Fermi-Decay Law of Bose–Einstein Condensate Trapped in an Anharmonic Potential

The Fermi-decay law of Bose–Einstein condensate, which is trapped by a cigar-shaped anharmonic trap and subjected to a weak random perturbation, is investigated by numerically calculating quantum fidelity (Loschmidt echo), to reveal the coherence loss of the condensate. We find that there are three indispensable factors, anharmonic trap, weak random perturbation and nonlinear interaction, in charging of the Fermi-decay law. The anharmonic trap creates anharmonic oscillations, and the weak random perturbation causes coherence loss by disturbing their coherent oscillations, while the nonlinear interaction enhances the loss to the Fermi-decay law. Based on the Fermi-decay law, some suggestions are presented to prolong the coherent time during coherently manipulating condensates.