Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity

TL;DR

This paper proposes a method to realize the Sachdev-Ye-Kitaev (SYK) model using ultracold gases, aiming to experimentally explore quantum gravity and black hole analogs through quantum simulation.

Contribution

It introduces a real-hopping variant of the SYK model and outlines how to implement and measure it with ultracold fermionic atoms in optical lattices.

Findings

The real-hopping SYK model is equivalent to the original in the large-N limit.

Proposes a feasible experimental setup with ultracold atoms and photo-association lasers.

Shows how to measure out-of-time-order correlators to identify chaos.

Abstract

We suggest that the holographic principle, combined with recent technological advances in atomic, molecular, and optical physics, can lead to experimental studies of quantum gravity. As a specific example, we consider the Sachdev-Ye-Kitaev (SYK) model, which consists of spin-polarized fermions with an all-to-all complex random two-body hopping and has been conjectured to be dual to a certain quantum gravitational system. Achieving low-temperature states of the SYK model is interpreted as a realization of a stringy black hole, provided that the holographic duality is true. We introduce a variant of the SYK model, in which the random two-body hopping is real. This model is equivalent to the origincal SYK model in the large-$N$ limit. We show that this model can be created in principle by confining ultracold fermionic atoms into optical lattices and coupling two atoms with molecular states via photo-association lasers. This development serves as an important first step towards an experimental realization of such systems dual to quantum black holes. We also show how to measure out-of-time-order correlation functions of the SYK model, which allow for identifying the maximally chaotic property of the black hole.