A quantum simulation scheme and equilibration/thermalization physics of the Sachdev-Ye-Kitaev (SYK) model

Abstract

The quest for a quantum theory of gravity has led to the discovery of quantum many-body systems that are dual to gravitational models with quantum characteristics. Amongst these the Sachdev-Ye-Kitaev (SYK) model has received tremendous research interest in recent years. The model 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. In this talk, we shall be discussing a possible implementation of the SYK model in cavity quantum electrodynamics platforms. Our detailed analytical and numerical analysis reveals that a cloud of fermionic atoms trapped in a multi-mode optical cavity subjected to a spatially disordered AC-Stark shift retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Furthermore, our work demonstrates that for local observables the out-of-equilibrium dynamics of the model is universal with respect to generic initial conditions. To reveal this, we develop a general open quantum system frame-work for the disorder averaged closed evolution, and reveal the universality through the spectral characteristics of the corresponding Liouvillian. In the non-Hermitian settings, the model clearly satisfies the markers of the Eigenstate Thermalization Hypothesis (ETH), demonstrating the applicability of ETH in chaotic non-Hermitian systems. Our works provide a blueprint for realising the SYK model in a scalable system, with the prospect of studying holographic quantum matter in the laboratory, and shed light on challenging questions for systems far from equilibrium, such as, thermalization of closed and open disordered quantum systems.