Towards Quantum Simulation of the Sachdev–Ye–Kitaev Model

Analogue quantum simulators have proven to be an extremely versatile tool for the study of strongly-correlated condensed matter systems both near and far from equilibrium. An enticing prospect is the quantum simulation of non- Fermi liquids which lack a quasiparticle description and feature prominently in the study of strange metals, fast scrambling of quantum information, as well as holographic quantum matter. Yet, large-scale laboratory realisations of such systems remain outstanding. In this thesis, we present a proposal for the analogue quantum simulation of one such system, the Sachdev–Ye–Kitaev (SYK) model, using cavity quantum electrodynamics (cQED). We discuss recent experimental advances in this pursuit, and perform analysis of this and related models. Through a combination of analytic calculations and numeric simulations, we show how driving a cloud of fermionic atoms trapped in a multi- mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift, can realise an effective model which retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Working towards the SYK model, we present results from a recent proof-of-principle cQED experiment which implemented the disordered light-shift technique to quantum simulate all- to-all interacting spin models with quenched disorder. In this context, we show analytically how disorder-driven localisation can be extracted from spectroscopic probes employed in cQED experiments, despite their lack of spatially resolved information. Further, we numerically investigate the post-quench dynamics of the SYK model, finding a universal, super-exponential equilibration in the disorder-averaged far-from-equilibrium dynamics. These are reproduced analytically through an effective master equation. Our work demonstrates the increasing capabilities of cQED quantum simulators, highlighting how these may be used to study the fascinating physics of holographic quantum matter and other disorder models in the lab.