Evidence for Vortex Rings with Multiquantum Circulation in He II

Abstract

Quantized vortex dynamics in superfluid $^4$He (He~II) are widely regarded as well established: circulation is quantized in units of $κ=h/m_4$, vortices carrying more than one quantum are expected to split into singly quantized filaments, and vortex rings shrink while accelerating due to dissipation from thermal-quasiparticle scattering. Using particle tracking velocimetry with frozen deuterium tracers, we uncover rare vortex-bound particle events that disrupt this canonical picture. In a class of events exhibiting the acceleration characteristic of shrinkage driven vortex ring motion, the measured kinematics cannot be reconciled with a singly quantized ring. Instead, they require an effective circulation $nκ$ with $n>1$, directly challenging the standard expectation that multiquantum vortices are short lived. A more prosaic possibility is that the inferred $nκ$ arises from a bundle of closely spaced singly quantized rings, which could generate similar large-scale motion. However, this scenario is disfavored by vortex-filament simulations that show rapid bundle dispersion. Furthermore, the persistence of particle trapping at the observed high speeds suggests a much deeper core trapping potential, consistent only with a truly multiquantum core. Together, these results point to anomalously long-lived multiquantum rings, a striking puzzle that calls for dedicated scrutiny beyond the prevailing paradigm.

Figures (4)

• Figure 1: Vortex-bound particle events suggesting multiquantum vortex-ring kinematics.a Schematic of the experimental setup. b,c Superimposed image sequences for two representative events recorded at heater-surface voltages $V_\mathrm{H}=0$ V and $+10$ V, respectively; red arrows indicate the direction of motion. d,e Measured particle speed $v_p(t)$ along the trajectories in b and c. Solid curves show the predicted ring propagation speed $v_{\parallel,n}(t)$ for various circulations $n\kappa$, with each curve initialized by matching the starting speed $v_p(0)$. Shaded bands represent the resulting spread in $v_{\parallel,n}(t)$ due to the uncertainty in $v_p(0)$.
• Figure 2: Deduced parameters of multiquantum vortex-ring events.a Best-matched circulation number $n$ and initial radius $R(0)$ for all events collected at different temperatures and heater-surface voltages $V_\mathrm{H}$. b Normalized radius evolution, $R^2(t)/R^2(0)$, plotted versus normalized time $t/\tau$ for representative events. Here $R(t)$ is inferred from the particle speed $v_p(t)$, and the time scale $\tau$ is defined in the text.
• Figure 3: Schwarz model simulations showing rapid dispersion of singly quantized vortex-ring bundles. For both cases at $T=1.65$ K and $2.0$ K, the bundle is initialized with five vortex rings of mean radius $R(0)=100$$\mu$m and an inter-ring spacing of 2 $\mu$m. The bundles at later times are rendered in different colors for better visibility.
• Figure 4: Ratio of the observed final particle speed $v_p(t_f)$ to the drag-limited detrapping threshold velocity $v_{th}=\rho_s(n\kappa)^2/18\pi^2 a_p\mu_n$.