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arXiv:cond-mat/9812080 · Physical Review Letters

Pressure Drag in Linear and Nonlinear Quantum Fluids

T. Winiecki, J F McCann, Charles S. Adams

Published Jun 28, 1999• 150 citations
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Abstract

We study the flow of a weakly interacting Bose-Einstein condensate around an obstacle by numerical solution of the Gross-Pitaevskii equation. We observe vortex emission and the formation of bow waves leading to pressure drag. We compare the drag law with that of an ideal Bose gas, and show that interactions reduce the drag force. This reduction can be explained in terms of a ``collisional screening'' of the obstacle.

DOI
10.1103/physrevlett.82.5186

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We study the flow of a weakly interacting Bose-Einstein condensate around an obstacle by numerical solution of the Gross-Pitaevskii equation. We observe vortex emission and the formation of bow waves leading to pressure drag. We compare the drag law with that of an ideal Bose gas, and show that interactions reduce the drag force. This reduction can be explained in terms of a ``collisional screening'' of the obstacle.
We investigate by numerical simulations the pattern formation after an oscillating attractive-repulsive obstacle inserted into the flow of a Bose-Einstein condensate. For slow oscillations we observe a complex emission of vortex dipoles. For moderate oscillations organized lined up vortex dipoles are emitted. For high frequencies no dipoles are observed but only lined up dark fragments. The results shows that the drag force turns negative for sufficiently high frequency. We also successfully model the ship waves in front of the obstacle. In the limit of very fast oscillations all the excitations of the system tend to vanish.
The motion of a body through a superfluid can generate phenomena distinct from a normal viscous fluid. This includes the absence of drag below a critical body speed with the shedding of quantised vortices and non-zero drag above this speed. These phenomena are often modelled using the Gross–Pitaevskii (GP) equation, which describes the wavefunction of a weakly interacting Bose–Einstein condensate and its superfluid dynamics. We study the drag experienced by a penetrable circular disk of radius, aaa , in the form of a two-dimensional potential barrier of height, V0V_0V0​ , that is moving in a superfluid of bulk density, n∞n_\inftyn∞​ , by solving the GP equation. The drag is found to exhibit a unimodal dependence on the disk speed for a fixed value of its barrier height. This behaviour is quantified analytically and confirmed using direct numerical solution. The maximum drag per unit length of Fdragmax≈5an∞V0F_{\textit{drag}}^{\textit{max}} \approx 5 a n_\infty V_0Fdragmax​≈5an∞​V0​ occurs when the barrier height coincides with the relative kinetic energy of the fluid particles. Flow excitations are diminished at a high particle kinetic energy with a commensurate reduction in the drag. This generates a saddle-node bifurcation in the dynamics of a moving disk under an applied force. These results advance understanding of the motion of bodies with finite penetrability, which is relevant to laser experiments probing the superfluidity of Bose–Einstein condensates.
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.
We derive a microscopic theory of drag for a Bose-Einstein condensate interacting with a moving reservoir. Starting from interactions between a condensate and a drifting fermionic bath, we integrate out the bath degrees of freedom within the Born--Markov approximation to obtain an effective Gross--Pitaevskii equation with a drag potential. From this potential we derive an effective drag force and obtain a closed expression for the drag coefficient, determined by the reservoir density fluctuations and the condensate density profile. As an application, we simulate the drag for an exciton--polariton condensate interacting with a drifting electron gas.
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.
Dark solitons dynamically generated from a potential moving in a one-dimensional Bose-Einstein condensate are displayed. Based on numerical simulations of the Gross-Pitaevskii equation, we find that the moving obstacle successively emits a series of solitons which propagate at constant speeds. The dependence of soliton emission on the system parameters is examined. The formation mechanism of solitons is interpreted as interference between a diffusing wavepacket and the condensate background, enhanced by the nonlinear interactions. PACS numbers: 03.75.Mn, 03.75.Lm, 05.30.Jp