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arXiv:cond-mat/0202234 · Physical Review A

Bistability and macroscopic quantum coherence in a Bose-Einstein condensate of 7Li

A. Montina, F. T. Arecchi

Published Jul 18, 2002• 15 citations
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Abstract

We consider a Bose-Einstein condensate of ${}^{7}\mathrm{Li}$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double-well potential, obtained by adding a standing-wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation leads, in fact, to a macroscopic quantum superposition or Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called macroscopic quantum coherence (MQC); we study the effects of losses on MQC.

DOI
10.1103/physreva.66.013605

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We consider Bose-Einstein condensates (BECs) in situations where the density undergoes a symmetry breaking, either in real space or in momentum space. This occurs for a suitable number of condensed atoms in a double well potential, obtained in real space for a BEC of lithium atoms by adding a standing wave light field to the trap potential, or in momentum space for rubidium atoms by Raman coupling two BECs in different magnetic states with two tilted light fields. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schrödinger cat (SC) and we evaluate the macroscopic quantum coherence between the two SC states.
We consider a Bose-Einstein bicondensate of 87Rb,{}^{87}\mathrm{Rb},87Rb, trapped in two different internal levels, in a situation where the density undergoes a symmetry breaking in momentum space. This occurs for a suitable number of condensed atoms within a double-well dispersion curve, obtained by Raman coupling two internal states with two tilted and detuned light fields. Evidence of bistability results from the Gross-Pitaevskii equation. By second quantization, we evaluate the tunneling rate between the two asymmetric states; the effects of losses on coherence are negligible.
We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.
We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.