Cold Atom Quantum Simulator for String and Hadron Dynamics in Non-Abelian Lattice Gauge Theory

Abstract: We propose an analog quantum simulator for simulating real time dynamics of $(1+1)$-d non-Abelian gauge theory well within the existing capacity of ultracold atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a 1-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on novel loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable, and particularly effective in simulating the theory in weak coupling regime, and also bulk limit of the theory in strong coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of exact spectrum and real time dynamics of lattice gauge theory to that of the atomic Hamiltonian with experimentally realizable range of parameters.