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

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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.

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  1. Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Masashi Ban

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Ban, M. Relaxation process of a two-level system in a coherent superposition of two environments. Quantum Inf Process 19, 351 (2020). https://doi.org/10.1007/s11128-020-02856-6

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