Nonlinear optical spectra from Rydberg-mediated photon-photon interactions

While Rydberg-Rydberg interactions are essential for quantum nonlinear optics and quantum information processing, their role in microwave and radio-frequency sensing remains poorly understood. Here we experimentally investigate Rydberg interaction-induced nonlinearity in cold-atom Rydberg electromagnetically induced transparency (EIT). In a three-level EIT system, increasing photon-photon interactions produces nonlinear spectral broadening accompanied by resonance shifts, while a microwave-dressed four-level system exhibits pronounced nonlinear broadening without detectable spectral shifts. Our three-level data can be explained by a conditional superatom model, whereas our four-level observations are surprisingly captured by a simple dephasing model. Comparisons with three representative models provide key insights to the role of many-body interactions in Rydberg EIT spectroscopy. Furthermore, our results clarify the conditions under which microwave field characterization can be performed in the nonlinear regime without introducing systematic bias. Our study advances both fundamental understanding of many-body physics and practical development of atomic sensors.

💡 Research Summary

In this work the authors investigate how Rydberg‑Rydberg interactions generate optical non‑linearity in electromagnetically induced transparency (EIT) spectra of cold‑atom ensembles, with a view toward both fundamental many‑body physics and practical microwave/radio‑frequency (MW/RF) sensing. Two experimental configurations are explored. First, a conventional three‑level ladder EIT is realized in 87Rb atoms coupling the ground state |1⟩ = 5S₁/₂(F = 2, mF = −2) to the intermediate state |2⟩ = 5P₃/₂(F = 3, mF = −3) and then to the Rydberg state |3⟩ = 61S₁/₂(mj = −½) using a weak σ⁻ probe and a strong σ⁺ control laser. By varying the probe photon rate Rp from 1.6 µs⁻¹ up to 70.5 µs⁻¹ the authors increase the effective photon‑photon interaction strength. They observe a clear reduction of the EIT transmission peak height together with a broadening of the linewidth Γ₃. Importantly, a small blue shift of up to 0.2 MHz appears as Rp grows, consistent with a mean‑field shift caused by the van‑der‑Waals C₆ interaction between S‑state Rydberg atoms.

Second, a microwave‑dressed four‑level system is built by adding a resonant MW field that couples the S‑state |3⟩ to the nearby P‑state |4⟩ = 61P₃/₂. A bias magnetic field (3.7 G) separates Zeeman sublevels, allowing a clean four‑level ladder. Under identical probe‑rate variations the authors again see strong spectral broadening, but now the resonance position remains essentially unchanged. This indicates that, in the presence of the MW field, the dominant interaction effect is dephasing rather than a deterministic level shift.

To interpret the data three theoretical frameworks are compared. All are based on the “superatom” picture, i.e. atoms within a blockade volume Vb act as a single two‑level system because multiple Rydberg excitations are energetically forbidden.

1. Conditional (superatom) model – The medium is discretized into superatoms. If a superatom contains a Rydberg excitation its polarizability reverts to that of a two‑level atom (blockade saturation). If it is unexcited, surrounding superatoms produce a mean‑field detuning shift. Monte‑Carlo sampling of excitation configurations yields probe transmission. This model reproduces both the linewidth broadening and the blue shift observed in the three‑level case.

2. Unconditional (mean‑field) model – No distinction is made between excited and unexcited superatoms; the entire ensemble experiences a uniform mean‑field shift derived by integrating the van‑der‑Waals potential from the blockade radius outward. This predicts large resonance shifts that are not seen experimentally, rendering the model unsuitable for either configuration.

3. Dephasing model – Interaction‑induced fluctuations are treated as additional decoherence rates for the Rydberg levels (Γ₃, Γ₄). No deterministic detuning shift is introduced. This approach captures the pure broadening observed in the microwave‑dressed four‑level system while leaving the resonance position intact.

Parameter values (atomic density ρ ≈ 2 × 10¹⁰ cm⁻³, blockade radius derived from C₆ and the control Rabi frequency, baseline dephasing ≈ 20 kHz) are extracted from low‑rate linear fits. The conditional and dephasing models share the same baseline dephasing, while the unconditional model requires an empirically larger Γ₃ (≈ 200 kHz) to match low‑rate data. Monte‑Carlo simulations with a 1‑D chain of superatoms (four blockade lengths along the probe propagation direction) reproduce the measured transmission curves quantitatively.

Beyond the physics, the study provides practical guidance for Rydberg‑based MW/RF sensors. In the three‑level regime, increasing probe power inevitably introduces a systematic frequency shift that would bias field measurements. Conversely, the four‑level microwave‑dressed configuration shows that strong non‑linearity can be tolerated without inducing a measurable shift, allowing accurate field characterization even when photon‑photon interactions are significant. This insight is crucial for designing high‑sensitivity, quantum‑limited sensors that operate at high optical depths or with strong probe fields.

In summary, the paper demonstrates that Rydberg‑mediated photon‑photon interactions can manifest either as a mean‑field level shift (three‑level ladder) or as pure dephasing (microwave‑dressed four‑level ladder). By benchmarking three competing theoretical models against careful measurements, the authors clarify which physical mechanisms dominate under different experimental conditions and establish the parameter regimes where nonlinear effects do not compromise microwave field sensing. The work advances both the fundamental understanding of many‑body effects in Rydberg EIT and the engineering of robust, high‑performance atomic sensors.