Direct excitation of Kelvin waves on quantized vortices

Abstract

Helices and spirals, prevalent across various systems, play a crucial role in characterizing symmetry, describing dynamics, and imparting unique functionalities, attributed to their inherent simplicity and chiral nature. A helical excitation on a quantized vortex, an example of a one-dimensional topological defect, emerges as a Nambu-Goldstone mode following spontaneous symmetry breaking, known as a Kelvin wave. Kelvin waves play a vital role in energy dissipation within inviscid quantum fluids. However, deliberately exciting Kelvin waves has proven to be challenging. Here, we introduce a controlled method for exciting Kelvin waves on a quantized vortex in superfluid helium-4. We used a charged nanoparticle, oscillated by a time-varying electric field, to stimulate Kelvin waves on the vortex. A major breakthrough in our research is the confirmation of the helical nature of Kelvin waves through three-dimensional image reconstruction, providing visual evidence of their complex dynamics. Additionally, we determined the dispersion relation and the phase velocity of the Kelvin wave and identified the vorticity direction, enhancing our understanding of quantum fluid behavior. This work elucidates the dynamics of Kelvin waves and pioneers a novel approach for manipulating and observing quantized vortices in three dimensions, thereby opening new avenues for exploring quantum fluidic systems.

Figures (4)

• Figure 1: Kelvin wave excitation and its dispersion relation. a-d, Single quantized vortex visualized using silicon nanoparticles before (a) and at different stages during (b-d) the application of AC electric fields at 0.8 Hz (b), 1.5 Hz (c) and 2.5 (d) Hz. e, Dispersion relation of the excited Kelvin wave with a theoretical fit line. Each error bar indicates the 99 % confidence interval.
• Figure 2: Experimental three-dimensional visualization of Kelvin wave dynamics along a quantized vortex a, Schematics of the experimental setup: one camera was positioned to capture a front view of the Kelvin wave, while the second camera used a mirror to achieve a bottom view. b,f,j, Front views of the Kelvin wave at $t=3.06$ s (b), $t=4.00$ s (e), and $t=4.93$ s (h). Red curves are traced splines representing the part of the vortex line. c,g,k, Corresponding bottom views. d,e,h,i,l,m, Reconstructed three-dimensional Kelvin wave. The color of the curve varies along its length in a rainbow spectrum, corresponding to the $x$-coordinate of each point, to enhance three-dimensional recognition. Green lines are guides to clarify the handedness of the Kelvin wave (see body text). Both the front (d, h, and l) and side (e, i, and m) views are crucial for fully appreciating the helical shape: the front view more clearly reveals the handedness, while the side view distinctly showcases the circular shape.
• Figure 3: Numerical simulation of Kelvin wave excitation on a quantized vortex. a, A straight quantized vortex filament before the excitation, with the red mark representing the charged nanoparticle and the purple arrow indicating the circular velocity field around the quantized vortex. b-d, Two Kelvin waves propagating in opposite directions with opposite handednesses. Green lines are provided as guides to clarify the handedness of the Kelvin wave.
• Figure 4: Propagation of Kelvin waves. a-d, the Kelvin wave shown in Fig. \ref{['fig:3d']} propagating to the right. e, Position of the phase front as a function of time. f, g. Propagation of right-handed (f) and left-handed (g) Kelvin waves. Red arrowheads and purple arrows indicate the directions of the vorticity. A right-handed Kelvin wave propagates parallel to the vorticity direction(f), while a left-handed Kelvin wave propagates anti-parallel to the vorticity direction(g).