Time-averaged properties of the Jaynes-Cummings model: Effects of detuning.

Abstract

We consider the atomic inversion in the Jaynes-Cummings model when the field mode is detuned from the atomic transition frequency. We find that, unlike in the resonant case, the time average of the inversion depends on the initial state of the atom. This time average is compared to that obtained from a semiclassical model in which the quantized field mode is replaced by a classical driving field. The averages are found to be identical. This similarity disappears when one examines the deviation of the inversion from its mean. The inversion is found to remain much closer to its mean, on average, with a quantum field rather than with a classical one. We also compare the trajectories described by inversions at different detunings. This is done by defining a distance between different trajectories. The distance between the trajectory at zero detuning and that at a detuning of \ensuremath{\Delta} is found to take sudden, discontinuous dips at certain values of \ensuremath{\Delta}.