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arXiv:cond-mat/0303308 · Physical Review Letters

Measurement of the Spatial Correlation Function of Phase Fluctuating Bose-Einstein Condensates

D. Hellweg, L. Cacciapuoti, M. Kottke, T. Schulte, K. Sengstock, Wolfgang A. Ertmer, J. Arlt

Published Jul 3, 2003• 138 citations
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Abstract

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.

DOI
10.1103/physrevlett.91.010406

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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.
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.
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.
We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\ensuremath{\Delta}t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\ensuremath{\Delta}t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.
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.