Exact nonequilibrium dynamics of a class of initial states in one-dimensional two-component integrable quantum gases

We present the numerically exact time-evolution of a class of initialstates in integrable one-dimensional two-component quantum gases. Thisspecial class of states, formed from a simple superposition ofeigenstates, contains a well-localized particle of one species and abackground gas containing a density-depletion (hole) in the vicinity ofthis particle, looking much like an exciton. The special structure ofthe initial states means that we can compute the time-evolution in anumerically exact manner for large numbers N= 100-1000 of interactingparticles, comparable with those studied in experiments on cold atomicgases. The initial state can be pictured as a linear superposition ofspin wave excitations, and has significant overlap with simple spin flipexcitations, which have been studied in existing experimental setups. Westudy both fermionic and bosonic quantum gases and highlight somedifferences between the two cases. In both cases, the initiallywell-localized exciton dissolves, with particle-hole excitationsspreading through the gas within a light cone. The behavior of the lightcone on varying the interaction strength and density of the gas can beunderstood from existing exact results for the spin wave mass in thesesystems. Within the light cone of the Bose gas, we see evidence ofadditional excitations about (finite momentum) roton-like minima in thespin wave dispersion