# Relaxation of Radiation-Driven Two-Level Systems Interacting with a Bose-Einstein Condensate Bath

## TL;DR

This paper presents a microscopic theory for the relaxation dynamics of a two-level system coupled to a Bose gas bath, revealing how the bath's phase transition to a Bose-Einstein condensate affects relaxation rates and providing signatures for detecting BEC transitions.

## Contribution

The authors develop a detailed microscopic framework using Keldysh formalism to analyze TLS relaxation in a Bose gas bath, including the effects of the BEC phase transition.

## Key findings

- Relaxation rates depend on the bath's phase (normal or BEC) and the TLS-light coupling strength.
- Phase transition to BEC causes non-monotonic changes in relaxation rates, serving as a detection signature.
- Relaxation rate is mostly independent of pump frequency at low temperatures in the normal phase.

## Abstract

We develop a microscopic theory for the relaxation dynamics of an optically pumped two-level system (TLS) coupled to a bath of weakly interacting Bose gas. Using Keldysh formalism and diagrammatic perturbation theory, expressions for the relaxation times of the TLS Rabi oscillations are derived when the boson bath is in the normal state and the Bose-Einstein condensate (BEC) state. We apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two-dimensional dipolar exciton gas. When the bath is in the BEC regime, relaxation of the Rabi oscillations is due to both condensate and non-condensate fractions of the bath bosons for weak TLS-light coupling and dominantly due to the non-condensate fraction for strong TLS-light coupling. Our theory also shows that a phase transition of the bath from the normal to the BEC state strongly influences the relaxation rate of the TLS Rabi oscillations. The TLS relaxation rate is approximately independent of the pump field frequency and monotonically dependent on the field strength when the bath is in the low-temperature regime of the normal phase. Phase transition of the dipolar exciton gas leads to a non-monotonic dependence of the TLS relaxation rate on both the pump field frequency and field strength, providing a characteristic signature for the detection of BEC phase transition of the coupled dipolar exciton gas.