Oscillating bound states in non-Markovian photonic lattices

It is known that the superposition of two bound states in continuum (BICs) leads to phenomenon an oscillating state, where excitations mediated by modes oscillate persistently. We perform exact calculations for BICs a one-dimensional photonic lattice coupled ``giant atom'' at multiple points. Our work significantly distinct from previous proposals continuous waveguide systems due presence finite energy band contributing band-edge effects. In particular, we show outside are detrimental BIC phenomenon, and can be suppressed increasing either number coupling points or separation between each point. Crucially, non-Markovianity necessary existence BICs, oscillation amplitude increases with characteristic delay time giant atom interactions. also propose initialization scheme subspace. experimentally implemented on current array platforms opens up prospects utilizing reservoir engineering storage quantum information lattices.