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Banach Center Publications

Wehrl entropy of the state in a two-atom Tavis-Cummings model

Debraj Nath, Pradip Das

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper we present an entropic description of quantum state obtained by interaction of one mode of quantized electromagnetic field with two two-level atoms inside a cavity, known as Tavis–Cumming model. Wehrl entropy has been calculated analyt
DOI
10.4064/bc96-0-19

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Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. Here we discuss a simple toy model: a system constituted by a two-level atom (atom 1) interacting with a single mode cavity field which is (weakly) coupled to a small environment (atom 2). We investigate the influence of the minimal environment on the dynamics of the linear entropy and the atomic dipole squeezing of atom 1, as well as the entanglement between atom 1 and the field. We also obtain the full analytical solution of the two-atom Tavis–Cummings model for both arbitrary coupling strengths and frequency detunings, necessary to analyse the influence of the field-environment detuning on the evolution of the system’s quantum properties. For complementarity, we discuss the role of the degree of mixedness of the environment by analysing the time-averaged linear entropy of atom 1.
The concept of the classical-like Wehrl entropy is shown to be a very sensitive and informative measure describing the time evolution of a quantum system. Its applications to the Jaynes-Cummings model reveal relevant aspects of the field dynamics. The Wehrl entropy provides a compact one-parameter description giving, among other things, a clear signature for the splitting of the Q function. It gives also a clear indication of the phase randomization of the coherent electromagnetic field states during the interaction with a two-level atom.
The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.