Interaction representation method for Markov master equations in quantum optics

Abstract

Conditions sufficient for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS. The unital property of a minimal quantum dynamical semigroup implies the uniqueness of the solution of the corresponding Markov master equation in the class of quantum dynamical semigroups and, in the corresponding representation, it ensures preservation of the trace or unit operator. We recall that only in the unital case the formal generator of MME determines uniquely the corresponding QDS.