We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-$1/2$ system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times $T_1$ and $T_2$ (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with $T_1$). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

• Received 4 April 2011

DOI:https://doi.org/10.1103/PhysRevA.83.062336