Hybrid sub- and superradiant states in emitter arrays with quantized motion

Ensembles of dipolar emitters which couple collectively to the radiation field display sub- and superradiance. These terms refer to a reduction or an enhancement of photon emission rates due to the interference of emission channels. Arrays of trapped neutral atoms constitute a promising platform for harnessing this phenomenon in technological applications, e.g. for excitation storage, single-photon switches and mirrors. However, vibrational motion of the atoms within their traps leads to position fluctuations that entangle the motion and the internal atomic degrees of freedom, which is expected to affect the collective photon emission. We develop here a theory for collective atom-light coupling in the presence of this quantized motion within the Lamb-Dicke limit. We show the existence of sub- and superradiant states, which are hybrids of electronic and vibrational excitations and explore their properties for analytically and numerically efficiently solvable cases.