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arXiv:1007.2136 · Physical Review A

Detection of small atom numbers through image processing

Caspar F. Ockeloen-Korppi, Atreju Tauschinsky, R. J. C. Spreeuw, S. Whitlock

Published Dec 16, 2010• 106 citations
arXivHTMLPDF

Abstract

We demonstrate improved detection of small trapped atomic ensembles through advanced postprocessing and optimal analysis of absorption images. A fringe-removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation in well-localized ensembles and is applied to real experimental data to measure the population differences and intrinsic atom shot noise between spatially separated ensembles each comprising between $10$ and $2000$ atoms. The combined techniques improve our signal-to-noise ratio by a factor of $3$, to a minimum resolvable population difference of $17$ atoms, close to our ultimate detection limit.

DOI
10.1103/physreva.82.061606

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We demonstrate improved detection of small trapped atomic ensembles through advanced postprocessing and optimal analysis of absorption images. A fringe-removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation in well-localized ensembles and is applied to real experimental data to measure the population differences and intrinsic atom shot noise between spatially separated ensembles each comprising between 101010 and 200020002000 atoms. The combined techniques improve our signal-to-noise ratio by a factor of 333, to a minimum resolvable population difference of 171717 atoms, close to our ultimate detection limit.
Optical absorption imaging is a basic detection technique for obtaining information from matter waves, in which the absorption signal can be obtained by comparing the recorded detection light field with the light field in the presence of absorption, thereby giving the spatial distribution of the atoms. The noise in detection arises mainly from differences between the two recorded light field distributions, which is difficult to avoid in experiments. In this work, we present an optimized fringe removal algorithm, developing a method to generate an ideal reference light field, avoiding the noise generated by the light field difference, and suppressing the noise signal to the theoretical limit. Using principal component analysis, we explore the optimal calculation area and how to remove noise information from the basis to allow optimal performance and speed. As an example, we consider scattering atomic peaks with a small number of atoms in a triangular lattice. Compared with the conventional processing method, our algorithm can reduce the measured atomic temperature variance by more than three times, giving a more reliable result.
Absorption imaging is the foundation for quantitative measurements in experiments on ultracold atoms. This technique mainly involves capturing images of both the probing light field and the atom absorption light field. In this process, the unavoidable jitter of the probing light introduces imaging noise of fringe patterns into the atomic optical density distribution OD. In conventional fringe removal algorithms, this type of noise can be normalized by constructing an optimal reference image from multiple reference images that have been actually taken, which shares similar fringe patterns to an absorption image (Fig. (a)). Although this method works well in the region without atomic signal, they often overlook the modulation of the noise signal due to atomic absorption effects, leading to persistent residual fringes on the atom clouds. This problem becomes more pronounced with atomic density increasing. Here, we propose an enhanced fringe removal algorithm that takes into account the effects of atomic absorption, and actively modulates the intensity of the noise signal in the reference image constructed by conventional fringe removal algorithms (Fig. (b)), effectively preventing the residual fringes from forming, thus significantly improving the signal-to-noise ratio of the atomic images. When applied to the absorption imaging of homogeneous Fermi gases with high density, as shown in Fig. (d), this new algorithm successfully reduces the relative standard deviation of optical depth characterizing atomic density fluctuations by approximately 37%, which is about 3 times the relative standard deviation by conventional algorithm. Three subgraphs in Fig. (e) show the optical depth distribution at corresponding data points labeled by square boxes in Fig. (d). Furthermore, we also use this technique to quantitatively determine the second sound in the unitary Fermi superfluid of 6Li atoms. Compared with conventional fringe removal methods, our new algorithm increases the correlation function’s contrast of the density wave nearly 4 times, therefore enhancing the intensity of the density response spectrum by approximately 15% with half the measured standard error, paving the way for quantitatively determining the speed and attenuation of the second sound. These results demonstrate that the enhanced fringe removal algorithm not only effectively suppresses fringe noise, but also facilitates the identification and detection of important physical phenomena in high-density atomic systems, such as some collective excitations and new quantum phases.
Absorption imaging is a widely employed technique for detecting cold atom clouds and Bose-Einstein condensates (BECs). There are situations where such images may suffer from unwanted interference fringes, resulting in uncertainties in determining crucial parameters such as the atom number, temperatures, or even dynamics in small timescales. Reducing the acoustic vibrations and recording image frames synchronized with the source of such vibrations can largely reduce these fringes; however, some residual fringes still need to be taken care of for precision measurements. In this study, we propose an efficient image post-processing technique for noise reduction that effectively mitigates such interference patterns. Our approach makes use of the well-known eigenface recognition algorithm, combined with an optimized masking strategy applied to the image of the atomic cloud using a small number of basis sets. The use of a limited basis set ensures minimal computational time, allowing this method to be readily incorporated into every experimental run. Through the application of our technique, we successfully reduce interference fringes and improve the accuracy of parameter estimation by 50% in the absorption imaging of cold atoms. The temperature uncertainties of cold 87 Rb atoms are reduced by more than 50% after the algorithm is applied. This approach holds significant promise for enhancing the reliability and precision of experimental measurements in diverse research fields where absorption imaging is employed.
High-sensitivity imaging of ultracold atoms is often challenging when interference patterns are imprinted on the imaging light. Such image noises result in low signal-to-noise ratio and limit the capability of extracting subtle physical quantities. Here we demonstrate an advanced fringe removal algorithm for absorption imaging of ultracold atoms, which efficiently suppresses unwanted fringe patterns using a small number of sample images without taking additional reference images. The protocol is based on an image decomposition and projection method with an extended image basis. We apply this scheme to raw absorption images of degenerate Fermi gases for the measurement of atomic density fluctuations and temperatures. A quantitative analysis shows that image noises can be efficiently removed with only tens of reference images, which manifests the efficiency of our protocol. Our algorithm would be of particular interest for quantum emulation experiments in which several physical parameters need to be scanned within a limited time duration.
Abstract The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Number-resolved fluorescence measurements with single-atom accuracy for 1 up to 30 atoms are presented. According to our noise analysis, we extrapolate that the single-atom accuracy extends to a limiting atom number of 390(20) atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of 7 atoms prepared on demand, we achieve a 92(2)% preparation fidelity and reach number fluctuations 18(1) dB below the shot noise level using real-time feedback on the magneto-optical trap.
The noise in absorption imaging of cold atoms significantly impacts measurement accuracy across a range of applications with ultracold atoms. It is crucial to adopt an approach that offers effective denoising capabilities without compromising the unique structure of atom clouds. Here, we introduce, to our knowledge, a novel image enhancement algorithm for cold atomic absorption imaging. The algorithm successfully suppresses background noise, enhancing image contrast significantly. Experimental results showcase that this approach can improve the image's signal-to-noise ratio by about 10 dB and enhance the uncertainty of cold atom number measurements by approximately tenfold, preserving the spatial distribution of the atom clouds. Moreover, the method exhibits exceptional performance and robustness when confronted with fringe noise and multi-component imaging scenarios, offering high stability. Importantly, this method can perform denoising based on a single image (without the need to establish a reference library), and the optimization process is entirely automated, eliminating the need for manual parameter selection. The method is both compatible and practical, making it applicable to various cold atom absorption imaging fields.