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

• Published in: Progress of theoretical and experimental physics Vol. 2017; no. 8
• Main Authors: Danshita, Ippei, Hanada, Masanori, Tezuka, Masaki
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.08.2017
• Subjects: Black holes; I22; B21; A63
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptx108

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 original 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.