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arXiv:cond-mat/9611101

Tests of Bose-broken Symmetry in Atomic Bose-Einstein Condensates

Wong, T., Matthew J. Collett, S. M. Tan, Daniel F. Walls, Ewan M. Wright

Published Nov 13, 1996• 0 citations
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Abstract

We present an elementary model of the collapses and revivals in the visibility of the interference between two atomic Bose-Einstein condensates. We obtain different predictions of the revival times whether we conserve or break atom number conservation from the outset. The validity of Bose-broken symmetry can be tested by observations of these collapses and revivals.

DOI
10.48550/arxiv.cond-mat/9611101

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We present an elementary model of the collapses and revivals in the visibility of the interference between two atomic Bose-Einstein condensates. We obtain different predictions of the revival times whether we conserve or break atom number conservation from the outset. The validity of Bose-broken symmetry can be tested by observations of these collapses and revivals.
We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of atomic detection. In the former case we show that the macroscopic wave function collapses and revives in time, and we calculate the characteristic times for current experiments. Collapses and revivals are also predicted in the interference between two Bose-Einstein condensates which are initially in Fock states, a relative phase between the condensates being established via atomic detections corresponding to uncertainty in the number difference between them.
Quantum collapses and revivals are fascinating manifestations of interference. Of particular interest in recent years are macroscopic quantum interference effects in Bose-Einstein condensates. In this letter such effects will be studied for the two site Bose-Hubbard model that is a standard model for exploration of Bose-Einstein condensates. An analytic expression that is valid in the weak coupling limit for the difference in the occupation of the two sites is developed and tested numerically. It describes correctly the collapses and revivals. Moreover, it is demonstrated that a calculation to the first order in the interparticle interaction is required for the prediction of the collapse and revival times while the second order is required for the evaluation of the shape of the revival peaks. We believe that the result is relevant for a variety of situations where collapses and revivals are found.
We show that, when two Bose-Einstein condensates are combined, a spatial interference pattern ensues even if the condensates are in number states with no spontaneously broken gauge symmetry. In our measurement-theoretical approach the interference pattern arises from correlations between the detected positions of the atoms. We also simulate numerically experiments intended to distinguish number-state condensates and spontaneous symmetry breaking, the latter being modelled by coherent-state condensates. To detect the difference in the pair correlation functions, the experiment has to be repeated about a thousand times even for condensates with as few as five atoms each.
We present a scheme for determining if the quantum state of a small trapped atomic Bose-Einstein condensate is a state with a well-defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference measured by a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strengths of the mean-field interactions for the two components and the initial quantum state of the condensate.