Engineering random spin models with atoms in a high-finesse cavity

TL;DR

This paper demonstrates a controllable atomic system in a high-finesse cavity that realizes all-to-all interacting disordered spin models, enabling exploration of complex quantum phenomena and potential programmable quantum simulations.

Contribution

It introduces a method to engineer disordered and ordered all-to-all spin models using atoms in a cavity, bridging theoretical models with physical realization.

Findings

Disorder breaks strong collective coupling, creating weakly-mixed states.

Finite-size ferromagnetic ground state transitions to paramagnet with disorder.

Emergence of semi-localised eigenstates as disorder increases.

Abstract

All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics, over holographic duality in high-energy physics, to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realisations in nature. Here, we realise an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark state manifold cross over to a random distribution of weakly-mixed light-matter, "grey", states. In the Lipkin-Meshkov-Glick model the ferromagnetic finite-size ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localised eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present significant steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.