Liouvillian gap closing--bound states in the continuum connection and diverse dynamics in a giant-atom waveguide QED setup

TL;DR

This paper reveals a fundamental link between Liouvillian gap closing and bound states in the continuum in a giant-atom waveguide QED system, showing how BICs influence diverse quantum dynamics and can be engineered for control.

Contribution

It establishes a direct connection between Liouvillian gap closing and BIC formation, and demonstrates tunable dynamical regimes in a giant-atom waveguide platform.

Findings

LGC necessarily indicates BIC presence in the Hamiltonian spectrum.

Diverse dynamics such as Rabi oscillations and fractional decay depend on the number of BICs.

Degenerate BICs lead to steady states instead of persistent oscillations.

Abstract

In open quantum systems, reduced dynamics is commonly described by a master equation, whose Liouvillian gap closing (LGC) typically signals the emergence of decoherence-free subspace. By contrast, the dynamics of the full system-environment compound is governed by the underlying Hamiltonian spectrum, where bound states in the continuum (BICs) can protect long-lived quantum resources. Despite these parallel perspectives, the relation between LGC and BIC formation has remained largely unexplored. Here we bridge this gap in a paradigmatic giant-atom waveguide platform and show that the occurrence of LGC necessarily benchmarks the presence of a BIC in the full Hamiltonian description. By engineering the giant-atom geometry, we further demonstrate rich dynamical regimes-including Rabi oscillations, fractional decay, and complete exponential relaxation-depending on the number of supported BICs, which can be tuned from three to zero. Remarkably, when two BICs become frequency-degenerate, the long-time dynamics approaches a steady state rather than exhibiting persistent oscillations. Our results establish a direct spectral-dynamical connection between effective Markovian and underlying non-Markovian descriptions, and provide a route toward flexible control of open-system dynamics.