  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.
