Steady quantum coherence in non-equilibrium environment

TL;DR

This paper demonstrates that non-equilibrium environments can sustain steady quantum coherence in three-level systems, challenging the common secular approximation assumption that coherence only occurs transiently.

Contribution

It derives a master equation for non-equilibrium three-level systems and shows that transition interference effects lead to persistent steady quantum coherence, which was previously overlooked.

Findings

Steady quantum coherence increases with temperature difference between heat baths.

Interference effects in non-equilibrium environments sustain non-zero off-diagonal density matrix elements.

Secular approximation neglects these steady-state coherences in non-equilibrium systems.

Abstract

We study the steady state of a three-level system in contact with a non-equilibrium environment, which is composed of two independent heat baths at different temperatures. We derive a master equation to describe the non-equilibrium process of the system. For the three level systems with two dipole transitions, i.e., the $\Lambda$-type and V-type, we find that the interferences of two transitions in a non-equilibrium environment can give rise to non-vanishing steady quantum coherence, namely, there exist non-zero off-diagonal terms in the steady state density matrix (in the energy representation). Moreover, the non-vanishing off-diagonal terms increase with the temperature difference of the two heat baths. Such interferences of the transitions were usually omitted by secular approximation, for it was usually believed that they only take effect in short time behavior and do not affect the steady state. Here we show that, in non-equilibrium systems, such omission would lead to the neglect of the steady quantum coherence.