Loschmidt echo near a dynamical phase transition in a Bose-Einstein condensate

We show that the quantum Loschmidt echo can be employed to characterize the dynamical phase transition, from a tunnelling phase to a self-trapping phase, of a Bose-Einstein condensate in a double-well potential. The echo is found to have a relatively fast decay in the transition region, with a Gaussian decay in the self-trapping phase and a stretched exponential decay in the tunnelling phase