In non-Markovian light-matter interactions, a spectrally structured bath can alter the evolution of a quantum emitter by modifying the vacuum fluctuations experienced by the emitter. This raises the question of how the localization transition and the associated multifractal critical modes induced by a quasiperiodic potential shape the emitter dynamics. We investigate this scenario in the single-excitation sector for a two-level quantum emitter coupled to an Aubry-André-Harper (AAH) photonic lattice. By externally tuning the strength of the quasiperiodic onsite modulation, the lattice is tuned from the extended to the localized regime through a critical point characterized by multifractal modes. Using modal analysis, we show that the quasiperiodic modulation reshapes the local density of states at the coupling site and thereby controls the effective spectral coupling between the emitter and the lattice. The transient dynamics depend strongly on the spatial and spectral overlap between the emitter and the lattice modes: extended modes below the critical modulation generally produce rapid depopulation, whereas critical and localized modes give rise to coherent back-action and persistent Rabi-like oscillations, with particularly pronounced behavior at the critical point. We further identify emitter-photon bound states whose formation is controlled by the quasiperiodic spectral structure of the bath and whose overlap with the initially excited state leads to partial long-time population trapping. These results establish a direct connection between quasiperiodic localization, non-Markovian dynamics, and emitter-photon bound-state formation.
In non-Markovian light-matter interactions, a spectrally structured bath can alter the evolution of a quantum emitter by modifying the vacuum fluctuations experienced by the emitter. This raises the question of how the localization transition and the associated multifractal critical modes induced by a quasiperiodic potential shape the emitter dynamics. We investigate this scenario in the single-excitation sector for a two-level quantum emitter coupled to an Aubry-André-Harper (AAH) photonic lattice. By externally tuning the strength of the quasiperiodic onsite modulation, the lattice is tuned from the extended to the localized regime through a critical point characterized by multifractal modes. Using modal analysis, we show that the quasiperiodic modulation reshapes the local density of states at the coupling site and thereby controls the effective spectral coupling between the emitter and the lattice. The transient dynamics depend strongly on the spatial and spectral overlap between the emitter and the lattice modes: extended modes below the critical modulation generally produce rapid depopulation, whereas critical and localized modes give rise to coherent back-action and persistent Rabi-like oscillations, with particularly pronounced behavior at the critical point. We further identify emitter-photon bound states whose formation is controlled by the quasiperiodic spectral structure of the bath and whose overlap with the initially excited state leads to partial long-time population trapping. These results establish a direct connection between quasiperiodic localization, non-Markovian dynamics, and emitter-photon bound-state formation.
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.
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.
Non-Hermitian extensions of the Aubry-André-Harper (AAH) model reveal a rich variety of phase transitions arising from the interplay of quasiperiodicity and nonhermiticity. Despite their theoretical significance, experimental explorations remain challenging due to intricacies in realizing controlled nonhermiticity. Here, we present the first experimental realization of the unitary almost-Mathieu operator that simulates the AAH model by employing single-photon quantum walks. We systematically observe a phase transition between localized and delocalized regimes in the Hermitian limit. Subsequently, by introducing a nonreciprocal hopping, we experimentally probe the parity-time symmetry-breaking transition that is characterized by the emergence of complex quasienergies. Moreover, we identify a novel spectral transition exclusive to discrete-time settings, beyond which the real parts of all quasienergies vanish. These results clarify the interplay between localization, symmetry breaking, and topology in non-Hermitian quasicrystals, thereby paving the way for future exploration of synthetic quantum matter.
Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of Gtyp∼L−2 with system size L. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.
Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole–dipole interactions with tunable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state that inherits the anisotropic properties of the original dissipation and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.
Waveguide quantum electrodynamics platforms have emerged as promising candidates for exploring and implementing non-Markovian quantum phenomena. In this work, we investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters. By tuning the system parameters, we show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations. These states arise from the coexistence of bound states embedded in the energy continuum and bound states outside it, leading to hybrid oscillatory modes. We analytically derive the conditions required for the emergence of these states, numerically simulate their formation through spontaneous emission, and predict their long-time behaviour. Our results demonstrate that such bound-state superpositions enable the generation of emitter-emitter interaction through free evolution, while supporting oscillatory breathing modes of the photon density between the emitters.