Supercurrent and dynamical instability of spin-orbit-coupled ultracold Bose gases

We investigate the stability of supercurrents in a Bose-Einstein condensate with one-dimensional spin-orbit and Raman couplings. The consequence of the lack of Galilean invariance is explicitly discussed. We show that in the plane-wave phase, characterized by a uniform density, the supercurrent state can become dynamically unstable, the instability being associated with the occurrence of a complex sound velocity, in a region where the effective mass is negative. We also discuss the emergence of energetic instability in these supercurrent states. We argue that both the dynamical and the energetic instabilities in these systems can be generated experimentally through excitation of the collective dipole oscillation.

Figure 1

(a) Single-particle eigenenergy and (b) corresponding speed as a function of $k_1$ when $\Omega =1.7k_0^2/2m$. (c–f) $E_v$ for four values of $v$ [indicated in (b)], as a function of $k_1$. Local minima of $E_v$ are represented by orange circles, and local maxima by black circles. (a, b) The dynamically unstable region is shown by the dotted (red) line; the region which corresponds to the metastable states, by green lines; and the lowest energy states of $E_v$, by blue lines. The collective dipole oscillation occurs around one of the minima of the single-particle spectrum, as described in (a).

Figure 2

Critical velocity for the energetic instability of the supercurrent (in units of $k_0/m$) plotted against $\Omega$ (in units of $k_0^2/2m$) when the condensate has a positive momentum. The solid (blue) line corresponds to the lowest energy state, and the dashed (green) line to the metastable state, when $gn=0.48k_0^2/2m$. The dotted (red) line represents the onset of dynamical instability.

Figure 3

Critical momentum kick $\delta p$ to the condensate which causes instabilities (in units of $k_0$) as a function of $\Omega$ (in units of $k_0^2/2m$). The solid (blue) line and the dashed (green) line show the critical momentum required to reach energetic instability for the lowest energy state and the metastable state, respectively, when $gn=0.48k_0^2/2m$. The dotted (red) line represents the critical momentum kick required to get dynamical instability.