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arXiv:2609.08382

Non-Markovian dynamics of a qubit on the zigzag edge of photonic graphene

Enrico Di Benedetto

quant-phcond-mat.mes-hallSubmitted Sep 8, 2026• Announced Sep 9, 2026
arXivHTMLPDF

Abstract

We present an analytical study of the dynamics of a qubit coupled to the zigzag edge of a photonic honeycomb lattice. Leveraging a resolvent operator approach and exact lattice Green's functions, we map the spectrum of qubit-photon bound states and complex poles to uncover the long-time scaling laws of the qubit population. Unlike a qubit coupled to the bulk of graphene, the presence of a zero-energy flat band connecting the Dirac points suppresses long-time branch-cut-induced tails, instead driving damped Rabi oscillations. Potential experimental platforms are briefly discussed.

Journal reference
Il Nuovo Cimento C, Year 2026 - Issue 5-6 - September-December
DOI
10.1393/ncc/i2026-26171-7
Comments
4 pages, 1 figure

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We present an analytical study of the dynamics of a qubit coupled to the zigzag edge of a photonic honeycomb lattice. Leveraging a resolvent operator approach and exact lattice Green's functions, we map the spectrum of qubit-photon bound states and complex poles to uncover the long-time scaling laws of the qubit population. Unlike a qubit coupled to the bulk of graphene, the presence of a zero-energy flat band connecting the Dirac points suppresses long-time branch-cut-induced tails, instead driving damped Rabi oscillations. Potential experimental platforms are briefly discussed.
Abstract We investigate qubits coupled to the boundary of a two-dimensional photonic lattice that supports dispersionless edge modes—unlike conventional edge modes that sustain propagating photons. As a case study, we consider a honeycomb lattice ( photonic graphene ) of coupled resonators with a zigzag edge, where the edge modes form a flat band defined only over a restricted region of momentum space. We show that light–matter interactions are effectively captured by a dissipative cavity-QED model, wherein the emitter coherently couples to a localized mode emerging as a superposition of edge modes. This mode has support on only one sublattice and displays an unconventional power-law localization around the qubit—yet remaining normalizable in the thermodynamic limit—with a spatial range that can be tuned by introducing lattice anisotropy. We predict the occurrence of vacuum Rabi oscillations and state transfer between distant emitters. An experimental demonstration using superconducting circuits is proposed.
We investigate the band structure and topological phases of one- and two-dimensional bipartite atomic lattices mediated by long-range dissipative radiative coupling. By deriving an effective non-Hermitian Hamiltonian for the single-excitation sector, we demonstrate that the low-energy dynamics of the system are governed by a Dirac equation with a complex Fermi velocity. We analyze the associated topological invariants for both the SSH and honeycomb models, utilizing synthetic gauge fields to break time-reversal symmetry in the latter. Finally, we explicitly verify the non-Hermitian bulk-edge correspondence by deriving analytical solutions for edge states localized at domain boundaries.
We investigate the entanglement dynamics of two qubits interacting with a graphene nanodisk using the macroscopic quantum electrodynamics method. By modifying the free-space decay rate of each qubit, we study the coupling strength between the nanoparticle and the qubits. We find that as the free-space decay rate increases, the decaying Rabi oscillations featured in the qubit population dynamics change to complex non-Markovian dynamical population evolution. This is also reflected on the concurrence, which at weak or moderate light–matter coupling conditions, attains values up to 0.5, while as the coupling conditions become stronger, larger values are also transiently observed. Our findings indicate that graphene nanostructures can provide a platform for the realization of high degree of entanglement in the strong coupling regime at the nanoscale, essential for quantum technology applications.
We explore the non-local correlation dynamics in a Graphene sheet of disordered electrons in a two-dimensional honeycomb lattice, containing two sublattices, induced by the interaction range of impurity potentials of two Dirac points. The Bell function, uncertainty-induced non-locality, and concurrence are used to investigate the formation and robustness of the non-local correlation between the honeycomb lattice and the Dirac point. The generated lattice-point non-local correlations are explored when the lattice-point system is initially in the uncorrelated state. Due to the lattice-point interaction, the resulting Bell-function non-locality and entanglement concurrence satisfy the hierarchy principle. The generated uncertainty-induced non-locality correlation has a higher degree of stability and robustness than the Bell non-locality and concurrence. We analyze the robustness of the initial maximal non-local correlations under the effects of the band parameter, the intravalley scattering processes, the wave numbers, and the intrinsic decoherence. The formation and stability of lattice-point correlations are highly dependent on the honeycomb lattice and Dirac point characteristics.
Photonic graphene, possesses a honeycomb-like geometric structure, provides a superior platform for simulating photonic bandgap, Dirac physics, and topological photonics. Here, the photonic graphene with reconfigurable geometric structures is demonstrated in a 5S1/2–5P3/2–5D5/2 cascade-type 85Rb atomic ensembles. A strong hexagonal-coupling field, formed by the interference of three identical coupling beams, is responsible for optically inducing photonic graphene in atomic vapor. The incident weak probe beam experiences discrete diffraction, and the observed pattern at the output plane of vapor cell exhibits a clear hexagonal intensity distribution. The complete photonic graphene geometries from transversely stretched to longitudinally stretched are conveniently constructed by varying the spatial arrangement of three coupling beams, and the corresponding diffraction patterns are implemented theoretically and experimentally to map these distorted geometric structures. Moreover, the distribution of lattice sites intensity in photonic graphene is further dynamically adjusted by two-photon detuning and the coupling beams power. This work paves the way for further investigation of light transport and graphene dynamics.
The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.