Expansion of one-dimensional spinor gases from power-law traps

Free expansion following the removal of axial confinement represents a fundamental nonequilibrium scenario in the study of many-body ultracold gases. Using the stationary phase approximation, we analytically demonstrate that for all one-dimensional spinor gases with repulsive contact interactions, whether bosonic or fermionic, the asymptotic density and momentum distribution can be directly determined from the quasimomentum distribution (Bethe rapidities) of the trapped gas. We efficiently obtain the quasimomentum distribution numerically by solving the integral equations that characterize the ground state of the integrable system within the local density approximation. Additionally, we derive analytical solutions for both weakly and strongly interacting regimes. Unlike in bosonic gases, where rapidity distributions and density profiles vary significantly across interaction regimes, fermionic gases maintain similar profiles in both weakly and strongly interacting limits. Notably, the gas expands self-similarly only when released from a harmonic trap. For other power-law trapping potentials, the asymptotic density profile is strongly influenced by the initial confinement geometry. Our results extend readily to Bose-Fermi mixtures and finite temperatures.