Optical lattice platform for the SYK model

The Sachdev-Ye-Kitaev (SYK) model and its modifications have recently drawn broad theoretical interests due to their possibility to understand the non-Fermi liquid properties, maximally chaotic behavior, and holographic duality. A viable experimental realization of the SYK model is an important task that allows testing the basic understanding of the SYK physics going beyond the saddle point approximation and the conformally invariant solution. We show that the SYK Hamiltonian emerges from a system of spinless itinerant fermionic atoms in an optical Kagome lattice with disorders on random sites. We discuss the regimes supporting non-dispersive flat band spectra in a Kagome lattice. Random interaction between non-dispersive fermions is induced due to randomly distributed immobile impurities in the optical lattice that impede the presence of itinerant fermions at their locations. We show that the proposed setup represents a maximally chaotic system by checking that the distribution of eigenenergies satisfying the Wigner-Dyson ensemble. We discuss that the velocity distribution of the released fermions can be a sensitive probe of the spectral density while the averaged many-body Loschmidt echo scheme can measure two-point out-of-time-ordered correlation functions of the SYK system.