Spin Dynamics and Andreev-Bashkin Effect in Mixtures of One-Dimensional Bose Gases

We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum Monte Carlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.

Figure 1

Energy per particle of the homogeneous mixture as a function of the polarization $P$ for different values of the coupling strengths $\eta$. Panel (a) refers to $\gamma =2$ and panel (b) to $\gamma =20$. Energies are shown in units of ${\epsilon }_F=[({\hslash }^2{\pi }^2{n}^2)/(8m)]$ corresponding to the Fermi energy of the mixture when $\gamma =\infty$. The solid lines are best fits quadratic in $P$ and the dashed horizontal lines indicate the energy of the fully polarized ($P=1$) states. Statistical error bars are smaller than the symbol size.

Figure 2

Inverse susceptibility $1/\chi$ as a function of $\eta$ for various values of $\gamma$ ranging from the weak-coupling regime ($\gamma =0.04$) to the TG limit ($\gamma =\infty$). Here ${\chi }_F=[(4m)/({\hslash }^2{\pi }^{2}n)]$ is the susceptibility of the noninteracting mixture when $\gamma =\infty$. Dashed lines correspond to the mean-field result $1/\chi =(g-\tilde{g})/2$, whereas the dash-dotted line to the perturbation expansion $({\chi }_F/\chi )=1-(2\eta /{\pi }^2)$ holding in the TG limit. The solid line is obtained from the exact solution of the Yang-Gaudin model at finite polarization.

Figure 3

Superfluid drag as a function of $\eta$ for different values of $\gamma$. Dashed lines correspond to the weak-coupling result (3) for $\gamma =2$ and $\gamma =20$. The solid line refers to $\gamma =\infty$ and is obtained by inverting Eq. (5) with both $\chi$ and $v_s$ from the exact solution of the Yang-Gaudin model.

Figure 4

Spin-wave velocity $v_s$ as a function of $\eta$ for different values of $\gamma$. The units are provided by the spin-wave velocity in the absence of interspecies interactions, $v_s^0=\sqrt{\rho /m^2{\chi }_0}$. Open symbols refer to Eq. (5) and solid symbols to Eq. (8). The dashed line corresponds to the mean-field prediction $v_s=\sqrt{n(g-\tilde{g})/2m}$ and the solid line to the exact solution in the Yang-Gaudin model [38].