Dynamical quantum phase transitions in a mesoscopic superconducting system

We inspect the signatures of dynamical quantum phase transitions driven by quantum quenches acting on a correlated quantum dot embedded between superconducting and metallic reservoirs. Under stationary conditions, the proximity-induced electron pairing, competing with strong Coulomb repulsion, enforces the quantum dot to be either in the singly occupied or BCS-type ground state, depending on its energy level and coupling to the superconducting lead. By means of the time-dependent numerical renormalization group approach, we study the system???s time evolution upon traversing the phase boundary between these two states, examining the Loschmidt echo and revealing nonanalytic features in the low-energy return rate, which signal dynamical quantum phase transitions. We also show that these phase transitions are accompanied by the corresponding local extrema in the pairing correlation function and dot???s occupation. Since the proposed quench protocols can be realized in a controllable manner, the detection of this dynamical singlet-doublet phase transition should be feasible by performing tunneling spectroscopy measurements.