Spontaneous radiation and amplification of Kelvin waves on quantized vortices in Bose-Einstein condensates

Abstract

We propose a different type of Landau instability in trapped Bose-Einstein condensates by a helically moving environment. In the presence of quantized vortices, the instability can cause spontaneous radiation and amplification of Kelvin waves. This study gives a microscopic understanding of the Donnelly-Glaberson instability which was known as a hydrodynamic instability in superfluid helium. The Donnelly-Glaberson instability can be a powerful tool for observing the dispersion relation of Kelvin waves, vortex reconnections, and quantum turbulence in atomic Bose-Einstein condensates.

Quantum hydrodynamics

“…The instability can occur in superfluid 3 He-B in a rotating cylinder, where the rotating counterflow of a vortex-free superfluid component and a rotating normal fluid component is realized [154]. In atomic BECs, it was proposed that the Kelvin-wave instability can be induced as a spontaneous excitation of a kelvon, a quantum of a Kelvin wave due to the Landau instability [155]. The Kelvin-wave instability has also been discussed for quantized vortices in a rotating neutron star [156,157].…”

Quantized vortices in superfluid helium and atomic Bose– Einstein condensates

“…When an additional velocity V is applied along the z-axis, the dispersion of the vortex waves behaves as ω − V k z , and the frequency can become negative above the critical velocity. This is known as the Donnely-Glaberson instability in superfluid helium [203], and it results in the amplification of Kelvin waves [204]. This could induce reconnections of adjoining vortex lines, and eventually a turbulent state.…”

“…(a) Dispersion relation of the axisymmetric single-vortex state of Kelvin waves with l = −1 (dashed line), varicose waves with l = 0 (dotted line), and several surface waves with l > 0 (solid lines), calculated for a cylindrically symmetric condensate with a vortex (see Ref [204]…”

Nambu-Goldstone modes in segregated Bose-Einstein condensates

“…When there is a straight vortex along the z axis in a uniform system, the translational symmetries in the x and y directions are explicitly broken, and thus n SSB = 3. However, there are only two NG modes: the Kelvin mode with a quadratic dispersion, which causes helical deformation of a vortex line, and the varicose mode with a linear dispersion, which corresponds to a phonon propagating along the vortex core [10,13,14]. Another example can be seen in Tkachenko modes of two-dimensional vortex lattices in rotating superfluids [9].…”