The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling.This phase has been recently found experimentally [J.Li et al., Nature (London) 543, 91 (2017)].In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity.Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed.Moreover, due to the spin-orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity.Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.
The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling.This phase has been recently found experimentally [J.Li et al., Nature (London) 543, 91 (2017)].In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity.Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed.Moreover, due to the spin-orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity.Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.
Abstract The phase diagram of a spin–orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin–orbit coupling. This phase has been recently found experimentally [31]. In the present work, we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed. Moreover, due to the spin–orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity. Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities, the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.
The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.
The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.
We investigate the drag force on a moving impurity in a spin-orbit-coupled Bose-Einstein condensate. We prove rigorously that the superfluid critical velocity is zero when the impurity moves in all directions but one, in contrast to the case of liquid helium and superconductor, where it is finite in all directions. We also find that when the impurity moves in all directions except the two special ones, the drag force has nonzero transverse component with a small velocity. When the velocity becomes large and the states of the upper band are also excited, the transverse force becomes very small due to opposite contributions of the two bands. The characteristics of the superfluid critical velocity and the transverse force are results of the order-by-disorder mechanism in spin-orbit-coupled boson systems.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.
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 87Rb 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 vc 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 vc on the PW phase side of the transition is generally smaller than the one on the ZM phase side, and the jump amplitude of vc 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 vc 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.