Loschmidt Echo

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Abstract

In this article we review the past, present, and future of the Loschmidt Echo.

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An accurate and efficient scheme for propagating the time dependent Schrödinger equation

H. Tal‐Ezer, R. Kosloff (1984)

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Decay of Loschmidt Echo Enhanced by Quantum Criticality

, , … (2005)

We study the transition of a quantum system \(S \) from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system \(E\) coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of \(E\) modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of \(E\) strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing \(S\) vanish sharply.