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Physical Review B

Observation of an extrinsic critical velocity using matter wave interferometry

Yuki Sato, Aditya Joshi, R. E. Packard

Published Aug 13, 2007• 12 citations
Publisher

Abstract

We report an experiment that uses a superfluid helium quantum interference device to probe the initial onset of the motion of a single vortex line driven by axial flow in a macroscopic channel. When the superfluid velocity reaches a temperature independent critical value $({v}_{c}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{mm}∕\mathrm{s})$ periodic $2\ensuremath{\pi}$ phase slippage occurs with a frequency of the order of a few Hz. As the axial flow velocity increases, the frequency increases, possibly stepwise.

DOI
10.1103/physrevb.76.052505

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We report an experiment that uses a superfluid helium quantum interference device to probe the initial onset of the motion of a single vortex line driven by axial flow in a macroscopic channel. When the superfluid velocity reaches a temperature independent critical value (vc\ensuremath∼1mm∕s)({v}_{c}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{mm}∕\mathrm{s})(vc​\ensuremath∼1mm∕s) periodic 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ phase slippage occurs with a frequency of the order of a few Hz. As the axial flow velocity increases, the frequency increases, possibly stepwise.
Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing.
Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold vc{\mathit{v}}_{\mathit{c}}vc​. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.
We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose–Einstein condensate in the presence of a repulsive optical barrier. Using the Gross–Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier and decays through the mechanism of phase slippage performed by pairs of vortex–antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross–Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, v barr = c l . In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity v f is much lower than the observed critical velocity. We argue that this is a general feature of the Gross–Pitaevskii equation, where we have v f = c l with being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.
Abstract We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.