Reproducible nucleation and control of stable quantum vortex rings in Bose-Einstein condensates

Abstract

We propose and numerically validate an experimentally feasible on-demand protocol for the nucleation and manipulation of stable quantum vortex rings in trapped Bose-Einstein condensates. The method relies on sweeping a laser-sheet barrier that locally constricts the superflow and triggers vortex-ring formation. By tuning the barrier height and width, and by scanning the barrier velocity, we identify the onset of periodic generation of vortex rings above the critical velocity and achieve direct, deterministic control over the ring nucleation position, radius, and hence propagation speed. After its formation, ad-hoc optical potentials are applied to reshape the vortex ring, creating clean Kelvin-wave excitations. Our results provide a foundation for systematic studies of three-dimensional vortices in atomic superfluids and open the door to tailored vortex dynamics and interactions, enabling controlled access to quantum turbulence.

Figures (12)

• Figure 1: Stages of vortex ring nucleation and evolution, shown via BEC density isosurfaces at 5% of the maximum density and density $\rho$ -phase $\phi$ projections on the plane $y=0$ at different times in the reference frame where the barrier is stationary. Left panel: Ring generation triggered by the moving barrier (white arrow); red arrows in the phase snapshot indicate the circulation of the velocity field. Central panel: Shrinking across the barrier: the ring propagates opposite to the barrier motion (purple arrow) while its radius decreases. Right panel: Propagation in the bulk and periodic generation: the first ring reaches an asymptotic regime with constant radius and velocity; meanwhile, additional rings are generated periodically and eventually reach the same asymptotic properties. In the isosurfaces, the vortex rings are represented by circles displayed in different shades of blue. The red curves on the density-phase plots show the low-density isocontour at $2.5\%$ of the maximum density, marking the condensate edge and the density depletions corresponding to vortex cores.
• Figure 2: Critical velocity $v_c$ for vortex ring nucleation as a function of barrier height $V_0/\mu$ (pink stars, fixed $\sigma_b=5\xi$) and of barrier width $\sigma_b$ (purple circles, fixed $V_0=0.6\mu$). Inset: vortex nucleation frequency $\nu$ at fixed $V_0=0.6\mu$ and $\sigma_b=5\xi$ as a function of barrier velocity $v_b^\mathrm{max}>v_c$ (blue squares), spanning from $v_c$ to $1.78v_c$; the dashed line represents a linear fit of the data. Empty squares represent the cases where we observe leapfrogging events. Velocities are expressed in units of the density-averaged speed of sound $c_\infty=\sqrt{\mu/2}$.
• Figure 3: Top panel: Initial (light--blue squares) and asymptotic (lilac triangles) vortex ring radii $R$ at critical barrier velocity as a function of the barrier intensity $V_0/\mu$ with fixed $\sigma_b=5\xi$. Inset: $R$ as a function of barrier width $\sigma_b$ with fixed $V_0=0.6\mu$. Open lilac circles indicate asymptotic radii set to zero as the rings self-annihilate before reaching an asymptotic regime. Bottom panel: Asymptotic vortex ring axial velocity $V^z$ as a function of its asymptotic radius $R$ reported in the top panel. Inset: Kinetic energy $E$ of a cylindrical condensate in the presence of a vortex ring as a function of the ring's radius $R$; the dashed gray line at $R=0.5R_{\perp_\infty}$ marks where the slope would change sign in a homogeneous system. Here $n_0$ indicates the particle number density on the cylinder axis.
• Figure 4: Triggering of $m=2$ Kelvin waves on a vortex ring. Top panel: Time evolution of the eccentricity of the vortex ring projection on the $x$-$y$ plane. Left inset: BEC density iso-surface, with the two local vertical potentials $V_i(\mathbf{x})$ represented as pink columns. Right inset: when the ring approaches the obstacles, they break the symmetry and excite oscillations of its semiaxes $a$ and $b$; the dashed gray curve is a sinusoidal fit that matches the theoretical frequency of the $m=2$ Kelvin wave. Bottom panel: Time evolution of the mean radius $\bar{R}=(a+b)/2$ (left axis, lilac triangles) and the velocity $V^z$ of the vortex ring (right axis, light-pink circles). The blue area represents the region where the vortex interacts with the moving barrier, while the yellow area the region where it is affected by the vertical obstacles.
• Figure 5: Axial momentum $p_z$ of a cylindrical condensate in the presence of a vortex ring as a function of the ring's radius $R$.