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Physical Review A

Connection between the Liouvillian gap closing and bound states in the continuum: Diverse dynamics in a giant-atom waveguide QED setup

Anonymous, Mingzhu Weng, Zhihai Wang, Jin Wang

Published Aug 6, 2026• 0 citations
Publisher
DOI
10.1103/s2lt-6tzl

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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.
Giant atoms, which couple to a waveguide through multiple spatially separated connection points beyond the dipole approximation, provide a versatile route for quantum information processing based on interference-induced bound states in the continuum (BICs). While multi-giant-atom architectures are being developed toward giant-atom quantum networks, the role of direct coupling between the giant atoms, in particular the associated coupling phase, in atomic dynamics remains insufficiently understood. Here we take a first step toward addressing this issue by studying a two-giant-atom waveguide-QED model. We show that the coupling phase can be used to control both the number of BICs and their profiles for both of photon and atoms. More interestingly, the presence of BICs gives rise to a variety of dynamical behaviors, providing an effective mechanism for tailoring quantum-state evolution in giant-atom waveguide-QED systems. Our results highlight coupling-phase engineering as a useful tool for controlling interference, bound states, and quantum dynamics in nonlocal light--matter interfaces.