# Dark state with counter-rotating dissipative channels

## TL;DR

This paper investigates how counter-rotating terms affect the stability of dark states in a three-level quantum system, revealing leakage at zero temperature and proposing a method to restore coherence.

## Contribution

It demonstrates the impact of counter-rotating terms on dark state stability beyond the RWA and introduces a leakage elimination technique to recover quantum coherence.

## Key findings

- Counter-rotating terms cause dark state leakage at zero temperature.
- Leakage elimination operator can restore dark state coherence.
- Dark state stability is compromised without RWA assumptions.

## Abstract

Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the $\Lambda$-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a $\Lambda$-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.