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arXiv:cond-mat/0012463 · Physical Review A

Testing broken U(1) symmetry in a two-component atomic Bose-Einstein condensate

Christopher P. Search

Published Jun 6, 2001• 4 citations
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Abstract

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.

DOI
10.1103/physreva.64.013612

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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.
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.
We study an elementary model of two tunneling Bose-Einstein condensates with an atom detector in one of the traps. Stochastic simulations of atom detection in one trap show an oscillation of atom number between traps even though the condensates are initially in equal number Fock states. The oscillation has a random amplitude depending on the phase difference between the condensates, which coincides with that given by a spontaneously broken symmetry argument. \textcopyright{} 1996 The American Physical Society.
Taking Rosen-Zener tunneling as the underlying process，a scheme to achieve nonlinear Ramsey interferometry with a two-component trapped Bose-Einstein condensate is proposed. Abundant nonlinear Ramsey interference fringes are observed in time domain by the numerical simulations and these fringes are very different from the sinusoidal pattern for linear Ramsey interference due to the dominant nonlinear interaction between atoms. Furthermore，Fourier transformation results show that the fundamental frequency of Ramsey fringes can exactly reflect the information of nonlinearity or asymmetry. This finding provides an opportunity to measure atomic properties via measuring the frequency of fringes.