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

TL;DR

This work establishes a direct link between Liouvillian gap closing (LGC) in an effective Markovian description and the formation of bound states in the continuum (BICs) in the full system-environment Hamiltonian for a giant-atom waveguide QED setup. By engineering three braided giant atoms coupled to a coupled-resonator waveguide, the authors show that LGC occurs precisely when BICs exist, and that tuning the giant-atom geometry can morph the dynamics among three, two, one, or zero BICs. The resulting dynamics range from coherent Rabi-like oscillations to fractional or complete exponential decay, with a degenerate two-BIC sector yielding a nonoscillatory steady state. This work bridges Markovian and non-Markovian descriptions, offering flexible control over open-system dynamics and potential routes to protected quantum resources in experimental platforms such as superconducting circuits.

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.

Figures (4)

• Figure 1: Schematic of three braided giant atoms coupled to a CRW. The $i$th giant atom couples to the waveguide at two sites, labeled $n_i$ and $m_i$. Throughout this work, we consider equal-size giant atoms and impose a braided geometry for any pair of atoms, which is ensured by the condition $n_1<n_2<n_3<m_1$.
• Figure 2: Liouvillian gap $\lambda$ as a function of the atomic frequency $\Omega$. The parameters are $\Omega_{1}=\Omega_{2}=\Omega_{3}=\Omega$, $\omega_{c}=0$, and $g_{1}=g_{2}=g_{3}=0.1\xi$. The table specifies the atomic configuration in each panel.
• Figure 3: Imaginary parts of the three eigenvalues of the matrix $M(t)$. (a) Three BICs. (b) Two BICs. (c) One BIC. (d) No BIC. Parameters are $\Omega_{1}=\Omega_{2}=\Omega_{3}=\omega_{c}=0$ and $g_{1}=g_{2}=g_{3}=0.1\xi$. The atomic configuration for each panel is given in the table in Fig. \ref{['gap']}.
• Figure 4: Population dynamics of the three giant atoms. (a) Three BICs. (b) Two BICs. (c) One BIC. (d) No BIC. Parameters are $\Omega_{1}=\Omega_{2}=\Omega_{3}=\omega_{c}=0$ and $g_{1}=g_{2}=g_{3}=0.1\xi$. The atomic configuration for each panel is given in the table in Fig. \ref{['gap']}.