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arXiv:cond-mat/0406503

Revisiting the Hanbury Brown-Twiss Setup for Phase Fluctuating Bose Gases

Tarun Kanti Ghosh

Published Jun 22, 2004• 0 citations
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Abstract

The Hanbury Brown-Twiss experiment has proved to be an effective means of measuring two-point correlation function of identical particles. We analyze experimental observation of stripes formation of a phase fluctuating Bose-Einstein condensates in a highly elongated 3D traps [Dettmer {\em et al.}, Phys. Rev. Lett. {\bf 87}, 160406 (2001)] by means of axial two-point correlation functions. We also predict that the stripes are present in quasi-1D Bose gas in the mean-field as well as in the hard-core bosons regimes. These stripes can be realized by measuring the axial two-point correlation functions by using the Bragg interferometric method which is similar to the original Hanbury Brown and Twiss experimental setup.

DOI
10.48550/arxiv.cond-mat/0406503

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The Hanbury Brown-Twiss experiment has proved to be an effective means of measuring two-point correlation function of identical particles. We analyze experimental observation of stripes formation of a phase fluctuating Bose-Einstein condensates in a highly elongated 3D traps [Dettmer {\em et al.}, Phys. Rev. Lett. {\bf 87}, 160406 (2001)] by means of axial two-point correlation functions. We also predict that the stripes are present in quasi-1D Bose gas in the mean-field as well as in the hard-core bosons regimes. These stripes can be realized by measuring the axial two-point correlation functions by using the Bragg interferometric method which is similar to the original Hanbury Brown and Twiss experimental setup.
The coherence properties of phase fluctuating Bose-Einstein condensates are studied both theoretically and experimentally. We derive a general expression for the N-particle correlation function of a condensed Bose gas in a highly elongated trapping potential. The second-order correlation function is analyzed in detail, and an interferometric method to directly measure it is discussed and experimentally implemented. Using a Bragg diffraction interferometer, we measure intensity correlations in the interference pattern generated by two spatially displaced copies of a parent condensate. Our experiment demonstrates how to characterize the second-order correlation function of a highly elongated condensate and to measure its phase coherence length.
We measure the intensity correlation function of two interfering spatially displaced copies of phase fluctuating Bose-Einstein condensates. It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated condensates. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.
A fundamental property of a three-dimensional Bose-Einstein condensate is long-range coherence; however, in systems of lower dimensionality, not only is the long-range coherence destroyed but additional states of matter are predicted to exist. One such state is a "transverse condensate," first predicted by van Druten and Ketterle [Phys. Rev. Lett. 79, 549 (1997)], in which the gas condenses in the transverse dimensions of a highly anisotropic trap while remaining thermal in the longitudinal dimension. Here, we detect the transition from a three-dimensional thermal gas to a gas undergoing transverse condensation by probing Hanbury Brown-Twiss correlations.
Summary form only given. We have systematically studied BECs of /sup 87/Rb atoms in the regime of phase-fluctuating condensates. We observe the phase fluctuations by measuring the density distribution of the released cloud after ballistic expansion. By varying the temperature, the number of atoms in the condensate and the aspect ratio of the trapping potential, we studied the continuous transition from the usual 3D regime, where phase fluctuations are low, into the regime of strong phase fluctuations in the condensate. To determine the amount of phase fluctuations experimentally, we measured the formation and structure of stripes in the atomic density distribution after ballistic expansion as a function of the above mentioned parameters. The appearance of stripes after switching off the trapping fields can be understood as conversion of phase fluctuations respect. phase gradients into axial velocity fields and consecutive density distributions. These results are in good agreement with theoretical and numerical studies and set clear limitations on applications of BECs e.g. in interferometric measurements.