Many-body physics of Rydberg dark-state polaritons in the strongly interacting regime

TL;DR

This paper develops a one-dimensional model for Rydberg polaritons under EIT, demonstrating how time-dependent control fields can induce strong interactions and quasi crystalline order, supported by numerical simulations and Luttinger liquid theory.

Contribution

It introduces a dynamic control scheme to reach strongly interacting regimes of Rydberg polaritons and provides a comprehensive theoretical framework validated by simulations.

Findings

Strong interactions induce quasi crystalline order in Rydberg polaritons.

Time-dependent control fields enable access to the strongly interacting regime.

Theoretical analysis aligns with numerical simulations of polariton dynamics.

Abstract

Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of strongly interacting quasi-particles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions, which we verify by numerical two-excitation simulations. We determine conditions allowing for a description by an effective Hamiltonian of a single-species polariton, and calculate ground-state correlations by use of the density matrix renormalization group (DMRG). Under typical stationary slow-light EIT conditions it is difficult to reach the strongly interacting regime where the interaction energy dominates the kinetic energy. We show that by employing time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasi crystalline order. We analyze the dynamics and resulting correlations for a translational invariant system in terms of a time-dependent Luttinger liquid theory and exact few-particle simulations and address the effects of nonadiabatic corrections and initial excitations.