Dynamical quantum phase transition in a system of non-interacting bosons

We study a Bose-Einstein condensate 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 the dynamical phase transition by calculating Fisher zeros of the Loschmidt amplitude and showing that they cross the real time axis in 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 dynamical phase transition and its verification is proposed. We show that the behavior remains observable even by taking into account the environmental effects.