Synthetic Gauge Phase in Rydberg Electromagnetically Induced Transparency

We demonstrate a synthetic gauge phase in Rydberg electromagnetically induced transparency (EIT) using room-temperature rubidium vapor. By exploiting polarization selection rules in a ladder-type system involving ground, intermediate, and Rydberg states, multiple Zeeman sublevels form closed-loop transitions that acquire a gauge phase. We show that the relative polarization angle between the linearly polarized probe and coupling lasers directly controls this gauge phase, which modulates the EIT transmission and Rydberg state population, consequently controlling the linewidth of EIT due to Rydberg dipole-dipole interactions between atoms. Our approach provides a simple polarization-based method for realizing synthetic gauge physics and manipulating many-body interactions in atomic ensembles without requiring laser cooling and dipole traps.