Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids

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 px + ipy 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.

Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model

“…Extending this idea to the nonequilibrium realm, a DQPT at a critical time t * (instead of a critical control parameter) is said to occur when during the dynamics, such zeros are crossed [15]. A vast amount of recent theoretical research has been devoted to study this beautiful insight in systems of different nature, namely spin [15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], fermionic [33][34][35][36][37], bosonic [38][39][40][41][42][43], and hybrid models [44]. This effort also includes the analysis of the impact of ingredients such as disorder [45,46] and topological order [47,48].…”

Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing

“…We have theoretically demonstrated that the QFI can be used to robustly diagnose dynamical phase transitions. While our numerical study focused on the LMG model that can be realized in a range of experimental platform, our results should be widely applicable to models featuring a DPT [12,26,72,73]. Moreover, we developed a simple interferometric protocol combining dynamical echoes and measurement of simple observables that demonstrates DPTs can be a powerful resource for sub-SQL sensing in non-equilibrium many-body systems [74][75][76][77].…”

Dynamical quantum phase transitions in a mesoscopic superconducting system

“…So far, the studies of critical properties [22,23], dynamical order parameters [24,25], and spontaneously broken symmetries [26,27] have been mostly addressed in bulk systems, often in either spin chains [28][29][30][31][32][33][34] or topological insulators and superconductors [35][36][37][38][39][40][41][42][43][44]. Some studies have also addressed the superconducting transition [45,46]. On the other hand, empirical evidence for DQPTs has been reported only in a few cases, mainly using trapped ion systems [47], although alternative suggestions for measuring DQPTs exist [22,26,[48][49][50][51].…”