  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.
