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arXiv:1309.5000 · Review of Scientific Instruments

Optimally focused cold atom systems obtained using density-density correlations

Andika Putra, Daniel L. Campbell, Ryan M. Price, Subhadeep De, I. B. Spielman

Published Jan 1, 2014• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.4862046

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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.
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. (C) 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.
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.
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.
In cold atom experiments, each image of light refracted and absorbed by an atomic ensemble carries a remarkable amount of information. Numerous imaging techniques including absorption, fluorescence, and phase-contrast are commonly used. Other techniques such as off-resonance defocused imaging (ORDI, [1-4]), where an in-focus image is deconvolved from a defocused image, have been demonstrated but find only niche applications. The ORDI inversion process introduces systematic artifacts because it relies on regularization to account for missing information at some spatial frequencies. In the present work, we extend ORDI to use multiple cameras simultaneously at degrees of defocus, eliminating the need for regularization and its attendant artifacts. We demonstrate this technique by imaging Bose-Einstein condensates, and show that the statistical uncertainties in the measured column density using the multiple-camera off-resonance defocused (McORD) imaging method are competitive with absorption imaging near resonance and phase contrast imaging far from resonance. Experimentally, the McORD method may be incorporated into existing set-ups with minimal additional equipment.