Thermal equilibrium in the jaynes–cummings model

The master equation currently used to describe a two level atom interacting with a single mode field damped by contact with a thermal reservoir (the damped Jaynes–Cummings model) is shown not to have, as its steady state solution, the expected canonical density operator prescribed by the general principles of statistical mechanics for a system in thermal equilibrium. A modified master equation is derived here which satisfies this requirement. Except for a reservoir at zero temperature, this master equation differs from that which is currently used in that the damping terms contain contributions due to the atom–field interaction.