Abstract
We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/sqrt[8], neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.
Highlights
One cannot translate the classical definition of a Markov process directly to the quantum regime [7], several definitions and corresponding measures of nonMarkovianity for open quantum systems have been introduced [8–13]
In this Letter, we show that a driven two-level quantum system coupled to a non-Markovian environment can reach a unique set of steady states that are out of reach for the system coupled to a Markovian environment
We note that our measure does not attempt to quantify the degree of non-Markovianity in these systems but rather gives a quantitative measure on how one can distinguish these states from the states in the Markovian regime
Summary
One cannot translate the classical definition of a Markov process directly to the quantum regime [7], several definitions and corresponding measures of nonMarkovianity for open quantum systems have been introduced [8–13] These measures are all constructed to detect deviations from Markovianity by characterizing the system’s transient dynamics. In this Letter, we show that a driven two-level quantum system coupled to a non-Markovian environment can reach a unique set of steady states that are out of reach for the system coupled to a Markovian environment. Once the waveguide has been traced out, the distance to the mirror gives the environment seen by the TLS a distinct memory time This memory time enters the equations for the system dynamics as a time delay, which can be set to zero for comparison between a Markovian and a non-Markovian environment.
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