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.
Highlights
The effect of electromagnetically induced transparency (EIT) involving Rydberg-state atoms is of great interest currently
Rydberg polaritons are regarded as bosonic quasi-particles, and the dipole-dipole interaction (DDI)-induced phase shift and attenuation coefficient can infer the elastic and inelastic collision rates in the ensemble of these particles [35]
A mean field theory based on the nearest-neighbor distribution is developed to describe the DDI effect in the system of weakly-interacting EIT-Rydberg polaritons
Summary
The effect of electromagnetically induced transparency (EIT) involving Rydberg-state atoms is of great interest currently. D. Pritchard et al utilized the N -atom model to analyze experiment phenomena of the optical nonlinearity and attenuation in the Rydberg-EIT system. We considered the weakly-interacting Rydberg-EIT system, and developed a mean field model to describe the attenuation and phase shift of the output probe field induced by the DDI effect. With the probability function of NND and the atomlight coupling equations of EIT system, we calculated the mean field results of transmission and phase shift spectra, and further derived the analytical formulas of the DDI-induced attenuation coefficient and phase shift.
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