Non-Markovianity, Loschmidt echo, and criticality: a unified picture

Haikka, P.; Goold, John; McEndoo, Suzanne; Plastina, F.; Maniscalco, S.

Non-Markovianity, Loschmidt echo, and criticality: a unified picture

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Published Version

Date

2012

Authors

Haikka, P.

Goold, John

McEndoo, Suzanne

Plastina, F.

Maniscalco, S.

Publisher

American Physical Society

Published Version

10.1103/PhysRevA.85.060101

Abstract

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore, non-Markovianity is an indicator of criticality in the model considered here.

Keywords

Non-Markovianity , Loschmidt echo , Two-level system , Qubit , Quantum Ising ring

Citation

Haikka, P., Goold, J., McEndoo, S., Plastina, F. and Maniscalco, S. (2012) 'Non-Markovianity, Loschmidt echo, and criticality: A unified picture', Physical Review A, 85(6), 060101 (4pp). doi: 10.1103/PhysRevA.85.060101