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arXiv:cond-mat/0609007 · Physical Review Letters

Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas

Lorraine E. Sadler, James Higbie, Sabrina R. Leslie, Mukund Vengalattore, Dan Stamper-Kurn

Published Mar 12, 2007• 41 citations
arXivHTMLPDF

Abstract

We present coherence-enhanced imaging, an in situ technique that uses Raman superradiance to probe the spatial coherence of an ultracold gas. Applying this technique, we identify the coherent portion of an inhomogeneous degenerate (87)Rb gas and obtain a spatially resolved measurement of the first-order spatial correlation function. We find that the decay of spin gratings is enhanced in high density regions of a Bose-Einstein condensate, and ascribe the enhancement to collective atom-atom scattering. Further, we directly observe spatial inhomogeneities that arise generally in the course of extended-sample superradiance.

DOI
10.1103/physrevlett.98.110401

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We present coherence-enhanced imaging, an in situ technique that uses Raman superradiance to probe the spatial coherence of an ultracold gas. Applying this technique, we identify the coherent portion of an inhomogeneous degenerate (87)Rb gas and obtain a spatially resolved measurement of the first-order spatial correlation function. We find that the decay of spin gratings is enhanced in high density regions of a Bose-Einstein condensate, and ascribe the enhancement to collective atom-atom scattering. Further, we directly observe spatial inhomogeneities that arise generally in the course of extended-sample superradiance.
Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 87Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the non-condensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.
We report the first direct in situ observation of density fluctuations on the scale of the thermal de Broglie wavelength in an ultracold gas of bosons. Bunching of ^{87}Rb atoms in a quasi-two-dimensional system is observed by single-atom imaging using a quantum gas microscope. Compared to a classical ensemble, we observe a 30% enhancement of the second-order correlation function. We show the spatial and thermal dependence of these correlations. The reported method of detecting in situ correlations can be applied to interacting many-body systems and to the study of critical phenomena near phase transitions.
We describe theoretically the dynamics of the off-resonant superradiant Raman scattering of light in a prolate atomic Bose-Einstein condensate, from the initial stages governed by quantum fluctuations to the subsequent semiclassical regime, and within a multimode theory that fully accounts for propagation effects. Our results are in good agreement with recent experimental results that exploit Raman superradiance as an imaging technique to probe the long-range coherence of condensates, including the observed time-dependent spatial features, and account properly for the macroscopic shot-to-shot fluctuations resulting from the quantum noise that initiates the superradiance process.
We probe the spatial coherence properties of a magnetically trapped Bose gas. Two matter wave beams are extracted from two spatially separated regions of the trap and overlap outside the trapping region. The visibility of the resulting interference pattern measures the phase coherence between the regions of extraction. By varying the spatial separation between the two regions the first-order spatial correlation function of the trapped Bose gas can be measured. The location of the minima of the interference pattern is reproducible, which experimentally confirms that the trapped Bose-Einstein condensate is not fragmented into individual condensates.
A fluctuating regime associated with the Berenzinskii-Kosterlitz-Thouless (BKT) transition is studied in a two-dimensional system of near-degenerate bosons (87Rb atoms). Two imaging procedures, the in-situ imaging method and the focusing-imaging method, are implemented to image the coordinate-space and momentum-space density distributions. The scaled compressibility is extracted from the coordinate-space density distributions obtained from in-situ images. Comparing the measured compressibility to the prediction from our semiclassical mean-field model, an onset of a regime which is beyond the mean-field prediction is identified and first resolved at phase-space density nλ2 ≳ 3. Information about the coherence of the system is extracted from the momentum-space distributions obtained from the focusing images. The spatial extent of the coherence at a size of the high density region in the system only appears at a distinguishably higher phase-space density of nλ2 ≈8. Therefore, a very interesting regime that is beyond mean-field prediction, but not yet a condensate, is identified. This regime, which does not exist in three dimensions, is a product of the enhanced interactions associated with reduced dimensionality.
Our knowledge on ultracold quantum gases is strongly influenced by our ability to probe these objects. In situ imaging combined with single atom sensitivity is an especially appealing scenario as it can provide direct information on the structure and the correlations of such systems. For a precise characterization a high spatial resolution is mandatory. In particular, the perspective to study quantum gases in optical lattices makes a resolution well below one micrometer highly desirable. Here, we report on a novel microscopy technique which is based on scanning electron microscopy and allows for the detection of single atoms inside a quantum gas with a spatial resolution of better than 150 nm. Imaging a Bose-Einstein condensate in a one-dimensional optical lattice with 600 nm period we demonstrate single site addressability in a sub-um optical lattice. The technique offers exciting possibilities for the preparation, manipulation and analysis of quantum gases.