A cavity quantum electrodynamics implementation of the Sachdev--Ye--Kitaev model

TL;DR

This paper proposes a feasible cavity QED setup to implement the SYK model, enabling experimental investigation of quantum gravity analogs through disordered fermionic atom interactions.

Contribution

It introduces a scalable cavity QED platform for realizing the SYK model using disordered fermionic atoms, bridging theoretical physics and experimental quantum simulation.

Findings

Analytical and numerical validation of the implementation

Demonstration of all-to-all random interactions

Potential for studying holographic quantum matter

Abstract

The search for a quantum theory of gravity has led to the discovery of quantum many-body systems that are dual to gravitational models with quantum properties. The perhaps most famous of these systems is the Sachdev-Ye-Kitaev (SYK) model. It features maximal scrambling of quantum information, and opens a potential inroad to experimentally investigating aspects of quantum gravity. A scalable laboratory realisation of this model, however, remains outstanding. Here, we propose a feasible implementation of the SYK model in cavity quantum electrodynamics platforms. Through detailed analytical and numerical demonstrations, 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 retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Our work provides a blueprint for realising the SYK model in a scalable system, with the prospect of studying holographic quantum matter in the laboratory.