Regularity and chaos in cavity QED
Abstract
The interaction of a quantized electromagnetic field in a cavity with a set of twolevel atoms inside it can be described with algebraic Hamiltonians of increasing complexity, from the Rabi to the Dicke models. Their algebraic character allows, through the use of coherent states, a semiclassical description in phase space, where the nonintegrable Dicke model has regions associated with regular and chaotic motion. The appearance of classical chaos can be quantified calculating the largest Lyapunov exponent over the whole available phase space for a given energy. In the quantum regime, employing efficient diagonalization techniques, we are able to perform a detailed quantitative study of the regular and chaotic regions, where the quantum participation ratio (P _{ R }) of coherent states on the eigenenergy basis plays a role equivalent to the Lyapunov exponent. It is noted that, in the thermodynamic limit, dividing the participation ratio by the number of atoms leads to a positive value in chaotic regions, while it tends to zero in the regular ones.
 Publication:

Physica Scripta
 Pub Date:
 May 2017
 DOI:
 10.1088/14024896/aa6640
 arXiv:
 arXiv:1612.01509
 Bibcode:
 2017PhyS...92e4003B
 Keywords:

 Quantum Physics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 22 pages, 12 figures