Bath induced coherence and the secular approximation

TL;DR

This paper investigates the conditions under which Markovian master equations accurately describe the dynamics of coupled quantum systems interacting with a bath, highlighting the importance of the secular approximation.

Contribution

It demonstrates that a non-secular master equation provides a smooth crossover between different coupling regimes, justifying the use of time-local theories in complex quantum systems.

Findings

Non-secular master equations capture the crossover between coupling regimes.

Markov approximation fails at singular points in the dynamics.

Time-local theories are justified across the crossover.

Abstract

Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: does system-bath or inter-system coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution to different Markovian master equations, we find that a smooth crossover of the equations-of-motion between dominant inter-system and system-bath coupling exists -- but requires a non-secular master equation. We predict a singular behaviour of the dynamics, and show that the ultimate failure of non-secular equations of motion is essentially a failure of the Markov approximation. Our findings justify the use of time-local theories throughout the crossover between system-bath dominated and inter-system-coupling dominated dynamics.