# Driven-Dissipative Quantum Dynamics in Ultra Long-lived Dipoles in an Optical Cavity. (arXiv:1812.02291v1 [quant-ph])

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.