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arXiv:cond-mat/0204219 · Journal of Physics B Atomic Molecular and Optical Physics

Macroscopic quantum tunnelling in rotating Bose Einstein condensates

Yuan-Xiu Miao, Hui Zhai, Hong-Yu Yang, Lee Chang

Published Apr 14, 2003• 1 citation
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Abstract

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 .

DOI
10.1088/0953-4075/36/9/308

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Macroscopic quantum tunneling of Bose-Einstein Condensate in a double-well potential is discussed in the frame of an experimentally realizable Hamiltonian with ϕ 6 interaction under the two-mode approximation. Concentrating on a special case Δ E = Λ = 0, we analyze the stationary states and dynamics of the system to find that such system possesses very small phase spaces for Josephson oscillation and usually lies in the macroscopic quantum self-trapping state (MQST). Importantly we obtain three kinds of MQSTs and in terms of them show the phase diagrams of the system.
We study the quantum coherent tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slow and rapid varying in the time trap potential are considered. In the case of a slowly varying trap, we study the nonlinear resonances and chaos in the oscillations of the relative atomic population. Using the Melnikov function approach, we find the conditions for chaotic macroscopic quantum-tunneling phenomena to exist. Criteria for the onset of chaos are also given. We find the values of frequency and modulation amplitude which lead to chaos on oscillations in the relative population, for any given damping and the nonlinear atomic interaction. In the case of a rapidly varying trap, we use the multiscale expansion method in the parameter $\ensuremath{\varepsilon}=1/\ensuremath{\Omega},$ where \ensuremath{\Omega} is the frequency of modulations, and we derive the averaged system of equations for the modes. The analysis of this system shows that new macroscopic quantum self-trapping regions, in comparison with the constant trap case, exist.
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We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double-well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn=n1−n2 measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.