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

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 weaklyinteracting 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 weaklyinteracting 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.

A Weakly-Interacting Many-Body System of Rydberg Polaritons Based on Electromagnetically Induced Transparency

“…The experimental data of the attenuation coefficient and the phase shift influenced by the DDI are consistent with the predictions of the mean field theory developed in Ref. [39]. Furthermore, we measured the transverse momentum distribution of the Rydberg polaritons in the medium.…”

“…In Ref. [39], we developed a mean field theory to describe weakly-interacting Rydberg polaritons and predicted the DDI-induced phase shift and attenuation. In the present experiment we employed a laser-cooled atomic cloud with an OD of 80, and systematically studied the phase shift and attenuation of an output probe light for the EIT involving a Rydberg state of |32D 5/2 .…”

“…The mean field model developed in Ref. [39] is summarized in this paragraph. Rydberg excitations are randomly distributed and can be considered approximately as particles of an ideal gas due to their weak interaction.…”

“…where β 0 and φ 0 are the attenuation coefficient and phase shift in the absence of DDI [39]. The mean field theory predicted that both β and φ depend on Ω 2 p linearly, and the dependence of Ω 2 p comes from the Rydberg-state population ρ 22 .…”