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

TL;DR

The paper proposes an experimental route to study quantum gravity by realizing the Sachdev-Ye-Kitaev model with ultracold fermions in optical lattices, leveraging holographic duality to connect SYK physics with AdS2 black holes. It introduces a real-J variant of the SYK model and shows it can be implemented in principle by coupling atomic pairs to multiple molecular states via photoassociation lasers, yielding an effective all-to-all random two-body hopping. A detailed scheme using degenerate perturbation theory and a double-well optical lattice is presented to generate the required random couplings, alongside a protocol to measure OTOCs and Green's functions with a control qubit to diagnose maximal chaos. The authors discuss practical bottlenecks—especially the large number of lasers and linewidth requirements—and suggest possible workarounds and future directions, positioning this as a foundational step toward experimental quantum gravity in optical lattices.

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.

Figures (13)

• Figure 1: (a): Distribution of $J_{ij,kl}=\frac{(2N)^{3/2}}{\sqrt{n_{\rm ms}}J}\left(\sum_{s:{\rm even}}g_{s,ij}g_{s,kl}-\sum_{s:{\rm odd}}g_{s,ij}g_{s,kl}\right)$ with only the off-diagonal components (i.e. $(i,j)\neq (k,l),(l,k)$); (b): Distribution of $J_{ij,ij}=\frac{(2N)^{3/2}}{\sqrt{n_{\rm ms}}J}\left(\sum_{s:{\rm even}}g_{s,ij}^2-\sum_{s:{\rm odd}}g_{s,ij}^2\right)$. The numbers of samples taken are $10^4$ (a) and $10^5$ (b), respectively. (c): The energy spectrum for $N=10$, $Q=N/2$, and $10^4$ samples. For all of (a), (b), and (c), the weight of real $g_{s,ij}$ is Gaussian, $\frac{e^{-g_{s,ij}^2/(2\sigma_g^2)}}{\sqrt{2\pi}\sigma_g}$ with $\sigma_g^2 = (2N)^{-3}J^2$ while $\nu_s=+\sqrt{n_{\rm ms}}J$ for even $s$ and $\nu_s=-\sqrt{n_{\rm ms}}J$ for odd $s$.
• Figure 2: Schematic illustrations of the energy levels of the atomic and molecular states relevant to our protocol (a) and the PA process (b) for $N=4$ and $n_{\rm ms} = 1$.
• Figure 3: Spatial profile of the optical lattice of Eq. (\ref{['eq:DWL']}) for $V_0<0$, $R=0.59$, and $\theta = \pi/6$. The dark and light colors indicate the high- and low-potential regions. This means that the lightest (darkest) spots correspond to the atomic (molecular) sites.
• Figure 4: Schematic illustrations of the qubit states (a) and the configulation for measuring the OTOC functions of Eq. (\ref{['eq:OTOC']}) (b).
• Figure 5: Spatial profile of the optical lattice of Eq. (\ref{['eq:DWLq-bit']}) for qubit atoms, where $V_0'<0$ and $R=0.3$. The dark and light colors indicate the high- and low-potential regions. This means that the lightest spots correspond to the sites for the qubit atoms.