We simulate periodically driven Rydberg arrays with purely imaginary-phase driving, showing that it reshapes both internal dynamics and the structure of coupled vacuum fluctuations. In a driven Rydberg array, this interplay produces\emph{hybrid vacuum--photonic quasienergy channels}---coherent,directional modes arising from Floquet-induced modulation of theelectromagnetic local density of states (LDOS). These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range andexhibit stability characteristic of attractor-like Floquet fixed points. Using a microscopic Hamiltonian with spatiotemporally structureddipole--vacuum coupling, we derive a Floquet--Magnus expression for theeffective LDOS:\[\rho_{\rm eff}(\omega)=\sum_m J_m^2(A)\,\rho_0(\omega+m\Omega),\]revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.
We simulate periodically driven Rydberg arrays with purely imaginary-phase driving, showing that it reshapes both internal dynamics and the structure of coupled vacuum fluctuations. In a driven Rydberg array, this interplay produces\emph{hybrid vacuum--photonic quasienergy channels}---coherent,directional modes arising from Floquet-induced modulation of theelectromagnetic local density of states (LDOS). These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range andexhibit stability characteristic of attractor-like Floquet fixed points. Using a microscopic Hamiltonian with spatiotemporally structureddipole--vacuum coupling, we derive a Floquet--Magnus expression for theeffective LDOS:[\rho_{\rm eff}(\omega)=\sum_m J_m^2(A),\rho_0(\omega+m\Omega),]revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.
I introduce a modular framework for constructing long-range, high-fidelity quantum channels via Floquet-engineered quasienergy structures in driven atomic arrays embedded in structured electromagnetic backgrounds. Periodic driving sculpts the local density of states (LDOS) to produce emergent transport channels whose properties can be precisely tailored by the drive pattern. Using large-scale mean-field Floquet simulations, I demonstrate coherent bridging of four physically disconnected sub-arrays into a single collective mode: a probe wavepacket launched in one region spreads symmetrically and reaches perfect amplitude locking across all four regions, maintaining exact balance for over 20,000 drive periods with only negligible numerical jitter. Remarkably, this transport occurs while deliberately violating standard Floquet-theoretical invariants, including local linearity, isotropy, time-reversal symmetry, and naive correlation-front shape conservation, confirming that these assumptions are not required for stable, controllable causal connectivity. Local synthetic curvature emerges along the channels, producing measurable geodesic-like deviations in wavepacket trajectories without inducing instability or decoherence. These results establish a concrete, modular platform for scalable, concatenable quantum transport and provide the first explicit demonstration that emergent quasi-spacetime causal structure can arise in driven quantum systems independent of physical adjacency or previously assumed invariants.
We propose and analyze a general scheme to engineer programmable and nonreciprocal interactions in an array of atoms coupled to a photonic waveguide. By subjecting each atom to a local harmonic frequency modulation with a defined phase ${\ensuremath{\theta}}_{i}$, we demonstrate the emergence of effective long-range couplings whose parameters are dynamically controllable. For atoms coupled to a conventional waveguide, the modulation dresses the atomic operators, leading to effective interactions governed by the Bessel function J0 whose argument depends on the phase differences $\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij}$. For atoms coupled to a photonic crystal waveguide near its band edge, where the density of states is sharply varying, the modulation can be tuned to selectively activate the J12 term, which simultaneously scales both the coherent and dissipative components of the complex coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$. Crucially, the spatial profile of the local modulation phases imprints a factor $exp(\mathrm{i}\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij})$ onto the waveguide-mediated coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$, enabling the synthesis of nonreciprocal quantum interactions. Our approach thus provides a flexible toolbox for simulating a wide range of non-Hermitian Hamiltonians on waveguide-QED platforms.
