Vacuum tunneling of vortices in two-dimensional $^4$He superfluid films

Abstract

At low temperature T we expect vacuum tunneling processes to occur in superfluid $^{4}$ He films. We distinguish between extrinsic processes, in which single vortices nucleate by tunneling off boundaries in the system, and intrinsic processes, in which vortex/anti-vortex pairs nucleate far from boundaries. It is crucial to incorporate the varying effective mass of the vortex in tunneling calculations. The intrinsic processes are the superfluid analogue of the Schwinger mechanism in quantum field theory; here they appear as a quantum phase transition at T = 0, driven by an external supercurrent. We calculate the tunneling rate for these processes, and describe a means of testing the predictions using a specific vortex counting experiment.

Figures (3)

• Figure 1: Two geometries for extrinsic processes; we view the superfluid from above (looking down on the xy-plane. In (a) we have a vortex in a circular cylinder of radius $R_0$, with the vortex at a distance $R_V$ from the centre. In (b) superflow moves at velocity $\boldsymbol{v}_s$ along the $\hat{x}$ axis past a semicircular protuberance or "bump" attached to a straight boundary with surface normal along the $\hat{y}$ axis. The vortex is at position vector ${\bf R}_V$, at distance $R_V$ from the bump centre, and ${\bf R}_V$ has angle $\alpha$ with respect to $\boldsymbol{v}_s$.
• Figure 2: A plot of the hydrodynamic superflow energy for the semicircular bump geometry of Fig \ref{['fig:Vortex-1']}(b), where this bump is depicted in red and the energy surface in blue-green. One can see that the tunneling probability is maximized along the trajectory $\alpha=\frac{\pi}{2}$, shown as a white line in the figure.
• Figure 3: A plot of the vortex/anti-vortex pair potential, in units of $E_0=\rho_s \kappa^2/4\pi$ in \ref{['eq:Vortex-Anti-Vortex WKB action']} for various values of the dimensionless external superflow velocity $u_{0}=v_0/v_c= 2\pi xi_0 v_s/\kappa$ and where the superflow critical velocity is $v_{c} = \kappa/2\pi xi_0$.