Quantum Simulation of Massive Relativistic Fields in 2 + 1 Dimensions

TL;DR

This paper demonstrates quantum simulation of massive relativistic fields in 2+1 dimensions using a Bose-Einstein condensate, enabling exploration of complex phenomena like topological defects and cosmological processes.

Contribution

It introduces a novel method to simulate 2+1D relativistic quantum fields with tunable parameters using ultracold atoms, including both perturbative and non-perturbative effects.

Findings

Relativistic dispersion observed in collective excitations.

Existence of topological domain walls with $2\pi$ phase winding.

Potential to study cosmological phenomena like preheating and vacuum decay.

Abstract

Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often extremely challenging, particularly in more than one spatial dimension. Analog simulation using tunable synthetic quantum systems can both verify existing theoretical predictions and lead to new physical insights. Here, we realize quantum simulation of massive relativistic fields in $2+1$ dimensions (two spatial dimensions and time), using two coherently coupled spin components in a uniform two-dimensional Bose-Einstein condensate. Specifically, we encode the paradigmatic sine-Gordon model in the field describing the relative phase, $\phi$, of the two components. We show that, in the perturbative regime, collective field excitations exhibit a relativistic dispersion with a tuneable mass gap. We also observe explicitly non-perturbative phenomena, including the existence of topological domain walls across which $\phi$ rapidly winds by $2\pi$. Our work opens possibilities for studies of cosmologically relevant phenomena including preheating, dynamics of topological defects, and relativistic false-vacuum decay.