arXiv:1404.6738 · Physical Review E

Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo

Utso Bhattacharya, Sayak Dasgupta, Amit Dutta

Published Aug 29, 2014• 21 citations

Abstract

We study the quantum critical behavior of the Dicke Hamiltonian with finite number of atoms and explore the signature of quantum chaos using measures like the ground-state fidelity and the Loschmidt echo and the time-averaged Loschmidt echo. We show that these quantities clearly point to the classically chaotic nature of the system in the superradiant (SR) phase. While the ground-state fidelity shows aperiodic oscillations as a function of the coupling strength, the echo shows aperiodic oscillations in time and decays rapidly when the system is in the SR phase. We clearly demonstrate how the time-averaged value of the echo already incorporates the information about the ground-state fidelity and stays much less than unity, indicating the classically chaotic nature of the model in the SR phase.

DOI: 10.1103/physreve.90.022920

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Comment on “Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo”

Ignacio García-Mata, Augusto J. Roncaglia, Diego A. Wisniacki

In a recent paper [Phys. Rev. E 90, 022920 (2014)] a study of the ground-state fidelity of the Dicke model as a function of the coupling parameter is presented. Abrupt jumps of the fidelity in the superradiant phase are observed and are assumed to be related to the transition to chaos. We show that this conclusion results from a misinterpretation of the numerics. In fact, if the parity symmetry is taken into account, the unexpected jumps disappear.

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Reply to “Comment on ‘Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo’ ”

Utso Bhattacharya, Sayak Dasgupta, Amit Dutta

Although we agree with the fact reported in García-Mata et al. [Phys. Rev. E 91, 036901 (2015)] that a computational error resulted in misinterpretation of the behavior of the ground-state fidelity only, we emphasize below that this does not alter the main conclusion of our paper. That is the main claim that we had made about the use of quantum information measures to study chaos in the Dicke model still holds true.

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