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arXiv:0905.1979 · Physical Review A

Revealing buried information: Statistical processing techniques for ultracold-gas image analysis

Stephen R. Segal, Quentin Diot, Eric Cornell, Alex A. Zozulya, Dana Z. Anderson

Published May 5, 2010• 46 citations
arXivHTMLPDF

Abstract

The techniques of principal and independent component analysis are applied to images of ultracold atoms. As an illustrative example, we present the use of these model-independent methods to rapidly determine the differential phase of a Bose-Einstein condensate interferometer from large sets of images of interference patterns. These techniques have been useful in the calibration of the experiment and in the investigation of phase randomization. The details of the algorithms are provided.

DOI
10.1103/physreva.81.053601

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The techniques of principal and independent component analysis are applied to images of ultracold atoms. As an illustrative example, we present the use of these model-independent methods to rapidly determine the differential phase of a Bose-Einstein condensate interferometer from large sets of images of interference patterns. These techniques have been useful in the calibration of the experiment and in the investigation of phase randomization. The details of the algorithms are provided.
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be extracted. Up until now, extraction algorithms typically rely on a fixed model of the patterns' spatial structure, which if inaccurate can lead to systematic errors caused by, for example, wavefront aberrations of the used lasers. In this paper we employ an algorithm based on Principal Component Analysis, which is capable of characterizing the spatial phase structure and per image phase offsets of an atom interferometer from a set of images. The algorithm does so without any prior knowledge about the specific spatial pattern as long as this pattern is the same for all images in the set. On simulated images with atom projection noise we show the algorithm's reconstruction performance follows distinct scaling laws, i.e., it is inversely-proportional to the square-root of the number atoms or the number of images respectively, which allows a projection of its performance for experiments. We also successfully extract the spatial phase patterns of two experimental data sets from an atom gravimeter. This algorithm is a first step towards a better understanding and complex spatial phase patterns, e.g., caused by inhomogeneous laser fields in atom interferometry.
To extract useful information about quantum effects in cold atom experiments, one central task is to identify the intrinsic fluctuations from extrinsic system noises of various kinds. As a data processing method, principal component analysis can decompose fluctuations in experimental data into eigenmodes, and give a chance to separate noises originated from different physical sources. In this paper, we demonstrate for Bose-Einstein condensates in one-dimensional optical lattices that the principal component analysis can be applied to time-of-flight images to successfully separate and identify noises from different origins of leading contribution, and can help to reduce or even eliminate noises via corresponding data processing procedures. The attribution of noise modes to their physical origins is also confirmed by numerical analysis within a mean-field theory. As the method does not rely on any a priori knowledge of the system properties, it is potentially applicable to the study of other quantum states and quantum critical regions.
Advanced data analysis techniques have proved to be crucial for extracting information from noisy images. Here we show that principal component analysis can be successfully applied to ultracold gases to unveil their collective excitations. By analyzing the correlations in a series of images we are able to identify the collective modes which are excited, determine their population, image their eigenfunction, and measure their frequency. Our method allows us to discriminate the relevant modes from other noise components and is robust with respect to the data sampling procedure. It can be extended to other dynamical systems, including cavity polariton quantum gases and trapped ions.
Bose-Einstein condensates have been the subject of intense research in recent years due to their potential applications in quantum computing and many other areas. However, measuring the shape and size of out-of-equilibrium Bose-Einstein condensates is a challenging task that requires sophisticated image processing techniques. We propose to study perturbed BEC based on general concepts of analysis, which are widely used in the image processing community. The mathematical basis underlying the algorithms is quite general and independent of the type of image studied. The morphological changes observed in the perturbed atomic clouds as a result of excitation amplitude were observed in a consistent manner. And the spatial expansion of the atomic clouds under free fall shows some symmetry, but it was only observed under certain conditions
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.
We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.