedback or iterative optimization. This correlation-based approach establishes an efficient framework for AO leveraging quantum light, offering a new route toward quantum-enhanced microscopy in regimes where conventional correction strategies become challenging.
We present a high resolution objective lens made entirely from catalog singlets that has a numerical aperture of 0.36. It corrects for aberrations introduced by a glass window and has a long working distance of 35 mm, making it suitable for imaging objects within a vacuum system. This offers simple high resolution imaging for many in the quantum gas community. The objective achieves a resolution of 1.3 μm at the design wavelength of 780 nm, and a diffraction-limited field of view of 360 μm when imaging through a 5 mm thick window. Images of a resolution target and a pinhole show quantitative agreement with the simulated lens performance. The objective is suitable for diffraction-limited monochromatic imaging on the D2 line of all the alkalis by changing only the aperture diameter, retaining numerical apertures above 0.32. The design corrects for window thicknesses of up to 15 mm if the singlet spacings are modified.
Recovering both amplitude and phase information from a system is a fundamental goal of optical imaging. At the same time, it is crucial to operate at low photon doses to avoid altering the sample, particularly in biological applications. Quantum imaging provides a powerful route to extract more information per photon than classical techniques, which are ultimately limited by shot-noise. However, the trade-off between quantum noise reduction and spatial resolution has long been regarded as a major obstacle to the application of quantum techniques to small cellular and sub-cellular structures, where they could offer the greatest benefits. Here, we overcome this limitation by demonstrating sub-shot-noise quantitative phase imaging of biological cells based on the transport-of-intensity equation, enabling high-fidelity, label-free imaging of key cellular and sub-cellular features. We achieve high-resolution phase imaging limited only by the numerical aperture, while simultaneously obtaining a resolution-independent quantum advantage. Unlike other quantum imaging approaches, our method operates in a quasi-single-shot, wide-field configuration, retrieves both phase and amplitude information, and does not rely on interferometric measurements, making it intrinsically fast and stable. These results pave the way for the immediate application of sub-shot-noise imaging in biological microscopy.
Programable spatial light modulators (SLMs) have significantly advanced the configurable optical trapping of particles. Typically, these devices are utilized in the Fourier plane of an optical system, but direct imaging of an amplitude pattern can potentially result in increased simplicity and computational speed. Here we demonstrate high-resolution direct imaging of a digital micromirror device (DMD) at high numerical apertures (NA), which we apply to the optical trapping of a Bose-Einstein condensate (BEC). We utilise a (1200 x 1920) pixel DMD and commercially available 0.45 NA microscope objectives, finding that atoms confined in a hybrid optical/magnetic or all-optical potential can be patterned using repulsive blue-detuned (532 nm) light with 630(10) nm full-width at half-maximum (FWHM) resolution, within 5% of the diffraction limit. The result is near arbitrary control of the density the BEC without the need for expensive custom optics. We also introduce the technique of time-averaged DMD potentials, demonstrating the ability to produce multiple grayscale levels with minimal heating of the atomic cloud, by utilising the high switching speed (20 kHz maximum) of the DMD. These techniques will enable the realization and control of diverse optical potentials for superfluid dynamics and atomtronics applications with quantum gases. The performance of this system in a direct imaging configuration has wider application for optical trapping at non-trivial NAs.