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Physical Review A

Quantum coherence of double-well Bose-Einstein condensates: An SU(2) coherent-state path-integral approach

Yi Zhou, Hui Zhai, Rong Lü, Zhan Wei Xu, Lee Chang

Published Apr 15, 2003• 16 citations
Publisher

Abstract

Macroscopic quantum coherence of Bose gas in a double-well potential is studied, based on an SU(2) coherent-state path-integral approach. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

DOI
10.1103/physreva.67.043606

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Macroscopic quantum coherence of Bose gas in a double-well potential is studied, based on an SU(2) coherent-state path-integral approach. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.
In this paper we investigate various macroscopic quantum tunnelling phenomena and the phase coherence property of rotating Bose–Einstein condensates. Based on the two-mode approximation, three different cases are studied. When the rotating frequency is independent of time t , by using the SU (2) coherent state path integral method, we discuss two cases: a superposition of two macroscopic states and a Josephson-type ground state. In addition, the specific conditions to reach the two cases are obtained. We also discuss the nonlinear Landau–Zener effect in the dynamic case in which the rotating frequency varies with time t .
We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground-state density profile of 23{}^{23}23Na atoms and the Bogoliubov spectrum of the elementary excitations as a function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.
An alternative method is used to investigate the tunneling between two weakly linked Bose-Einstein condensates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found macroscopic quantum self-trapping effect. Also an alternative kind of first-order crossover between different regions is predicted.
We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.
Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.