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New Journal of Physics

Dynamic phase fluctuations in potential-driven Bose–Einstein condensate

Decheng Ma, Vladimı́r Koval, Chenglong Jia

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Abstract We report on the dynamics of a Bose–Einstein condensate in one and two dimensions driven by the time-dependent harmonic trapping potential. Without the inter-particle interaction, the condensate exhibits the coherent behavior with the time-oscillating density distribution. When the inter-particle interaction is taken into consideration, the phase fluctuations, the multi-peak structure of the density distribution, and the coherence revival phenomenon, apart from the well-studied density oscillation behavior, can be observed in the condensate. Furthermore, it is demonstrated that due to the dimensional restriction these effects are more stable in the two and three-dimensional system, if compared to the one-dimensional case.

DOI
10.1088/1367-2630/ab67eb

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Abstract We report on the dynamics of a Bose–Einstein condensate in one and two dimensions driven by the time-dependent harmonic trapping potential. Without the inter-particle interaction, the condensate exhibits the coherent behavior with the time-oscillating density distribution. When the inter-particle interaction is taken into consideration, the phase fluctuations, the multi-peak structure of the density distribution, and the coherence revival phenomenon, apart from the well-studied density oscillation behavior, can be observed in the condensate. Furthermore, it is demonstrated that due to the dimensional restriction these effects are more stable in the two and three-dimensional system, if compared to the one-dimensional case.
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We investigate the phase fluctuations of a Bose-Einstein condensate in one- (1D) and three-dimensional (3D) elongated harmonic traps with the help of the numerical simulation using classical field approximation. By calculating the eigenvalues of the one-dimensional single-particle density matrix we show that the phase fluctuations of a Bose-Einstein Condensate in a 1D system are due to the thermal low-energy excitations. We find that the phase fluctuations depend on the temperature as has been predicted [Phys. Rev. Lett. 85, 3745 (2000), Phys. Rev. Lett. 87, 050404 (2001)]. Finally we show that the phase coherence length of a condensate in a harmonic trap depends on the aspect ratio of anisotropy (geometry) of the trap. We determine the border between the 3D and quasi-one-dimensional systems by calculating the phase coherence length of the condensate.
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Significance Understanding the combined effects of disorder and interactions in quantum many-body systems is a key topic of condensed matter physics. While most studies have considered a static disorder, here we investigate the relaxation dynamics of a three-dimensional Bose–Einstein condensate after switching on or off an optical disorder potential. We study, experimentally and numerically, the transient and steady-state atomic density distribution and the ability of the gas to hydrodynamically expand, directly reflecting long-range phase coherence. We find that, when the gas is exposed to disorder, long-range phase coherence breaks down one order of magnitude faster than the density distribution responds. In the opposite case, surprisingly, long-range coherence takes two orders of magnitude longer times to revive than the density relaxation.