Nonlinear optical spectra from Rydberg-mediated photon-photon interactions

TL;DR

The study probes how Rydberg–Rydberg interactions induce nonlinear optical spectra in cold-atom Rydberg EIT and assesses implications for microwave sensing. By comparing three representative models—the conditional SA model, the unconditional SA model, and a dephasing-based approach—against three-level and four-level (MW-dressed) EIT data, it reveals that nonlinearities manifest differently depending on the level structure: three-level EIT shows both peak broadening and a small blue shift consistent with blockade-driven conditioning, while four-level MW EIT exhibits broadening without measurable shifts. The conditional SA model best explains the three-level observations, whereas the dephasing model captures the four-level behavior, highlighting distinct many-body physics regimes and offering practical guidance for bias-free MW field characterization in nonlinear operating conditions. Overall, the results advance understanding of Rydberg many-body effects in EIT and inform the design of nonlinear, self-calibrated atomic sensors.

Abstract

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.

Figures (10)

• Figure 1: Nonlinearity in a three-level system. (a) Level scheme. (b) Measured EIT spectra vs probe detuning. For clarity, we smooth the data using a moving average of window size 9 (see Fig. \ref{['fig: EIT nonlinearity models']} for the raw data). The probe rate is $R_p=\{1.6,4.8,8.8,22.9,70.5\}~\mu\text{s}^{-1}$ for the {red, blue, green, orange, purple} colors. This color coding is kept the same as in panel (c,d). (c) $\Gamma_3$ is extracted by fitting the linear model to the raw data. (d) The peak position $\Delta_p^{pk}$ is determined by Gaussian fits to the raw data in the central region.
• Figure 2: Comparison of the three models (conditional model: blue solid line; dephasing model: green dashed line; unconditional model: orange dot-dashed line) with our three-level EIT data (same dataset as in Fig. \ref{['fig: EIT nonlinearity']}, shown as black dots). Panels (a–e) correspond to increasing probe rate.
• Figure 3: Nonlinearity in a four-level system. (a) Level scheme. (b) Measured MW EIT spectra vs control detuning. For clarity, we smooth the data using a moving average of window size 9 (see the dots in panel (e-g) for the raw data). The probe rate is $R_p=\{1.6,4.9,8.9\}~\mu\text{s}^{-1}$ for the {blue, green, orange} colors. The slight imbalance between the two peaks results from a small MW detuning $\Delta_m/(2\pi)=0.15~$MHz, which does not affect the extracted values of $\Omega_m$ within statistical uncertainties. The peak positions $\Delta_c^{pk}$ of the right and left peaks are determined by Gaussian fits to the raw data in the vicinity of each peak and plotted in panel (c) and (d). In panels (e-g), the red dashed and black solid lines are fit results from the linear model. The red dashed lines have independent $\Gamma_3$ and $\Gamma_4$, with fitted values $\Gamma_3/(2\pi)=\{0.17(8),0.6(1),1.3(1)\}~$MHz and $\Gamma_4/(2\pi)=\{0.21(7),0.11(8),0.10(9)\}$ MHz. The black solid lines enforces $\Gamma_3=\Gamma_4$, with fitted values $\Gamma_{3,4}/(2\pi)\ = \{0.19(2),0.32(3),0.68(5)\}$ MHz.
• Figure 4: Comparison of the unconditional model (black solid lines) and the dephasing model (red dashed lines) with our four-level MW EIT data (same dataset as in Fig. \ref{['fig: EIT nonlinearity 2']}, shown as dots.) Panel (d-f) show interaction-induced Rydberg dephasing in the dephasing model for the highest probe rate $R_p=8.9~\mu s^{-1}$, used for the red dashed curve in panel (c). (d) Contribution from the $C_6^{33}$ ($\sqrt{\text{Var}_{33}}/(2\pi)$, orange) and $C_6^{44}$ ($\sqrt{\text{Var}_{44}}/(2\pi)$, blue) terms. (e) Contribution from the $C_6^{34}$ term to level $\ket{3}$ ($\sqrt{\text{Var}^s_{34}}/(2\pi)$, orange), from the $C_6^{34}$ term to level $\ket{4}$ ($\sqrt{\text{Var}^s_{43}}/(2\pi)$, blue) and from the $C_3^{34}$ term to both level $\ket{3}$ and $\ket{4}$ ($\sqrt{\text{Var}^e_{34}}/(2\pi)$, green). (f) Total interaction-induced Rydberg dephasing for level $\ket{3}$ (orange) and $\ket{4}$ (blue).
• Figure 5: Nonlinearity in a four-level system at larger probe Rabi frequency. Panels (a-c) are the measured MW EIT spectra vs control detuning with the probe rate $R_p=\{1.6,22.6,70.5\}~\mu\text{s}^{-1}$ for the {blue, green, orange} colors. $\Omega_c/(2\pi)=3.19(8)$ MHz and $\Omega_m/(2\pi)=3.45(3)$ MHz are extracted through the fit result of (a) from the linear model with independent $\Gamma_3$ and $\Gamma_4$. The red dashed lines are the dephasing model, and the black solid lines are Gaussian fits to each peak, from which the peak position $\Delta_c^{\text{pk}}$ are extracted and plotted in panel (d) (right peaks) and (e) (left peaks).