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arXiv:2501.03607 · Physical Review A

Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions

Jiaqi Li, Tian-Yu Zhou, Xin Wang

Published Jul 14, 2025• 1 citation
arXivHTMLPDF

Abstract

Mobility edges (MEs) are critical boundaries in disordered quantum systems that separate localized from extended states, significantly affecting transport properties and phase transitions. Although MEs are well-understood in single-photon systems, their manifestation in many-body contexts remains an active area of research. In this work, we investigate a one-dimensional Bose-Hubbard chain with a quasiperiodic potential modulating photon-photon interactions, effectively creating a mosaic lattice. We identify MEs for doublon states (i.e, bound photon pairs resulting from strong interactions) within the two-photon subspace. Our analytical solutions and numerical simulations confirm the existence of these MEs, extending single-photon MEs theories to the two-photon regime. Additionally, we analyze the dynamics of two emitters coupled to the waveguide, enabling the emission of supercorrelated photon pairs into the waveguide. Our findings reveal that coupling to extended states results in Markovian dynamics, characterized by exponentially supercorrelated decay, while coupling to localized states gives rise to non-Markovian dynamics, marked by suppressed decay and persistent oscillations. Here, a transition from Markovian to non-Markovian behavior occurs around the MEs of the doublons. Finally, we propose a feasible experimental implementation using superconducting circuits, providing a platform to observe the interplay between interactions and disorder in quantum systems.

DOI
10.1103/4mql-32sg

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Mobility edges (MEs) are critical boundaries in disordered quantum systems that separate localized from extended states, significantly affecting transport properties and phase transitions. Although MEs are well-understood in single-photon systems, their manifestation in many-body contexts remains an active area of research. In this work, we investigate a one-dimensional Bose-Hubbard chain with a quasiperiodic potential modulating photon-photon interactions, effectively creating a mosaic lattice. We identify MEs for doublon states (i.e, bound photon pairs resulting from strong interactions) within the two-photon subspace. Our analytical solutions and numerical simulations confirm the existence of these MEs, extending single-photon MEs theories to the two-photon regime. Additionally, we analyze the dynamics of two emitters coupled to the waveguide, enabling the emission of supercorrelated photon pairs into the waveguide. Our findings reveal that coupling to extended states results in Markovian dynamics, characterized by exponentially supercorrelated decay, while coupling to localized states gives rise to non-Markovian dynamics, marked by suppressed decay and persistent oscillations. Here, a transition from Markovian to non-Markovian behavior occurs around the MEs of the doublons. Finally, we propose a feasible experimental implementation using superconducting circuits, providing a platform to observe the interplay between interactions and disorder in quantum systems.
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The manipulation of localization in quasiperiodic systems by mobility edges or localization transition holds significant physical importance. In this letter, we demonstrated that the dissipation can induce the emergence of anomalous mobility edges and extended-localized transition in emitter-cavity arrays controlled by quasiperiodic potentials. Specifically, we observe that the localization properties of emitters is governed by the nature of quantum bound states, either discrete or embedded in continuum, providing a unified mechanism linking the emitter-photon bound physics to quasiperiodic criticality. Depending on the bound state discrete or continuumlike, the induced effective excitation hopping exhibits either exponentially decaying or sinusoidally oscillating, giving rise to the formation of localized or critical states, respectively. Through a generalized duality transformation, we analytically determine the anomalous mobility edges and the critical strength of potential, enabling the construction of a full phase diagram. The study reveals that the physical characteristics of cavity exert a significant influence on excitation localization. Therefore, the manipulation of excitation localization can be achieved solely by adjusting the cavity fields.
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Waveguide quantum electrodynamics (QED) studies the interaction between quantum emitters and guided photons in one dimension. When the waveguide hosts interacting photons, it becomes a platform to explore many-body quantum optics. However, the influence of photonic correlations on emitter dynamics remains poorly understood. In this work, we study the collective decay and coherent interactions of quantum emitters coupled to a one-dimensional Bose-Hubbard waveguide, an array of coupled photonic modes with repulsive on-site interactions that supports superfluid and Mott insulating phases. We show that photon-photon interactions alone can trigger a superradiant burst, independent of emitter spacing and transition frequency. In the off-resonant regime, emitters exhibit two distinct types of mediated interactions. Delocalized superfluid excitations yield persistent, long-range couplings, challenging the noninteracting paradigm, where long-range (dissipative) couplings occur in band, whereas short-range and coherent interactions occur in a bandgap. In the Mott limit, quasiparticles generate short-range interactions mediated by doublons and holons. Our work bridges many-body physics and waveguide QED, revealing how photonic many-body states shape emitter dynamics.
Abstract We investigate the quantum dynamics of two two-level atoms coupled to a one-dimensional resonator waveguide. Using the resolvent method, we obtain exact analytical solutions for the atomic evolution and photon scattering processes within the single-excitation subspace. The photonic band structure of the waveguide dictates distinctly different dynamical regimes. For atomic frequencies at the band center and small interatomic separation, the system exhibits Markovian decay and relaxes into a steady-state subradiant Bell entangled state. In contrast, near the band edge, non-Markovian dynamics dominates, leading to the formation of atom-photon bound states that mediate persistent, coherent interactions between the atoms. Furthermore, we demonstrate that the atomic detuning and separation provide effective control over singlephoton scattering, enabling a tunable quantum interface.