Spin Waves in a One-Dimensional Spinor Bose Gas

We study a one-dimensional (iso)spin $1/2$ Bose gas with repulsive $\delta$-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or “spin-charge”) separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

Figure 1

Inverse effective mass $m/m^{*}$ as a function of the dimensionless coupling constant $\gamma$ (logarithmic scale). The stars (*) show numerical results for $N=111$ particles, the solid curve represents the behavior in the strong coupling limit [Eq. (13)], and the dashed curve the behavior for a weak coupling [Eq. (18)].