Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids

TL;DR

This paper analytically investigates the Loschmidt echo in nonequilibrium fermionic superfluids, revealing limitations of dynamical quantum phase transitions as indicators of long-term dynamics but highlighting their role in topology changes and soliton formation.

Contribution

It introduces a generalized grand canonical Loschmidt echo and demonstrates that DQPTs are not reliable for long-term dynamics but can indicate topological changes and solitons.

Findings

Non-analyticities in the Loschmidt echo are phase-dependent.

A generalized grand canonical Loschmidt echo is proposed.

DQPTs do not reliably indicate long-term dynamics.

Abstract

Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical quantum phase transitions [DQPTs], are a recently introduced attempt to classify the myriad of possible phenomena which can occur in far from equilibrium closed quantum systems. In this work, we analytically investigate the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$ fermionic superfluids. We find that the presence of non-analyticities in the echo is not invariant under global rotations of the superfluid phase. We remedy this deficiency by introducing a more general notion of a grand canonical Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator for the long time dynamics of an interacting system. In particular, there are no DQPTs to tell apart distinct dynamical phases of quenched BCS superconductors. Nevertheless, they can signal a quench induced change in the topology and also keep track of solitons emerging from unstable stationary states of a BCS superconductor.