Coherent Tunneling of Bose-Einstein Condensates: Exact Solutions for Josephson Effects and Macroscopic Quantum Self-Trapping

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  • 23 June 1997
Abstract
We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates (BEC) at T=0 in (possibly asymmetric) double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. The evolution of the inter-well fractional population imbalance (related to the condensate phase difference) is obtained in terms of elliptic functions, generalizing well-known Josephson effects such as the `ac' effect, the `plasma oscillations', and the resonant Shapiro effect, to nonsinusoidal regimes. We also present exact solutions for a novel `macroscopic quantum self-trapping' effect arising from nonlinear atomic self-interaction in the GPE. The coherent BEC tunneling signatures are obtained in terms of the oscillation periods and the Fourier spectrum of the imbalance oscillations, as a function of the initial values of GPE parameters. Experimental procedures are suggested to make contact with theoretical predictions.

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