Direct observation of Kelvin waves excited by quantized vortex reconnection

Abstract

Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid 4 He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system. topological defects | turbulence | cascade V orticity in superfluids and Bose-Einstein condensates is constrained to line-like topological defects called quantized vortices (1). The evolution of a tangle of such line vortices defines a dynamical state known as quantum turbulence (see, e.g., refs. 2, 3). Quantum turbulence is in some ways similar to classical turbulence; for example, both show a Kolmogorov energy spectrum (4, 5). However, many features of quantum turbulence, such as its velocity statistics (6, 7), are distinct from classical flows.A fundamental question in quantum turbulence is the nature of dissipation in the zero-temperature limit (8) where the effects of friction vanish. The vortex-tangle decay, observed experimentally even for T < 0.1 K (9), requires a different dissipation mechanism from the classical case; a promising candidate is the excitation of waves by reconnecting vortices (Fig. 1). In his pioneering work (11), Kelvin showed that a helical deformation of a line vortex propagates as a wave. Kelvin waves have long been used to understand a wide range of flow problems, such as airplane wakes (12), tornadoes (13), and the dynamics of neutron stars (14), and are also conceptually related to whistler waves in plasmas (15). Theory and simulations indicate that a cascade of Kelvin waves transfers energy from large length scales (the intervortex spacing) to small scales (the vortex-core size) (16-18), where energy is removed from the system via phonon emission (19-21).Kelvin waves have been visualized in classical fluids only on thin line vortices (22, 23) and on knotted vortex rings (24). Here we present a unique direct observation of Kelvin waves on quantized vortices and give unique experimental evidence of the emission of Kelvin waves after vortex reconnection. Because our fluid is inviscid and the amplitude H of the waves we observe is much larger than the vortex core size a 0 (we have H=a 0 > 10 5 ), our system satisfies most of the assumptions originally made by Kelvin for his eponymous waves.Kelvin waves on quantized vortices were first detected indirectly, using torsional oscillators (1, 25), beginning with the work of Hall in 1958 (26). However, the interpretation of such experiments has been criticized (27); additional evidence is therefore needed (1). Ashton and Glaberson (28) measured the velocity of ions passing through the superfluid as a function of an ...

Introduction to quantum turbulence

“…Kelvin waves arise from the tension of the vortex lines (the kinetic energy of a circulating superfluid about a unit length of line). Their direct observation is reported in the article by Fonda et al (9). At finite temperatures, Kelvin waves are damped by mutual friction, but, below 1 K, they propagate more freely and lead to acoustic emission at large values of k. The transfer of energy to such large k by a Kelvin wave cascade (analogous to the Kolmogorov cascade of classical turbulence) explains the observed decay of turbulence at low temperatures, as discussed in the articles by Barenghi et al (10) and by Walmsley et al (11); in the weak-amplitude regime, Kelvin waves can be studied using wave-turbulence theory [see the article by Kolmakov et al (12)].…”

Gapless excitations of axially symmetric vortices in systems with tensorial order parameter

“…We have shown that in the case that γ 23 = 0 the classical low energy theory includes the translational modulus fields presenting the well studied Kelvin excitations (see [2,3,4,5,6,7,8,9]). In addition, the theory contains three additional moduli from the breaking of the nonAbelian U(1) A × SO(3) J int to the locked orbital-phase U(1) A+J int z group.…”

“…Specifically, we have shown that out of the five moduli emerging from the broken symmetry, only three appear as independent Goldstone modes after quantization. Two of these are the type A Kelvin mode and the type B axial U(1) A mode, which have been well studied both experimentally and theoretically [2,3,4,5,6,7,8]. The additional mode is the type A internal non-Abelian mode resulting from the breaking of SO(3) J int by the vortex line.…”

“…In that work we provided a method for determining the type and number of moduli appearing on mass vortices under the restriction that the 3 × 3 matrix order parameter contained only its diagonal (δ µi ) and antisymmetric off-diagonal (ε µik χ k ) elements, setting its symmetrictraceless part to zero. Although this restriction was not necessarily experimentally sound, it allowed the calculations to be carried out with relative ease while still providing enough complexity to illustrate the development of non-Abelian moduli and their interactions with the already well studied translational moduli (Kelvin modes) [2,3,4,5,6,7,8,9]. The presentation of that work was also purely classical and we made no attempt to discuss time dependence or quantization, which may alter the number of gapless excitations determined from the modulus fields.…”

Scaling laws of wave-cascading superfluid turbulence

“…52 The physics of Kelvin-wave and its cascade is less understood from an experimental point of view; there are only little direct observations. 52,53 Three-wave couplings among the Kelvin waves themselves are forbidden because of the violation in the energy and momentum conservations. Kelvin wave self-interactions are a four-wave or a six-wave coupling in the lowest orders 54 and there are competing models on the cascade process (e.g., Kozik-Svistunov model and L'vov-Nazarenko model).…”