Quantum simulation with fermions in optical lattices with software-programmable geometry

Abstract

Quantum simulation refers to the use of inherently quantum systems in simulating and studying phenomena that would be otherwise computationally inaccessible to any traditional (classical) computer. There are many possible physical systems that could implement quantum simulation, of which we focus on ultracold atoms in optical lattices, which consist of atoms trapped in potential wells caused by interfering beams of light. We specifically consider fermions in optical lattices, which exemplify the Fermi-Hubbard model, and work towards the goals of an experimental setup which can produce software-programmable lattice geometries, as well as the study of the kinetic-frustration-based emergence of magnetic polarons specifically in a triangular-geometry lattice structure. Towards the former goal, we consider first a method of using a phase-only spatial light modulator (SLM), along with a mask in the Fourier plane of a \(4f\) optical system, to generate arbitrary optical lattices—we are able to successfully generate a triangular-lattice pattern via this method, but due to concerns of intensity disorder, we switch to a method of superimposing a 1D lattice on a 2D square-lattice setup. We are again able to generate triangular lattices, and this second method still has the potential to programmatically create a variety of lattice geometries, including honeycombs, 1D tubes, triangles, Kagome lattices, and Lieb lattices. Towards the latter goal, using quantum gas microscopy to characterize \(n\)-point correlations in lattice structures, we see the emergence of antiferromagnetic-order magnetic polarons around holes and ferromagnetic-order polarons around doublons in the triangular Fermi-Hubbard model, with good qualitative agreement with numerical determinant quantum Monte Carlo (DQMC) simulations.