Self-induced glassy phase in multimodal cavity quantum electrodynamics

TL;DR

This paper demonstrates that a multimodal cavity QED system can exhibit a self-induced glassy phase arising from Euclidean correlations, without the need for disorder, and explores its thermodynamic and computational properties.

Contribution

It introduces a disorder-free model of a glassy phase in cavity QED, showing how Euclidean correlations induce glassiness and analyzing the complexity of its ground states.

Findings

Presence of a low-temperature glassy phase in the model

Exponential growth of metastable states for rational interaction parameters

Intractability of ground state determination due to high energy barriers

Abstract

We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. Notably, for rational values of the only free adimensional parameter $\alpha=p/q$ of the interaction, the number of metastable states at low temperature grows exponentially with $q$ and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high energy barriers and ergodicity breaking occurs.