# Driven-Dissipative Quantum Dynamics in Ultra Long-lived Dipoles in an Optical Cavity

## TL;DR

This paper investigates the complex quantum dynamics of many-body atomic arrays in an optical cavity, revealing how interactions influence transient behaviors and oscillations, especially in systems with long-lived atomic states.

## Contribution

It demonstrates that interactions alter transient dynamics without changing steady states, highlighting new oscillatory behaviors in driven-dissipative quantum systems with long-lived dipoles.

## Key findings

- Interactions do not change steady states but affect dynamics.
- Transient oscillations become faster with increasing atom number.
- Distinct transient behaviors depend on initial states.

## Abstract

We study the quantum dynamics of many-body arrays of two-level atoms in a driven cavity subject to collective decay and interactions mediated by the cavity field. We work in the bad cavity limit accessible, for example, using long-lived electronic clock states of alkaline earth atoms, for which the bare atomic linewidth is much less than the cavity linewidth. In the absence of interactions, our system reduces to previously studied models of collective fluorescence. We show that while interactions do not qualitatively change the steady state properties, they lead to a drastic change in the dynamical properties. We find that, for some interval of driving strengths, the system shows two very distinct types of transient behaviors that depend on the initial state of the system. In particular, there is a parameter regime where the system features oscillatory dynamics with a period of oscillation that becomes much shorter than the duration of the overall transient dynamics as the atom number increases. We use both mean field and exact numerical calculations of the quantum system to investigate the dynamics.