Quantum Emitters in Two-dimensional Structured Reservoirs in the Non-Perturbative Regime

We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which can not be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band we predict an exponential relaxation at a rate different from that predicted by the Fermi's Golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.