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

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.

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

“…In this sense the J ij kl 's asymptotically form independent Gaussian random variables as in Ref. [23]. Corrections to Wick's theorem do nevertheless introduce a proliferation of new Feynman diagrams that may qualitatively alter SYK-model physics over some energy scales [57].…”

“…As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.…”

“…And finally, the host platform must carry sufficient disorder to at least approximate independence among the large number of random J ij kl 's. References [23,38] proposed SYKmodel platforms using cold atoms and topological insulators, respectively, while Ref. [24] suggested a qubit simulation of the model capable of probing correlations.…”

Jarzynski-like equality for the out-of-time-ordered correlator

“…This quasiprobability has been inferred from weak-measurement experiments [50][51][52][53][54]. Weak measurements have been performed on cold atoms [58], which have been proposed as platforms for realizing scrambling and quantum chaos [15,16,59].…”

“…Interference and weak measurement have been performed with cold atoms [58], which have been proposed as platforms for realizing scrambling and quantum chaos [15,16,59]. Yet cold atoms are not necessary for measuringà ρ .…”