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arXiv:1511.00886 · Physical Review A

Noncollinear drag force in Bose-Einstein condensates with Weyl spin-orbit coupling

Renyuan Liao, Oleksandr Fialko, Joachim Brand, Ulrich Zülicke

Published Feb 17, 2016• 8 citations
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Abstract

We consider the motion of a pointlike impurity through a three-dimensional two-component Bose-Einstein condensate subject to Weyl spin-orbit coupling. Using linear-response theory, we calculate the drag force felt by the impurity and the associated anisotropic critical velocity from the spectrum of elementary excitations. The drag force is shown to be generally not collinear with the velocity of the impurity. This unusual behavior is a consequence of condensation into a finite-momentum state due to the spin-orbit coupling.

DOI
10.1103/physreva.93.023625

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We consider the motion of a pointlike impurity through a three-dimensional two-component Bose-Einstein condensate subject to Weyl spin-orbit coupling. Using linear-response theory, we calculate the drag force felt by the impurity and the associated anisotropic critical velocity from the spectrum of elementary excitations. The drag force is shown to be generally not collinear with the velocity of the impurity. This unusual behavior is a consequence of condensation into a finite-momentum state due to 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.
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.
We study the motion of a pointlike impurity in a Bose-Einstein condensate at T=0T=0T=0. By solving the Gross-Pitaevskii (GP) equation in a perturbative manner we calculate the induced mass of the impurity and the drag force on the impurity in three-, two-, and one-dimensional (1D) cases. The relationship between the induced mass and the normal mass of fluid is found, and coincides with the result of the Bogoliubov theory. The drag force appears for the supersonic motion of the impurity. In 1D the drag force is investigated also on the basis of the exact Lieb-Liniger theory, using the dynamic form factor, which has been evaluated by the Haldane method of the calculation of correlation functions. In this theory the force appears for an arbitrarily small velocity of the impurity. The possibility of measuring the form factor in existing experiments is noted.
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 We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose–Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey–Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes’ drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity’s speed.
It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.