Landau critical velocity of spin-orbit-coupled Bose-Einstein condensate across quantum phase transition

He Li^{1}, Yu Zeng-Qiang^{2}

1. College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China;
2. Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China

An impurity immersed in a superfluid can move without friction when its velocity is below a critical value. This phenomenon can be explained by the famous Landau criterion, according to which, the critical velocity is determined by the elementary excitation spectrum of the superfluid. Landau critical velocity has been measured in the isotropic superfluid, such as the liquid He-Ⅱ and the Bose-Einstein condensates of dilute atomic gases, where the onset of dissipation is due to the creation of roton and phonon, respectively. The recent realization of synthetic spin-orbit coupling in quantum gas opens up possibilities for the study of novel superfluidity with ultracold atoms. To date, a specific type of spin-orbit coupling, which is generated by a pair of Raman laser beams, has been achieved in a Bose-Einstein condensate of ^{87}Rb experimentally. Remarkably, the excitation spectrum of this system is anisotropic and can be feasibly tuned by the external laser field. While the anisotropic dynamics has been observed experimentally, the critical velocity has not been measured so far. It is a conventional wisdom that in an anisotropic superfluid, the critical velocity is determined by the excitation spectrum in the moving direction of the impurity. However, this is not always the case. In this work, we investigate the motion of a point-like impurity in a spin-orbit-coupled condensate with the spin-dependent interatomic interaction. In the vicinity of the quantum phase transition between the plane-wave (PW) phase and the zero-momentum (ZM) phase, the onset of the dissipation is due to the emission of a phonon, and the Landau critical velocity v_{c} depends on the anisotropic sound velocity. While the sound velocity varies smoothly across the PW-ZM phase transition, the critical velocity in the direction perpendicular to the axis of spin-orbit coupling exhibits a sudden jump at the phase boundary. The value of v_{c} on the PW phase side of the transition is generally smaller than the one on the ZM phase side, and the jump amplitude of v_{c} is an increasing function of the spin-dependent interaction strength. Beyond the critical velocity, the energy dissipation rate of the impurity is explicitly calculated via a perturbation approach. The discontinuity of v_{c} at the phase boundary can be clearly seen from the dissipation curves, which can be measured through the heating of the condensate. Our prediction can be tested in the current experiments with ultracold atoms.

Project supported by the National Natural Science Foundation of China (Grant No. 11674202), and the Applied and Fundamental Research Program of Shanxi Province, China (Grant No. 201601D011014).