Classical and quantum regimes of the inhomogeneous Dicke model and its Ehrenfest time

Oleksandr Tsyplyatyev and Daniel Loss
Phys. Rev. B 82, 024305 – Published 27 July 2010

Abstract

We show that in the few-excitation regime, the classical and quantum time evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N1. In the presence of a single excitation only, the leading term in an 1/N expansion of the classical equations of motion reproduces the result of the Schrödinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schrödinger equation exactly for two excitations and a particular inhomogeneity, we obtain 1/N corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by τE=N/g2, where g2 is an effective coupling strength between the two-level systems and the boson.

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  • Received 20 February 2010

DOI:https://doi.org/10.1103/PhysRevB.82.024305

©2010 American Physical Society

Authors & Affiliations

Oleksandr Tsyplyatyev and Daniel Loss

  • Department of Physics, University of Basel, Klingelbergstraße 82, CH-4056 Basel, Switzerland

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Issue

Vol. 82, Iss. 2 — 1 July 2010

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