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

The Sachdev-Ye-Kitaev (SYK) model is a prototype of non-Fermi liquids and holographic quantum matter: it has no quasi-particles, displays maximal chaos, and shares salient features with Jackiw-Teitelboom gravity. A quantum simulation of the SYK model would thus allow to controllably probe rich physics that is of interest across a variety of fields. However, its implementation is extremely challenging: it requires fully-connected, random, and independently distributed two-body interactions. As a result, scalable laboratory implementations remain still elusive.

In this talk, I will propose a scalable implementation of the SYK model in a cavity quantum electrodynamics platform. The model emerges as an effective description of a cloud of ultracold fermionic atoms in a multi-mode optical cavity, which are off-resonantly driven and subjected to a spatially disordered AC-Stark shift. Detailed analytical and numerical demonstrations that start from a microscopic description show how the system retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. As our careful microscopic analysis reveals, the effective distribution of SYK-interactions follows a Cauchy rather than a Gaussian distribution. This feature appears to be quite common, as we identify it also in previous proposals. Interestingly, we find this modification to leave the physics qualitatively unchanged. Further, I will discuss an unexpected universality in the dynamics of equal-time observables that could be a first experimental indicator of the chaoticity of the SYK model.

Our work thus provides a blueprint for realising the SYK model in a scalable quantum simulator. This opens the prospect of studying holographic quantum matter and non-Fermi-liquid behavior in a highly controlled environment. Even more, it yields insights into a much broader question, namely: what are the necessary ingredients to observe holographic quantum matter in the laboratory.