  We consider the non-equilibrium dynamics of two-component one dimensional
quantum gases in the limit of extreme population imbalance where the minority
species has but a single particle. We consider the situation where the gas is
prepared in a state with a single spatially localized exciton: the single
particle of the minority species is spatially localized while the density of
the majority species in the vicinity of the minority particle sees a
depression. Remarkably, we are able to consider cases where the gas contains on
the order of $N=100$ particles, comparable to that studied in experiments on
cold atomic gases. We are able to do by exploiting the integrability of the gas
together with the observation that the excitonic state can be constructed
through a simple superposition of exact eigenstates of the gas. The number of
states in this superposition, rather than being exponentially large in the
number of particles, scales linearly with $N$.
  We study the evolution of such spatially localized states in both strongly
interacting Bose and Fermi gases. The behavior of the light cones when the
interaction strength and density of the gas is varied can be understood from
exact results for the spin excitation spectrum in these systems. We argue that
the light cone in both cases exhibits scaling collapse. However unique to the
Bose gas, we show that the presence of gapped finite-momentum roton-like
excitations provide the Bose gas dynamics with secondary light cones.
