Fidelity of a Bose-Einstein condensates

We investigate fidelity for the quantum evolution of a Bose-Einstein condensate and reveal its general property with a simple model. We find the fidelity decay with time in various ways depending on the form of initial states as well as on mean-field dynamics. When the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power-law, having a close relation to the classical mean-field dynamics. With the initial state prepared as a maximally entangled state, we find the behavior of fidelity has no classical correspondence and observe a novel behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.