Exact rate equations for semiclassical atom-field interactions

S. Swain

Masamoto Takatsuji

A phase transition in a system of interacting two-level atoms and an electric field can be explained semiclassically at least semiquantitatively. The optical Bloch equations for two-level atoms interacting through a longitudinal field are solved exactly to support the thermodynamic result.

Yochai Werman

A recent proposal by Hallam et al. suggested using the chaotic properties of the semiclassical equations of motion, obtained by the time dependent variational principle (TDVP), as a characterization of quantum chaos. In this paper, we calculate the Lyapunov spectrum of the semiclassical theory approximating the quantum dynamics of a strongly interacting Rydberg atom array, which lead to periodic motion. In addition, we calculate the effect of quantum fluctuations around this approximation, and obtain the escape rate from the periodic orbit. We compare this rate to the rate extracted from the exact solution of the quantum theory, and find an order of magnitude discrepancy. We conclude that in this case, chaos in the TDVP equations does not correpond to phsyical properties of the system. Our result complement those of Ho et al. regarding the escape rate from the semiclassical periodic orbit.

Miguel Orszag

W.‐H. Steeb, Norbert Euler, P. Mulser

The semiclassical model equations for a quantum system of N two-level atoms interacting with a single-mode field in a resonant cavity are discussed. For this system of ordinary differential equations the Painlevé test is performed and first integrals are found. It is also shown that exact solutions can be found with the help of the Painlevé test.