Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory -art. no. 013605

We study the dynamics of a two-mode Bose-Einstein condensate in the vicinit y of a mean-held dynamical instability. Convergence to mean-field theory (M FT), with increasing total number of particles N, is shown to be logarithmi cally slow. Using a density-matrix formalism rather than the conventional w ave-function methods, we derive an improved set of equations of motion for the mean-field plus the fluctuations, which goes beyond MFT and provides ac curate predictions for the leading quantum corrections and the quantum brea k time. We show that the leading quantum corrections appear as decoherence of the reduced single-particle quantum state; we also compare this phenomen on to the effects of thermal noise. Using the rapid dephasing near an insta bility, we propose a method for the direct measurement of scattering length s.