Dynamical quantum phase transition in mesoscopic superconducting system

We investigate the dynamics of correlated quantum dot sandwiched between the metallic and superconducting electrodes. In particular, we consider two quench protocols feasible experimentally. The first quench is performed in the coupling between the dot and the superconductor, while the other one abruptly shifts the energy of the orbital level. The time-dependent charge occupancy, on-dot pair correlations and transient currents reveal non-trivial interplay between the proximity induced electron pairing with correlations caused by the on-dot Coulomb repulsion.

Furthermore, we examine the singlet-doublet dynamical phase transition upon quantum quench traversing the phase boundaries in parameter space between two distinct ground states. We evaluate Loschmidt echo and find non-analytic features in the associated return rate. The cusps arise periodically at critical times and coincide with the local extrema in the pairing correlation function manifesting occurrence of dynamical phase transition.