Mimicking interacting relativistic theories with stationary pulses of light

TL;DR

This paper proposes a novel quantum optical system using polarized photons in a nonlinear medium to simulate the Thirring model, enabling exploration of relativistic field theories through accessible optical experiments.

Contribution

It introduces a method to simulate the entire Thirring model using stationary light pulses, bridging quantum optics and relativistic field theory.

Findings

Successfully reproduces all regimes of the Thirring model

Enables measurement of correlation scalings via optical coherence functions

Provides a practical platform for studying relativistic quantum field theories

Abstract

One of the most well known relativistic field theory models is the Thirring model (TM). Its realization can demonstrate the famous prediction for the renormalization of mass due to interactions. However, experimental verification of the latter requires complex accelerator experiments whereas analytical solutions of the model can be extremely cumbersome to obtain. In this work, following Feynman's original proposal, we propose a alternative quantum system as a simulator of the TM dynamics. Here the relativistic particles are mimicked, counter-intuitively, by polarized photons in a quantum nonlinear medium. We show that the entire set of regimes of the Thirring model -- bosonic or fermionic, and massless or massive -- can be faithfully reproduced using coherent light trapping techniques. The sought after correlations' scalings can be extracted by simple probing of the coherence functions of the light using standard optical techniques.