Relaxation process of a two-level system in a coherent superposition of two environments

Abstract

Relaxation processes are studied for a two-level system which is placed under the influenced by a superposition of two environments. Two cases are treated: one is that the two-level system interacts with the environment via both linear dissipative coupling and pure dephasing coupling in the Markovian limit and the other uses an exactly solvable single-excitation spin-boson model. In both the cases, an ancillary two-level system determines which environment of the two actually interacts with the relevant two-level system. In the Markovian limit, the reduced time-evolution of the two-level system is characterized by the longitudinal relaxation time $$T_{1}$$ and the transversal relaxation time $$T_{2}$$ which satisfy the inequality $$2T_{1}\ge T_{2}$$ . If the strict inequality $$2T_{1}>T_{2}$$ is fulfilled, the coherence of the two-level system can be definitely enhanced by the environmental superposition effect. If the equality $$2T_{1}=T_{2}$$ holds, it can be improved probabilistically. On the other hand, in the exactly solvable model, although the non-Markovian effect is observed in the reduced time-evolution, the coherence can be improved only probabilistically since the model does not include a pure dephasing coupling.