Multiscale dynamics of open three-level quantum systems with two quasi-degenerate levels

TL;DR

This paper analyzes the dynamics of a three-level quantum system with two nearly degenerate levels interacting with a thermal reservoir, revealing a manifold of quasi-stationary states and two distinct time scales for relaxation.

Contribution

It introduces a detailed analysis of multiscale dynamics in a three-level quantum system with quasi-degenerate levels, highlighting the emergence of quasi-stationary states and multiple relaxation time scales.

Findings

Existence of a manifold of quasi-stationary states.

Two characteristic time scales in the system's evolution.

Long-term convergence to a unique equilibrium state.

Abstract

We consider a three-level quantum system interacting with a bosonic thermal reservoir. Two energy levels of the system are nearly degenerate but well separated from the third one. The system-reservoir interaction constant is larger than the energy difference of the degenerate levels, but it is smaller than the separation between the latter and the remaining level. We show that the quasi-degeneracy of energy levels leads to the existence of a manifold of quasi-stationary states, and the dynamics exhibits two characteristic time scales. On the first, shorter one, initial states approach the quasi-stationary manifold. Then, on the much longer second time scale, the final unique equilibrium is reached.