The Sachdev-Ye-Kitaev (SYK) model consists of Q fermions with an all-to-

all random two-body hopping [1,2]. Its static state is a non-Fermi 

liquid with nonzero entropy at vanishing temperature, which is called 

the Sachdev-Ye (SY) state [3]. Since the SY state has been conjectured 

to be holographically dual to charged black holes with two-dimensional 

anti-de Sitter horizons, the SYK model has attracted much attention as a 

new theoretical tool for studying quantum gravity (see, e.g., Ref. [4]). 

In this work, we propose a possible route for realizing the SYK model 

experimentally with use of ultracold gases in optical lattices [5]. We 

also show how to measure out-of-time-order correlators of the SYK model, 

which may allow for capturing one of the most crucial characteristics of 

a black hole, namely maximally chaotic property.

[1] A. Y. Kitaev, “A simple model of quantum holograpy”, KITP string 

seminar and Entanglement 2015 program (Feb. 12, April 7, and May 27, 

2015). http://online.kitp.ucsb.edu/online/entangled15/.

[2] S. Sachdev, Phys. Rev. X 5, 041025 (2015).

[3] S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993). 

[4] J. Maldacena and D. Stanford, Phys. Rev. D 94, 106002 (2016).

[5] I. Danshita, M. Hanada, and M. Tezuka, arXiv:1606.02454v2 [cond-mat.

quant-gas], to appear in PTEP.