Emergent Coherent Transport and Synthetic Geometry in Simulated Floquet-Driven Rydberg Arrays via Vacuum--Photonic Quasienergy Channels

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.