Macroscopic quantum fluctuations in the Josephson dynamics of two weakly linked Bose-Einstein condensates

We study analytically the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are (1) to investigate dynamical regimes at the borderline between the classical and quantum behavior of the bosonic field, and (2) to search macroscopic quantum coherence phenomena not observable with other superfluid/superconducting systems. Quantum fluctuations renormalize the classical Josephson oscillation frequencies. Large amplitude phase oscillations are modulated, exhibiting collapses and revivals. We describe an interwell oscillation mode with a vanishing (ensemble averaged) mean value of the observables, but with oscillating mean square fluctuations. We finally discuss the limit in which the classical Gross-Pitaevskii (Josephson) dynamics is recovered.