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arXiv:2006.09190 · Optics Express

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution

Shih-Si Hsiao, Ko-Tang Chen, Ite A. Yu

Published Sep 1, 2020• 11 citations
arXivHTMLPDF

Abstract

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

DOI
10.1364/oe.401310

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•Oct 13, 2021•0 citations
The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.
Abstract The combination of Rydberg atoms and electromagnetically induced transparency (EIT) has been extensively studied in the strong-interaction regime. Here we proposed utilizing an EIT medium with a high optical depth (OD) and a Rydberg state of low principal quantum number to create a many-body system of Rydberg polaritons in the weak-interaction regime. The phase shift and attenuation induced by the dipole–dipole interaction (DDI) were still significant, and can be viewed as the consequences of elastic and inelastic collisions among Rydberg polaritons. We further observed that the width of the transverse momentum distribution of Rydberg polaritons at the exit of the system became notably smaller as compared with that at the entrance. The observation demonstrates the cooling effect in this system. The μs-long interaction time due to the high-OD EIT medium plus the μm2-size collision cross section due to the DDI suggests a feasible platform of polariton Bose–Einstein condensation.
We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state $|32{D}_{5/2}\ensuremath{\rangle}$ in the weak-interaction regime. The present effect of attenuation and distortion cannot be explained by considering only the dipole-dipole interaction (DDI) between Rydberg atoms in $|32{D}_{5/2}\ensuremath{\rangle}$. Our observation can be attributed to the atoms in the dark Rydberg states rather than those in the bright Rydberg state, i.e., $|32{D}_{5/2}\ensuremath{\rangle}$, driven by the coupling field. The dark Rydberg states are all the possible states in which the population decaying from $|32{D}_{5/2}\ensuremath{\rangle}$ accumulated over time, and they were not driven by the coupling field. Consequently, the DDI between the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg polaritons. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to the dark Rydberg states. In the theoretical model, we included the decay process from the bright to the dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. This study points out an additional decoherence rate in the Rydberg-state electromagnetically induced transparency effect and provides a better understanding of the Rydberg-polariton system.
Electromagnetically induced transparency (EIT) in a ladder system involving a Rydberg level is known to yield giant optical nonlinearities for the probe field, even in the few-photon regime. This enhancement is due to the strong dipole-dipole interactions between Rydberg atoms and the resulting excitation blockade phenomenon. In order to study such highly correlated media, ad hoc models or low-excitation assumptions are generally used to tackle their dynamical response to optical fields. Here, we study the behavior of a cavity Rydberg-EIT setup in the nonequilibrium quantum field formalism, and we obtain analytic expressions for elastic and inelastic components of the cavity transmission spectrum, valid up to higher excitation numbers than previously achieved. This allows us to identify and interpret a polaritonic resonance structure, to our knowledge unreported so far.
Transmission properties of a weak probe field traveling through a sample of interacting cold 87Rb atoms driven into the three-level ladder configuration, which is a typical Rydberg electromagnetically induced transparency (EIT) system, are investigated. Rydberg atoms are considered to be a perfect platform in the research fields of quantum optics and quantum information processing due to some exaggerated properties of Rydberg atoms with high principal quantum number, especially, the dipole-dipole interaction between Rydberg atoms leads to the so-called dipole blockade effect accommodating at most one Rydberg excitation within a mesoscopic volume. The dipole blockade effect may be mapped onto the spectrum of EIT, and the EIT exhibits the cooperative optical nonlinearity which is usually characterized by two indicators, i.e., the probe intensity and the photonic correlation. The cooperative optical nonlinearity is also found here in the phase of transmission spectrum, and the phase can be regarded as the third indicator of nonlinearity in Rydberg EIT. However, there are tremendous differences between the phase and probe transmission (photonic correlation) though they both originate from the conditional polarization. Specifically, the phase is not sensitive to neither the incident probe intensity nor the initial photonic correlation at the resonant probe frequency under the condition of the Autler-Townes (AT) splitting where two other indicators exhibit significant cooperative nonlinearity. The nonlinearity in phase spectrum occurs only in the regime between the resonant probe frequency and the AT splitting and especially is remarkable at the frequency where the probe field is classical. Finally, influence of the principal quantum number and the atomic density on the transmitted phase are examined. In the nonlinear regime, the absolute value of the phase becomes smaller and smaller as the principal quantum number and the atomic density are raised. This indicates that the nonlinearity is strengthened by increasing them. The probe phase provides an attractive supplement to study in depth the cooperative optical nonlinearity in Rydberg EIT and offers us the considerable flexibility to manipulate the propagation and evolution of a quantum light field.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light in a laser-cooled electromagnetically-induced-transparency (EIT) medium with the Rydberg state of ∣32D5/2⟩|32D_{5/2}\rangle∣32D5/2​⟩. The present effect of attenuation and distortion was caused by the dipole-dipole interaction between Rydberg atoms in a weak-interaction regime, i.e., the mean distance between Rydberg atoms was far greater than the dipole blockade radius. Our observation can be attributed to the atoms self-accumulated in dark Rydberg states other than those in the bright Rydberg state ∣32D5/2⟩|32D_{5/2}\rangle∣32D5/2​⟩ driven by the coupling field. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to dark Rydberg states. In the theoretical model, we included the decay process from the bright to dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. The systematic study presented in this work provides a better understanding of the Rydberg-EIT system.