Quantum theory of damping: A new approach to temporal evolution of density operator without the rotating wave approximation

Abstract

The Lindblad master equation is the standard framework for describing dissipative dynamics of the open quantum system context. Its conventional derivation, however, relies on the rotating-wave approximation (RWA), which neglects the counter rotating terms in the system-reservoir interaction. Here, we derive a generalized Lindblad master equation beyond the RWA within the density operator formalism, retaining the full systemreservoir coupling. We consider two prototypical open quantum systems, a two-level atom and a single-mode quantized field, each interacting with thermal or squeezed reservoirs described by the Wigner-Weisskopf theory. The resulting master equations are applied to the evolution of representative physical observables and compared with the conventional RWA based formulation. We show that counter-rotating terms produce significant modifications to the dissipative dynamics and therefore cannot, in general, be neglected. For a thermal reservoir, increasing the mean thermal photon number, nth, enhances the decay of hσ^yi beyond the RWA but suppresses it within the RWA. Likewise, the evolution of hσ^zi exhibits opposite damping behavior with increasing Γt and squeezing parameter r. These findings demonstrate the importance of including counter rotating terms for an accurate description of open quantum systems.