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arXiv:2402.06514 · Journal of Physics B Atomic Molecular and Optical Physics

Spatial calibration of high-density absorption imaging

Toke Vibel, M B Christensen, M A Kristensen, Jeppe Juhl Thuesen, Laurits Nikolaj Stokholm, Carrie Ann Weidner, J. Arlt

Published Jun 3, 2024• 7 citations

Abstract

Abstract The accurate determination of atom numbers is an ubiquitous problem in the field of ultracold atoms. For modest atom numbers, absolute calibration techniques are available, however, for large numbers and high densities, the available techniques neglect many-body scattering processes. Here, a spatial calibration technique for time-of-flight absorption images of ultracold atomic clouds is presented. The calibration is obtained from radially averaged absorption images and we provide a practical guide to the calibration process. It is shown that the calibration coefficient scales linearly with optical density and depends on the absorbed photon number for the experimental conditions explored here. This allows for the direct inclusion of a spatially dependent calibration in the image analysis. For typical ultracold atom clouds the spatial calibration technique leads to corrections in the detected atom number up to ≈ 12 % and temperature up to ≈ 14 % in comparison to previous calibration techniques. The technique presented here addresses a major difficulty in absorption imaging of ultracold atomic clouds and prompts further theoretical work to understand the scattering processes in ultracold dense clouds of atoms for accurate atom number calibration.

DOI: 10.1088/1361-6455/ad53ae

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We describe an experimental method to calibrate an absorption imaging system for ultracold atom clouds. Optical density profiles of an atom cloud are obtained for various probe beam intensities and are analyzed to determine the correction factor for the effective probe beam intensity directly from saturation effects. We find that the temporal shape of the probe-beam pulse needs to be taken into account for a quantitative analysis of the optical density measured in saturation absorption imaging. We show that this pulse-shape effect can lead to distortion of the density profile due to its nonlinear dependence on the optical depth.

We report on a far above saturation absorption imaging technique to investigate the characteristics of dense packets of ultracold atoms. The transparency of the cloud is controlled by the incident light intensity as a result of the nonlinear response of the atoms to the probe beam. We detail our experimental procedure to calibrate the imaging system for reliable quantitative measurements and demonstrate the use of this technique to extract the profile and its spatial extent of an optically thick atomic cloud.

Abstract Cold atom experiments often use images of the atom clouds as their exclusive source of experimental information. The most commonly used technique is absorption imaging, which provides accurate information about the shapes of the atom clouds, but requires care when seeking the absolute atom number for small atom samples. In this paper, we present an independent, absolute calibration of the atom numbers. We directly compare the atom number detected using dark-ground imaging to the one observed by fluorescence imaging of the same atoms in a magneto-optical trap. We normalise the signal using single-atom resolved fluorescence imaging. In order to be able to image the absorption of the very low atom numbers involved, we use diffractive dark-ground imaging as a novel, ultra-sensitive method of in situ imaging for untrapped atom clouds down to only 100 atoms. We demonstrate that the Doppler shift due to the acceleration of the atoms by the probe beam has to be taken into account when measuring the atom-number.

Absorption imaging of ultracold atoms is the foundation for quantitative extraction of information from experiments with ultracold atoms. Due to the limited exposure time available in these systems, the signal-to-noise ratio is largest for high intensity absorption imaging where the intensity of the imaging light is on the order of the saturation intensity. In this case, the absolute value of the intensity of the imaging light enters as an additional parameter making it more sensitive to systematic errors. Here, we present a novel and robust technique to determine the imaging beam intensity in units of the effective saturation intensity to better than 5%. We do this by measuring the momentum transferred to the atoms by the imaging light while varying its intensity. We further utilize the method to quantify the purity of the polarization of the imaging light and to determine the correct imaging detuning.

The quantum state of ultracold atoms is often determined through measurement of the spatial distribution of the atom cloud. Absorption imaging of the cloud is regularly used to extract this spatial information. Accurate determination of the parameters which describe the spatial distribution of the cloud is crucial to the success of many ultracold atom applications. In this work, we present modified deep learning image classification models for image regression. To overcome challenges in data collection, we train the model on simulated absorption images. We compare the performance of the deep learning models to least-squares techniques and show that the deep learning models achieve accuracy similar to least-squares, while consuming significantly less computation time. We compare the performance of models which take a single atom image against models which use an atom image plus other images that contain background information, and find that both models achieved similar accuracy. The use of single image models will enable single-exposure absorption imaging, which simplifies experiment design and eases imaging hardware requirements.

We demonstrate that phase-contrast imaging (PCI) can reliably reconstruct the in situ density profile even for highly spatially and optically dense samples. In our experiment, we achieve high spatial densities of up to 7.9 × 1013 atoms/cm3 and optical depths up to 64 in a dense cold atomic cloud of 88Sr atoms. The use of a spatial light modulator instead of a fixed phase plate in the PCI setup provides enhanced flexibility and control of imaging parameters, making this imaging technique robust against imaging artifacts and adaptable to varying experimental conditions. Moreover, we quantify the conditions under which the standard single-atom polarizability model remains accurate for PCI in a density regime where collective effects should modify the atomic response of the system. We experimentally validate our statements by showing excellent agreement with time-of-flight measurements even at the highest densities. Our results establish PCI as a reliable and versatile method for characterizing spatially dense atomic clouds.