Thermal relaxation of a QED cavity

Abstract. We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed ac-cording to the canonical ensemble at temperature T> 0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renor-malized temperature T ∗. Our result is non-perturbative in the strength of the atom-field cou-pling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.