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Optics Express

Focus and depth of field tunable detection system for compact quantum sensors

Kai Frye-Arndt, Arne Wacker, Patrick Brunssen, Til Dralle, Holger Ahlers, Waldemar Herr, Ernst Maria Rasel, Christian Schubert

Published Jan 14, 2026• 0 citations
Publisher

Abstract

Absorption imaging is a well-established method for determining both the atom number and spatial distribution of atomic ensembles, traditionally limited to a single focal plane and a fixed depth of field. However, as atom optics experiments grow more complex, atomic clouds can exceed the depth of field or leave the focal plane, as seen in large atomic arrays or bubble Bose-Einstein condensates (BECs). Here, we present an absorption imaging system that allows for tuning the object distance of 88.9 mm by ±5 mm and the depth of field from 26 µm to 203 µm. We determine performance metrics relevant for atomic experiments, such as the resolution and the optical distortion.

DOI
10.1364/oe.582238

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Absorption imaging is a well-established method for determining both the atom number and spatial distribution of atomic ensembles, traditionally limited to a single focal plane and a fixed depth of field. However, as atom optics experiments grow more complex, atomic clouds can exceed the depth of field or leave the focal plane, as seen in large atomic arrays or bubble Bose-Einstein condensates (BECs). Here, we present an absorption imaging system that allows for tuning the object distance of 88.9 mm by ±5 mm and the depth of field from 26 µm to 203 µm. We determine performance metrics relevant for atomic experiments, such as the resolution and the optical distortion.
We present a novel imaging system for ultracold quantum gases in expansion. After release from a confining potential, atoms fall through a sheet of resonant excitation laser light and the emitted fluorescence photons are imaged onto an amplified CCD camera using a high numerical aperture optical system. The imaging system reaches an extraordinary dynamic range, not attainable with conventional absorption imaging. We demonstrate single-atom detection for dilute atomic clouds with high efficiency where at the same time dense Bose-Einstein condensates can be imaged without saturation or distortion. The spatial resolution can reach the sampling limit as given by the 8 μm pixel size in object space. Pulsed operation of the detector allows for slice images, a first step toward a 3D tomography of the measured object. The scheme can easily be implemented for any atomic species and all optical components are situated outside the vacuum system. As a first application we perform thermometry on rubidium Bose-Einstein condensates created on an atom chip.
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.
Research into Bose-Einstein condensates is currently a thriving field in physics. Much of the experimental research involves the detection of cold atom clouds under various conditions. Consequently, the fundamental and technical limitations of the imaging techniques and technologies utilized will have a dramatic influence on the results of these experiments. Therefore a detailed analysis of the restrictions on a Bose-Einstein condensate imaging system is overdue and will facilitate further developments in the field due to an increase in the signal to noise ratio; hence a greater level of detail available in experimental images. ¶ The work carried out in this thesis focuses on the properties of absorption imaging techniques, in the quest for an optimized imaging system. Optimization was proposed to be achieved through maximization of the signal to noise ratio by any and all means available. A detailed investigation of the diverse influences on the signal to noise ratio was performed with a focus on eliminating technical restrictions and minimizing fundamental constraints. By studying a 2f - absorption imaging system the maximal signal to noise ratio of 35 was calculated. This corresponded to imaging a cloud of 105 87Rb atoms in a (50 micron) square box with a 31.8MHz detuned, 780nm laser at an intensity of 570W/(m.m) for 35 micro-s. These optimal imaging parameters correspond to our imaging system being limited by the well depth of our detector, not by a fundamental physical process. Furthermore, current experimental noise is identified as the most significant inhibitor to the achievement of an optimized absorption image. ¶ This study represents a first analysis of the quality of current Bose-Einstein condensate imaging techniques and limitations.
Optical imaging plays a central role in ultracold atom experiments by enabling quantitative measurements of atomic density, temperature, atom number, and condensate dynamics. Achieving high-fidelity absorption imaging requires a well-characterized optical system with accurately calibrated magnification and spatial resolution. In this work, I designed, implemented, and experimentally characterized a dual-view optical imaging platform for future absorption imaging of ultracold sodium atoms. The system consists of two independent three-lens relay imaging systems providing top and side views of the atomic sample. Two low-magnification configurations with nominal magnification 0.6 were developed for imaging the relatively large sodium magneto-optical trap (MOT), while higher-magnification configurations with nominal magnifications of 4 and 10 were designed for Bose–Einstein condensate (BEC) imaging. The work included the integration and optimization of the laser cooling and trapping apparatus, improvements to the magnetic-field control system, and the alignment and calibration of both imaging paths. Characterization using a laser and a USAF 1951 resolution target yielded measured magnifications of 0.653 ± 0.033 and 0.521 ± 0.016 for the side and top MOT imaging systems, with corresponding spatial resolutions of 13.92 µm and 9.84 µm. The BEC imaging systems achieved measured magnifications of 4.094 ± 0.060 (top) and 10.817 ± 0.172 (side), with spatial resolutions of 9.84 µm and 6.20 µm, respectively. These measurements agree well with the theoretical diffraction-limited resolutions of 7.19 µm for the 0.6 and 4 magnification systems and 2.87 µm for the 10 magnification system, with the remaining differences attributed primarily to practical optical aberrations and alignment tolerances. The calibrated dual-view imaging platform provides the spatial resolution and quantitative accuracy required for absorption imaging of ultracold sodium atoms and establishes the experimental foundation for future investigations of sodium magneto-optical traps, Bose–Einstein condensation, and coherent spin dynamics in spinor sodium gases.
Abstract Absorption imaging is a fundamental technique for quantitatively extracting information from ultracold atom experiments. Since ultracold 6Li atoms are prepared and detected under high magnetic fields, the suitable detuning of the probe light can reach the GHz level compared to zero-field imaging. Therefore, based on the energy level structure of 6Li atoms and the requirements of subsequent experiments, we design a high-field imaging system with a large frequency range and good robustness, starting from the rationality of the optical layout design and employing offset locking techniques. This imaging system covers the entire crossover region from Bose–Einstein condensate to Bardeen–Cooper–Schrieffer (BEC–BCS) and realizes free switching between zero-field and high-field imaging. Additionally, by introducing a proportionality coefficient to correct for the intensity fluctuations of the probe light, we mitigate its disturbance on the statistical measurement of particle numbers in the experiment. This work not only provides a design reference for other quantum gas experiments requiring absorption imaging under strong bias magnetic fields, but also serves as an important reference for improving the imaging performance.
Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of field, making the identification of the optimally focused configuration difficult. Here we describe a systematic technique for bringing Bose-Einstein condensates (BEC) and other cold-atom systems into an optimal focus even when the ratio of the thickness to the depth of field is large: a factor of 8 in this demonstration with a BEC. This technique relies on defocus-induced artifacts in the Fourier-transformed density-density correlation function (the power spectral density, PSD). The spatial frequency at which these artifacts first appear in the PSD is maximized on focus; the focusing process therefore both identifies and maximizes the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects.