Dynamical quantum phase transition in Bose-Einstein condensates

We study Bose-Einstein condensates at the low-energy limit and show that their collective dynamics exhibit interesting quantum dynamical behavior. The system undergoes a dynamical quantum phase transition after a sudden quench into a properly distributed static force, provided its dispersion relation is linear. We corroborate the occurrence of a dynamical phase transition by calculating the Fisher zeros of the Loschmidt amplitude and showing that they cross the real time axis in the thermodynamic limit. A connection is established between the order of nonanalycity in the return rate function and the spectral density of the force. Furthermore, it is shown that a logarithmic or power-law scaling holds at the critical times depending on the displacement spectrum. The scaling behaviors are studied for three different cases. Eventually, a scheme for the quantum simulation of such a dynamical phase transition and its verification is proposed. We show that by taking into account the environmental effects the behavior remains observable.