Non-Markovian steady states of a driven two-level system

TL;DR

This paper demonstrates that non-Markovian environments enable a driven two-level quantum system to reach unique steady states with exotic properties, providing a potential method to detect non-Markovianity without analyzing transient dynamics.

Contribution

It introduces a novel approach to identify non-Markovian effects via steady states in a driven two-level system, highlighting behaviors not possible in Markovian regimes.

Findings

Non-Markovian steady states exhibit population inversion.

Steady-state coherence can exceed 1/√8 in non-Markovian regimes.

Time delays influence quantum interference and decay rates.

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.