Oscillating bound states in non-Markovian photonic lattices

TL;DR

This paper investigates oscillating bound states in a 1D photonic lattice coupled to a giant atom, revealing the role of non-Markovian effects and finite band structures in their formation and stability.

Contribution

It provides exact calculations showing how bound states outside the band hinder oscillations and how non-Markovianity and system parameters influence the phenomenon.

Findings

Oscillating BICs are affected by bound states outside the energy band.

Increasing coupling points or their separation suppresses detrimental bound states.

Non-Markovianity is essential for oscillating BICs, with amplitude linked to delay time.

Abstract

It is known that the superposition of two bound states in the continuum (BIC) leads to the phenomenon of an oscillating bound state, where excitations mediated by the continuum modes oscillate persistently. We perform exact calculations for the oscillating BICs in a 1D photonic lattice coupled to a "giant atom" at multiple points. Our work is significantly distinct from previous proposals of oscillating BICs in continuous waveguide systems due to the presence of a finite energy band contributing band-edge effects. In particular, we show that the bound states outside the energy band are detrimental to the oscillating BIC phenomenon, and can be suppressed by increasing either the number of coupling points or the separation between each coupling point. Crucially, non-Markovianity is necessary for the existence of oscillating BIC, and the oscillation amplitude increases with the characteristic delay time of the giant atom interactions. We also propose a novel initialization scheme in the BIC subspace. Our work be experimentally implemented on current photonic waveguide array platforms and opens up new prospects in utilizing reservoir engineering for the storage of quantum information in photonic lattices.