Strong periodic driving of cavity-quantum electrodynamics (QED) in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. However, modeling such a regime is a significant theoretical challenge, including a number of subtle problems such as the need to ensure gauge invariance for truncated matter-cavity systems with time-dependent driving. To fill this theoretical gap, we introduce a nonsecular Floquet generalized master equation framework for strongly driven open cavity-QED systems, formulated in the dressed basis of the quantum Rabi model and applicable to structured reservoirs without rotating-wave approximations. Our theory can thus model Floquet-driven dynamics in open ultrastrong-coupling cavity-QED, and demonstrates a wide range of quantum state control. Using strong optical pumping and parametric mechanical modulation, we compute long-time populations, fluorescence spectra, and the Floquet-Liouville eigenspectra, resolving observable resonances into hybridized quasienergy channels and decay rates. By systematically comparing with conventional time-independent dressed-basis generalized master equations, we show that static approaches only reproduce steady-state populations in restricted excitation regimes, and fail for frequency-resolved observables and break down under appropriate Floquet engineering, surprisingly, even for spectrally flat baths. Structured environments, such as Lorentzian-Ohmic reservoirs, further amplify these discrepancies through sideband-selective decay. Our results demonstrate that dissipation in driven ultrastrong cavity-QED is intrinsically quasienergy resolved and we establish Floquet-dissipative theory as an accurate and powerful framework for predicting spectra, controlling decay pathways, and engineering nonequilibrium quantum states and reservoirs.
Driven--dissipative quantum fluids in two dimensions typically decohere rapidly. We report a new dynamical regime in which a Floquet-driven 2D quantum fluid with weak Rydberg-dressing feedback self-organizes into long-lived directional \emph{transport corridors}. These channels form in a sharply bounded region of nonlocality, warp coupling, and Floquet twist. Corridor states exhibit coherence dip--recovery, spectral sharpening, persistent drift, and global Rydberg participation. We map the model to implementable neutral-atom tweezer experiments and propose a routing protocol for experimental verification. We further derive a continuum-limit description and a minimal reduced model capturing the essential attractor structure. These results identify a new class of nonlinear coherent transport modes in driven quantum matter.
This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.
Floquet engineering treats periodically driven quantum systems with classical time-periodic Hamiltonians, while cavity quantum electrodynamics (QED) treats the drive itself as a quantized field. The precise connection between the two descriptions beyond weak coupling has remained subtle. Building on the program of [1], in which the cavity field is represented in a large-photon-number phase basis so that the time-dependent Schrödinger equation of a classically driven system emerges as a controlled limit of the fully quantized dynamics, we supply a quantitative bridge with three components. First, we derive the effective classical drive amplitude Ω = 2g√N and its finite-photon-number corrections, showing that the classical limit is approached as a power law in the mean photon number n̄, not exponentially: the relative amplitude correction scales as 1/(2√n̄), bounded conservatively by 1/√n̄. Second, we quantify the gauge-inconsistency phase error per drive cycle incurred by ignoring photon-number quantization, obtaining π/√n̄ to 2π/√n̄ radians, and connect the resulting geometric phase to the gerbe-level structure of adiabatic Floquet theory [4], with the mixed-state operational phase of [6] as the natural observable when fluctuations are retained. Third, we derive entanglement-depletion bounds tied to the Schmidt-gap phenomenology of pulsed Dicke dynamics [7]. For a representative cavity at n̄ = 10⁴ we compute: an effective drive frequency of 10 ± 1.1 GHz for strong-coupling parameters (g/ω_c = 0.01, ω_c/2π = 5 GHz); a 0.5% relative amplitude correction; a per-cycle gauge phase error of 0.031–0.063 radians; and a classical-regime crossover at n̄ ≈ 3.9 × 10⁵ photons for 0.01-radian phase resolution. These numbers convert the formal claims of [1] into falsifiable experimental targets. ## 1. Introduction Periodic driving is a cornerstone of modern quantum control, enabling synthetic Hamiltonians, topological band structures, and dynamical stabilization. In the Floquet Full text and updates: papers.qnfo.org/papers/classical-floquet-drives-from-quantized-cavity-fields-error-budgets-geometric-ph/