Observation of an extrinsic critical velocity using matter wave interferometry

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 $(v_c\sim 1\mathrm{mm}∕\mathrm{s})$ periodic $2\pi$ phase slippage occurs with a frequency of the order of a few Hz. As the axial flow velocity increases, the frequency increases, possibly stepwise.

Figure 1

Schematic of our experimental configuration. The inside of the flow tube is filled with superfluid ${}^4\mathrm{He}$ and the entire apparatus is immersed in a bath of liquid helium. A resistive heater and a thin Cu sheet serve as a heat source and a sink. The tube is made of Stycast 1266 (insulating) to minimize the heat loss through the walls. The tube is connected to a superfluid helium quantum interference device (SHeQUID)[12] at two locations (separated by distance $l$) enabling us to monitor the phase difference $\Delta \varphi$ that exists between them. Here, $v_s$ and $v_n$ indicate superfluid and normal fluid velocities, respectively.

Figure 2

Interferometer output $[\propto \cos (\Delta \varphi ∕2)]$ as a function of time when (a) $\dot{Q}<{\dot{Q}}_c$ and (b) $\dot{Q}>{\dot{Q}}_c$. These data are taken at $T_{\lambda }-T\approx 16\mathrm{mK}$. At this temperature, ${\dot{Q}}_c\approx 130\mu \mathrm{W}$, and the phase difference $\Delta \varphi$ at ${\dot{Q}}_c$ is on the order of $250\times 2\pi$.

Figure 3

Frequency of interferometer output oscillation as a function of power input. Zero frequency means that the interferometer signal $[\propto \cos (\Delta \varphi ∕2)]$ is constant in time. Plots are separated for clarity.