Dissipations in coupled quantum systems

Abstract

We investigate the dynamics of a composite quantum system, comprised of coupled subsystems, of which only one is significantly interacting with the environment. The validity of the conventional ad hoc approach--assuming that relaxation terms can be extracted directly from the master equation of the subsystem interacting with the reservoir--was examined. We derived the equation of motion for the composite system's reduced density matrix--applying only the factorization approximation, but not the conventional sequence of Markoff, coarse grain, and secular approximations. From our analysis, we concluded that the conventional ad hoc approach is applicable to zero-temperature reservoir, but fails for finite temperatures. It is further shown that at finite temperatures, the standard procedure does not even yield a master equation for the composite system, and its dynamics has to be studied by the equations of motion which are developed here. For demonstration we considered a system of a three-level atom, the two excited states are coupled to each other, and only one of them communicates with the ground state via a radiation reservoir.