Wigner Crystallization of Single Photons in Cold Rydberg Ensemble

TL;DR

This paper explores how single photons in a cold Rydberg ensemble can form a Wigner crystal through controlled adiabatic processes, combining DMRG simulations and Luttinger liquid theory to analyze the conditions for crystallization.

Contribution

It demonstrates the possibility of inducing Wigner crystallization of Rydberg polaritons by adiabatically increasing their effective mass, supported by theoretical and numerical analysis.

Findings

Wigner crystal formation is hindered by kinetic energy at typical conditions.

Adiabatic mass increase enables true crystalline order.

Time-dependent Luttinger theory describes the dynamics of crystallization.

Abstract

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of Rydberg polaritons which are quasi-particles with tunable effective mass and long-range interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which due to the long-range character of the repulsive interaction can form a Wigner crystal. We calculate the Luttinger $K$ parameter using density-matrix renormalization group (DMRG) simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.