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.

💡 Research Summary

In this work the authors demonstrate a synthetic gauge phase in a Rydberg electromagnetically induced transparency (EIT) system realized in a room‑temperature rubidium vapor. By employing a ladder‑type three‑level scheme that includes a highly excited Rydberg state, two intermediate Zeeman sublevels (|e₁⟩ and |e₂⟩) provide parallel excitation pathways from the ground state |g⟩ to the Rydberg state |r⟩. When both the weak probe (420 nm) and the strong coupling (1013 nm) lasers are linearly polarized, each field can be decomposed into σ⁺ and σ⁻ components. The combination of σ⁺–σ⁻ and σ⁻–σ⁺ cascades creates closed‑loop transitions whose accumulated phase θ = φ₂ − φ₁ + ψ₂ − ψ₁ is directly set by the relative polarization angle between the two lasers.

Theoretical modeling uses a Hamiltonian that includes the four states and the associated Rabi frequencies (Ω_p, Ω_c) together with Lindblad decay terms for the intermediate (κ_e) and Rydberg (κ_r) levels. A mean‑field shift δ_eff = δ + η ρ_rr accounts for the long‑range dipole‑dipole interaction among Rydberg atoms; η is proportional to the interaction strength. Numerical steady‑state solutions show that when θ = 0 the two pathways interfere constructively, yielding a pronounced EIT transparency window, whereas θ = π leads to destructive interference and the disappearance of the window. Intermediate values of θ produce sinusoidal modulation of both the transmission peak and the slope of the transmission curve. The presence of a finite η introduces asymmetry and a shift of the resonance, reflecting the nonlinear response induced by Rydberg interactions.

Experimentally, a heated 87Rb cell at 370 K is illuminated by counter‑propagating probe and coupling beams. Polarization purity is ensured by PBSs; half‑wave plates rotate the linear polarization continuously, while a quarter‑wave plate allows switching to circular polarization for control measurements. The probe power is kept at 1 mW (diameter ≈ 1.5 mm) and the coupling power is varied from 16 mW to 190 mW (diameter ≈ 2.7 mm). The probe detuning is calibrated via saturated absorption spectroscopy, and a lock‑in detection scheme (130 kHz modulation on the coupling beam) extracts the weak EIT signal.

When both beams are linearly polarized, the measured EIT spectra display a clear sinusoidal dependence of the transmission peak on the relative angle, confirming that θ = 2 × (angular difference). The data match the theoretical prediction quantitatively. Switching the coupling beam to circular polarization removes the closed‑loop structure; the transmission then becomes essentially independent of the probe polarization angle, confirming that the observed modulation originates from the synthetic gauge phase.

Further measurements reveal that the EIT linewidth also oscillates with θ, indicating that the Rydberg population—and therefore the dipole‑dipole interaction strength—is modulated by the gauge phase. Increasing the coupling power enhances both the peak transmission and the linewidth, as expected for stronger Rydberg excitation. Across the full power range, the θ = 0 configuration consistently yields higher transmission and a steeper slope |∂T/∂δ|_max than the θ = π case, demonstrating that the synthetic gauge phase can be used to tune the effective nonlinearity of the medium.

In conclusion, the authors have shown that a simple rotation of linear polarizations provides a robust, experimentally convenient knob to generate and control a synthetic gauge phase in a Rydberg‑EIT system. This phase simultaneously governs the linear optical response (transparency window) and the nonlinear many‑body response (Rydberg interaction‑induced broadening and asymmetry). Because no cooling, trapping, or complex lattice engineering is required, the technique opens a pathway toward exploring topological photonics, quantum simulation of gauge fields, and enhanced sensing applications in warm atomic vapors.