Collective dissipation of oscillator dipoles strongly coupled to one-dimensional electromagnetic reservoirs

We study the collective dissipative dynamics of dipoles modeled as harmonic oscillators coupled to one-dimensional electromagnetic reservoirs. The bosonic nature of the dipole oscillators as well as the reservoir modes allows an exact numerical simulation of the dynamics for arbitrary coupling strengths. At weak coupling, apart from essentially recovering the dynamics expected from a Markovian Lindblad master equation, we also obtain non-Markovian effects for spatially separated two-level emitters. In the so-called ultrastrong coupling regime, we find the dynamics and steady state depends on the choice of the reservoir which is chosen as either an ideal cavity with equispaced, unbounded dispersion or a cavity array with a bounded dispersion. Moreover, at even higher coupling strengths, we find a decoupling between the light and matter degrees of freedom attributable to the increased importance of the diamagnetic term in the Hamiltonian. In this regime we find that the dependence of the dynamics on the separation between the dipoles is not important and the dynamics is dominated by the occupation of the polariton mode of lowest energy.