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arXiv:2608.16527

Two-Photon Bound States in the Continuum: A No-Go Theorem and Long-Lived Quasi-Bound States

Yue Chang

quant-phSubmitted Aug 17, 2026• Announced Aug 18, 2026• 0 citations
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Abstract

Two-photon bound states in the continuum provide a stringent setting in which quantum interference must suppress radiative decay despite photon--photon interactions. Here, we prove a no-go theorem showing that a single nonlinear mode linearly coupled to a noninteracting bosonic continuum cannot support an interaction-active two-photon bound state in the continuum, provided the local spectral density vanishes only at isolated energies. Apart from this regularity condition, the result is independent of the continuum dispersion and the frequency-dependent coupling. Although such an exact bound state is forbidden, long-lived two-photon quasi-bound states remain possible. For a giant Kerr cavity nonlocally coupled to a waveguide, we derive the asymptotic scaling of the two-photon decay rate with the coupling-point separation from weak nonlinearity to the hard-core limit. We further identify a regime in which the two-photon resonance is substantially longer lived than the single-photon excitation. Our work establishes the limits of exact multiphoton confinement while opening a route to engineering long-lived interacting few-photon states.

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SIAM Journal on Mathematical Analysis•Jun 3, 2024•3 citations
Two-photon bound states in the continuum provide a stringent setting in which quantum interference must suppress radiative decay despite photon--photon interactions. Here, we prove a no-go theorem showing that a single nonlinear mode linearly coupled to a noninteracting bosonic continuum cannot support an interaction-active two-photon bound state in the continuum, provided the local spectral density vanishes only at isolated energies. Apart from this regularity condition, the result is independent of the continuum dispersion and the frequency-dependent coupling. Although such an exact bound state is forbidden, long-lived two-photon quasi-bound states remain possible. For a giant Kerr cavity nonlocally coupled to a waveguide, we derive the asymptotic scaling of the two-photon decay rate with the coupling-point separation from weak nonlinearity to the hard-core limit. We further identify a regime in which the two-photon resonance is substantially longer lived than the single-photon excitation. Our work establishes the limits of exact multiphoton confinement while opening a route to engineering long-lived interacting few-photon states.
Bound states in the continuum (BICs) can confine photonic excitations in open systems without conventional cavities or band gaps, making them natural candidates for long-lived quantum storage and single-photon control. Their use is limited, however, by two obstacles: they are dark to incident photons, and they lack spectral-gap protection from the surrounding continuum. We overcome both limitations in a giant atom coupled to a one-dimensional waveguide using two temporal control knobs. Atomic-frequency modulation breaks and restores the destructive-interference condition, enabling deterministic capture and release of mode-matched single photons. Coupling modulation instead preserves the BIC condition while tuning the atomic and photonic weights of the stored state. A key result is that this embedded state can nevertheless be controlled adiabatically despite the absence of a spectral gap, with an intrinsic leakage probability linear in the ramp rate. By separating radiative access from BIC-preserving deformation, the protocol turns a dark BIC into a single-photon memory whose fidelity is set by the intrinsic continuum-induced leakage law, providing a route to embedded-state control in open photonic platforms.
We study the bound states in the continuum (BIC) in a system of two identical two-level giant atoms coupled to a one-dimensional waveguide. By deriving general dark-state conditions, we clarify how coupling configurations and atomic parameters influence decay suppression. Through analysis of the long-time dynamical behaviors of atoms and bound photons, we carry out a detailed classification of bound states and explore the connections between these dynamical behaviors and the system's intrinsic light-matter interactions. The system supports static bound states with persistent atomic excitations, and oscillating bound states with periodic atom-photon or atom-atom excitation exchange. Under certain conditions, oscillating bound states can contain more harmonic components owing to the emergence of additional quasi-dark modes, rendering them promising platforms for high-capacity quantum information processing. These findings advance the understanding of BIC in waveguide quantum electrodynamics with multiple giant atoms and reveal their prospective applications in quantum technologies.
Quantum limit of dissipation-free photon-photon interactions at the few photon level is studied in the context of giant Kerr nonlinearities in cavity electromagneti cally induced transparency (EIT). It is shown that photon-photon interaction is largest when the cavity contains a sing le atom. In contrast to conventional nonlinearities, increasing the number of atoms cannot in crease the interaction strength but will in general degrade the performance by enhancing di spersion. In the non-perturbative regime, the single-atom photon-photon interaction can be limited by lossy states excited from long-lived EIT states. Asymptotically, in the strong coupling limit, photon-photon interaction is determined by the single photon-atom coupling strength. Photon blockade occurs for single atoms but only partial blockade can occur for low dispersion and not at all in the high-dispersion limit of the multi-atom case.
Bound states in the continuum (BICs) are spatially localized modes embedded in the spectrum of extended states, typically stabilized by symmetry or interference. While extensively studied in single-particle and linear systems, the many-body regime of BICs remains largely unexplored. Here, we demonstrate that giant atoms, quantum emitters coupled nonlocally to structured waveguides, can host robust doublon BICs, i.e., two-photon bound states stabilized by destructive interference and interactions. We first analyze a driven two-photon emission process and show how doublon BICs arise and mediate decoherence-free interaction between distant atoms. We then demonstrate that these many-body BICs also emerge under natural, undriven dynamics via a virtual two-photon emission process in three-level giant atoms. Our results reveal an interference-based mechanism for stabilizing many-body localization in open quantum systems, with potential applications in quantum simulation, non-ergodic dynamics, and protected quantum information processing.
Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
Abstract. We consider the quantum optics of a single photon interacting with a system of two-level atoms. The wave properties of this interacting system are determined by the spectral properties of a matrix Hamiltonian, involving a nonlocal partial differential operator, acting on photonic and atomic degrees of freedom. We study the spectral problem via a reduction to a spectral problem for a scalar nonlocal operator, which depends nonlinearly on the spectral parameter. We investigate two classes of solutions: Bound states are solutions that decay at infinity, while resonance states have locally finite energy and satisfy a non–self-adjoint outgoing radiation condition at infinity. We have found necessary and sufficient conditions for the existence of bound states, along with an upper bound on the number of such states. We have also considered these problems for atomic models with small, high-contrast inclusions. In this setting, we have derived asymptotic formulas for the resonances. Our results are illustrated with numerical computations.