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We consider the non-equilibrium dynamics of two-component one dimensionalquantum gases in the limit of extreme population imbalance where the minorityspecies has but a single particle. We consider the situation where the gas isprepared in a state with a single spatially localized exciton: the singleparticle of the minority species is spatially localized while the density ofthe majority species in the vicinity of the minority particle sees adepression. Remarkably, we are able to consider cases where the gas contains onthe order of $N=100$ particles, comparable to that studied in experiments oncold atomic gases. We are able to do by exploiting the integrability of the gastogether with the observation that the excitonic state can be constructedthrough a simple superposition of exact eigenstates of the gas. The number ofstates in this superposition, rather than being exponentially large in thenumber of particles, scales linearly with $N$.  We study the evolution of such spatially localized states in both stronglyinteracting Bose and Fermi gases. The behavior of the light cones when theinteraction strength and density of the gas is varied can be understood fromexact results for the spin excitation spectrum in these systems. We argue thatthe light cone in both cases exhibits scaling collapse. However unique to theBose gas, we show that the presence of gapped finite-momentum roton-likeexcitations provide the Bose gas dynamics with secondary light cones.

Light cone dynamics in excitonic states of two-component Bose and Fermi gases