Abstract
We show that in the few-excitation regime, the classical and quantum time evolution of the inhomogeneous Dicke model for two-level systems coupled to a single boson mode agree for . In the presence of a single excitation only, the leading term in an 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 sufficiently large. By solving the Schrödinger equation exactly for two excitations and a particular inhomogeneity, we obtain 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 , where is an effective coupling strength between the two-level systems and the boson.
- Received 20 February 2010
DOI:https://doi.org/10.1103/PhysRevB.82.024305
©2010 American Physical Society