Simulating one-dimensional systems with stationary Rydberg dark polaritons

TL;DR

This paper proposes a stationary light scheme with Rydberg dark polaritons to independently control their speed and interactions, enabling simulations of one-dimensional quantum systems like the Tonks-Girardeau gas.

Contribution

It introduces a novel stationary light scheme that allows independent tuning of polariton velocity and interactions for one-dimensional quantum simulations.

Findings

Enables control of effective contact interactions between polaritons.

Proposes a protocol to observe spatial correlations in 1D polariton systems.

Facilitates simulation of fermionic behavior in photonic systems.

Abstract

Electromagnetically-induced transparency (EIT) with Rydberg atoms enables strong interactions between atoms to be controlled and measured by pulses of light. Consequently, Rydberg dark polaritons are a promising platform for quantum simulations. Of particular interest are simulations of one-dimensional systems, known to exhibit unique properties compared to their higher-dimensional counterparts. One limitation of standard EIT is that reducing the polariton group velocity to bring the dark polaritons to rest also implies activating strong Rydberg interactions. To achieve independent control of polariton speed and interaction strength, we propose a stationary light-scheme to bring Rydberg polaritons to a stand-still. This allows them to remain primarily photonic and, therefore, non-interacting, before Rydberg interactions are turned on. Once activated, in the dilute regime and in the presence of strong transverse confinement, the strong polarizabilities of Rydberg atoms give rise to an effective contact interaction between polaritons. By tuning the various parameters of the stationary-light scheme, the effective one-dimensional scattering length may be adjusted to yield various kinds of physics, including the regime of a Tonks-Girardeau gas, when polaritons exhibit fermionic behavior. We outline a protocol to observe the resulting spatial correlations between neighboring polaritons.