Analysis of matter-wave emission dynamics and polariton formation in a quantum-emitter array coupled to a band structure

Recent progress on a spontaneous emitter for atomic matter waves [1] has enabled studies of exotic emission phenomena in bandgap materials. Here we present analytic solutions for the single excitation dynamics in a 1D sinusoidal lattice potential and a finite or infinite array of emitters. The calculated phenomenology ranges from non-Markovian decay into bound states for the case of one emitter, to the emergence of an additional band structure of polaritons for the case of infinite emitters.

¹L. Krinner, M. Stewart, A. Pazmiño, J. Kwon, D. Schneble, Nature 559, 598 (2018).