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Bulletin of the American Physical Society

Decay of the Loschmidt echo in an open, out of equilibrium quantum system

Silvia Viola Kusminskiy, Mark Thomas, Torsten Karzig, Felix von Oppen

Published Mar 4, 2014• 0 citations
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The decay of the Loschmidt echo and its relation to the frequency response of the underlying classical dynamics are investigated in an open Duffing system by means of the Wigner function. The initial Wigner function of the system is Gaussian and centered at a phase point ( x 0 , p 0 ). For different ( x 0 , p 0 ), significant peaks are observed in the frequency response curves of the Loschmidt echo decay during the evolution of the Wigner function. Furthermore, there is good correspondence between the frequency response curves of the Loschmidt echo decay and the underlying classical dynamics. This can be attributed to the increase of the fringes of the Wigner function by the external driving force, which can be revealed by the frequency response of the underlying classical dynamics.

Europhysics Letters (EPL)•Nov 1, 2015•0 citations
A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system size and the distance from a critical point with equilibrium critical exponents. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We confirm the validity and the generality of the predicted dynamical scaling laws with a diverse range of critical models such as Ising spin models with a short and long range interaction, a finite-component system phase transition, and a topological phase transition. Moreover, using the integrability of systems in the thermodynamic limit, we derive such scaling laws analytically from a microscopic analysis. Our finding promotes the Loschmidt echo to a quantitative non-equilibrium probe of criticality and allows for quantitative predictions on the role of criticality on various physical scenarios where the Loschmidt echo is central to describing non-equilibrium dynamics.
Abstract We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.
The decay of the Loschmidt echo and its relation to the frequency response of the underlying classical dynamics are investigated in an open Duffing system by means of the Wigner function. The initial Wigner function of the system is Gaussian and centered at a phase point ( x 0 , p 0 ). For different ( x 0 , p 0 ), significant peaks are observed in the frequency response curves of the Loschmidt echo decay during the evolution of the Wigner function. Furthermore, there is good correspondence between the frequency response curves of the Loschmidt echo decay and the underlying classical dynamics. This can be attributed to the increase of the fringes of the Wigner function by the external driving force, which can be revealed by the frequency response of the underlying classical dynamics.