QUANTUM-OPTICAL MASTER-EQUATIONS - AN INTERACTION PICTURE

Quantum-optical master equations - exemplified by the Jaynes-Cummings model with damping-are turned into numerical partial differential equa tions of first order for phase-space functions, which are generalizati ons of the Wigner function and its relatives. The time dependence of t hese phase-space functions originates solely in the atom-photon intera ction; all other time dependences, in particular the dissipative contr ibution of the photon damping, are accounted for by the time-dependent operator bases to which the phase-space functions refer. The judiciou s choice of operator basis also effects the absence of second-order de rivatives in the partial differential equation. Our first-order equati ons are hyperbolic and can be integrated conveniently along their char acteristics. As an illustrative application we study how the Jaynes-Cu mmings revivals are affected by photon damping. We show how to handle squeezed reservoirs and how to apply the method to laser cooling.