Synthetic Gauge Phase in Rydberg Electromagnetically Induced Transparency

Abstract

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.

Figures (4)

• Figure 1: (a) Diamond-type energy level configuration for Rydberg EIT, with synthetic gauge phase $\theta$ accumulated in a closed-loop transition. (b) Schematic of counter-propagating probe and control lasers interacting with Rydberg atom ensemble in a vapor cell. (c) Transmission ($T$) spectra for $\theta=0$ (solid line) and $\theta=\mathrm{\pi}$ (dashed line). (d) EIT spectra with (red line) and without (blue line) Rydberg interaction for $\theta=0,\ 0.3\mathrm{\pi,\ 0.6\pi}$ (top to bottom). (e) EIT transmission peak as a function of $\theta$. (f) Maximum transmission slope versus $\theta$ with (red line) and without (blue line) Rydberg interaction.
• Figure 2: (a) Schematic of the experimental setup. PBS: polarization beam splitter; HWP: half-wave plate; QWP: quarter-wave plate; DM: dichroic mirror; PD: photodiode. (b) Relevant energy levels of rubidium atoms. (c) Saturated absorption spectrum (SAS) (top) and the probe absorption profile (bottom) obtained by scanning the probe laser detuning ($\delta_\mathrm{p}$), with and without coupling laser ($P_\mathrm{c}=$100mW). (d) EIT spectrum versus probe laser detuning, with the coupling laser frequency locked to the $\left|6P_{3/2}, F=3\right\rangle \rightarrow \left|70S_{1/2}\right\rangle$ transition. EIT signals are detected using lock-in amplification with modulation acting on the coupling laser while the frequency of the coupling laser and the intensity of the probe laser are fixed. The probe and coupling laser powers are 1mW and 100mW (0mW), with horizontal and left circular polarizations, respectively. The EIT signal is acquired as the voltage $U$.
• Figure 3: (a) Level diagram depicting excitation by a linear probe (purple) and a linear (red) or left circular (orange) coupling field. (b) EIT spectra for (i) parallel (H-H), (ii) intermediate, and (iii) perpendicular (H-V) alignment between the linear polarization directions of coupling and probe lasers, and the circular polarized coupling laser EIT spectra as shown. (c) EIT peak amplitude ($U_\mathrm{peak}$) versus the gauge phase $\theta$, which is derived as two times of the relative polarization angle between coupling and probe lasers.
• Figure 4: (a) EIT linewidth versus $\theta$ for linear (blue) and circular (red) polarized coupling lasers. (b) Rydberg EIT spectra (H-H polarization configuration) for different coupling laser powers $P_\mathrm{c}$. (c) Rydberg EIT peak transmission versus $P_\mathrm{c}$ for parallel (H-H, blue) and perpendicular (H-V, red) polarization configurations. (d) Maximum spectral slop versus $\theta$.