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arXiv:2610.11897

Emergent SSH physics and localization in a cavity--atom system beyond the rotating-wave approximation

H. Shen, J. Cao, R. Wang, X. Z. Zhang

quant-phSubmitted Oct 8, 2026• Announced Oct 9, 2026• 0 citations
v1 · Oct 8, 2026v2 · Nov 1, 2026
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Abstract

We investigate a cavity--atom system beyond the rotating-wave approximation and recast its dynamics as an effective tight-binding problem in the excitation-number basis. The same experimentally relevant light--matter platform exhibits two distinct regimes controlled by the photon number. In the large-photon-number regime, the hopping amplitudes become nearly uniform and the effective lattice reduces to a dimerized SSH-type chain subject to a linear energy gradient. The spectrum then organizes into one or two Wannier--Stark ladders, giving rise to controllable Bloch and Bloch--Zener oscillations and quantitatively explaining the observed revival patterns. In the small-photon-number regime, the intrinsic $\sqrt{\bar n+(\cdots)}$ dependence produces a pronounced hopping deformation, namely dimerized couplings that increase along the excitation-number lattice. This deformation reshapes the density of states, enhances collective localization, and generates an energy-resolved spatial bias of the eigenstates. The corresponding real-time dynamics displays direction-dependent anomalous diffusion together with Bloch-like revivals and beat phenomena in selected parameter windows. Our results show that the same cavity--atom platform can realize both emergent ladder spectra and hopping-induced localization in excitation-number space.

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We investigate a cavity--atom system beyond the rotating-wave approximation and recast its dynamics as an effective tight-binding problem in the excitation-number basis. The same experimentally relevant light--matter platform exhibits two distinct regimes controlled by the photon number. In the large-photon-number regime, the hopping amplitudes become nearly uniform and the effective lattice reduces to a dimerized SSH-type chain subject to a linear energy gradient. The spectrum then organizes into one or two Wannier--Stark ladders, giving rise to controllable Bloch and Bloch--Zener oscillations and quantitatively explaining the observed revival patterns. In the small-photon-number regime, the intrinsic nˉ+(⋯ )\sqrt{\bar n+(\cdots)}nˉ+(⋯)​ dependence produces a pronounced hopping deformation, namely dimerized couplings that increase along the excitation-number lattice. This deformation reshapes the density of states, enhances collective localization, and generates an energy-resolved spatial bias of the eigenstates. The corresponding real-time dynamics displays direction-dependent anomalous diffusion together with Bloch-like revivals and beat phenomena in selected parameter windows. Our results show that the same cavity--atom platform can realize both emergent ladder spectra and hopping-induced localization in excitation-number space.
We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with | g / ω | ∼ 0.07 , where g is the atom-field coupling constant and ω is the field frequency, for the quantum state with average photon number n ¯ ∼ 10 4 . We map the original Hamiltonian to an effective one, which describes a tight-binding chain subjected to a staggered linear potential. It is shown that the photon probability distribution of a Gaussian-type state exhibits amplitude-modulated Bloch oscillations (BOs), which are a superposition of two conventional BOs with a half-BO-period delay between them and are essentially another type of Bloch–Zener oscillation. The probability transition between the two BOs can be controlled and suppressed by the ratio g n ¯ / ω , as well as the in-phase resonant oscillating atomic frequency Ω ( t ), leading to multiple zero-transition points.
We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate that this technique allows for a local and time-dependent control over all system parameters, and additionally allows for single-site resolved detection of atomic populations. We demonstrate full control over site-to-site off-diagonal tunneling elements (amplitude and phase) and diagonal site energies, through the observation of continuous-time quantum walks, Bloch oscillations, and negative tunneling. These capabilities open up new prospects in the experimental study of disordered and topological systems.
We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian (J1=J2J_1 = J_2J1​=J2​) and non-Hermitian (J1≠J2J_1 \neq J_2J1​=J2​) hopping regimes are analyzed. Within the framework of Floquet theory, the time-dependent Hamiltonian is mapped onto an effective static Floquet Hamiltonian, enabling a detailed study of the quasi-energy spectrum as function of the driving frequency ωωω. By applying a gauge transformation, we find that critical frequencies ωcω_cωc​ emerge, at which nearly equidistant quasi-energy ladders appear, as revealed by a pronounced minimum in the normalized variance Δ(ω)Δ(ω)Δ(ω) of the level spacings. This spectral regularity leads to robust periodic revivals and Bloch-like oscillations in the time evolution. Numerical simulations confirm that such coherent oscillations persist even in the non-Hermitian regime, where the periodic driving stabilizes an almost real and uniformly spaced quasi-energy ladder.
The spectral and transport properties of a non-Hermitian tight-binding lattice with unidirectional hopping are theoretically investigated in three different geometrical settings. It is shown that, while for the infinitely-extended (open) and for the ring lattice geometries the spectrum is complex, lattice truncation makes the spectrum real. However, an exceptional point of order equal to the number of lattice sites emerges. When a homogeneous dc force is applied to the lattice, in all cases an equally-spaced real Wannier-Stark ladder spectrum is obtained, corresponding to periodic oscillatory dynamics in real space. Possible physical realizations of non-Hermitian lattices with unidirectional hopping are briefly discussed.
Abstract Parametric squeezing provides a route to enhancing virtual-photon-mediated interactions, but single-sided squeezing also breaks the symmetry between spatially separated quantum nodes and generates anomalous interaction channels. We study coherent excitation exchange between two atoms hosted in tunnel-coupled cavities, with a degenerate parametric drive applied to only one cavity. After an exact Bogoliubov transformation, both the local atom–cavity coupling and the intercavity tunneling are enhanced, leading to an effective exchange interaction that approximately follows a cosh 2 ⁡ r scaling. The same asymmetric driving produces unequal dispersive shifts of the two atomic branches, while the anomalous Bogoliubov channels introduce an additional Bloch–Siegert-type correction to the resonance condition. After compensating these shifts, squeezing substantially accelerates the interatomic exchange while preserving near-unit population transfer in coherent closed-system dynamics. These results demonstrate a controllable route to accelerating virtual exchange between spatially separated cavity-quantum electrodynamics nodes and clarify the roles of asymmetric dispersive shifts and anomalous Bogoliubov channels in the squeezing-enhanced dynamics.
The effects of counter-rotating terms (CRTs) on Rabi splitting and the dynamic evolution of atomic population in the Jaynes—Cummings model are studied with a coherent-state approach. When the coupling strength increases, the Rabi splitting becomes of multi-Rabi frequencies for the initial state of an excited atom in a vacuum field, and the collapses and revivals gradually disappear, and then reappear with quite good periodicity. Without the rotating-wave approximation (RWA), the initial excited state contains many eigenstates rather than two eigenstates under the RWA, which results in the multi-peak emission spectrum. An analytical approximate solution for the strong coupling regime is obtained, which gives a new oscillation frequency and explains the recovery of collapses and revivals due to the equal energy spacing.