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 the
electromagnetic local density of states (LDOS). 
These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range and
exhibit stability characteristic of attractor-like Floquet fixed points.

Using a microscopic Hamiltonian with spatiotemporally structured
dipole--vacuum coupling, we derive a Floquet--Magnus expression for the
effective 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 reshaping
produces long-lived, quasienergy-resolved photonic corridors, along
which correlation fronts propagate with direction-dependent velocities.

We further show that the system's long-time behavior is well described
by an \emph{effective geometric picture}: anisotropic correlation
fronts define a synthetic light cone, LDOS-induced anisotropies define
an emergent spatial metric, and wavepacket bundle separation obeys a
geodesic-deviation-like equation whose curvature is determined directly
from simulated trajectories over thousands of drive periods.

We conclude with a speculative perspective: if driven matter can imprint
stable geometric structure onto the vacuum LDOS, then controlled analog
spacetime engineering---without material waveguides or external
photonic scaffolds---may be achievable.