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arXiv:0812.0863 · Physical Review A

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

Hiromitsu Takeuchi, Kenichi Kasamatsu, Makoto Tsubota

Published Mar 18, 2009• 14 citations
arXivHTMLPDF

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 the 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.

DOI
10.1103/physreva.79.033619

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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 the 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.
The Donnelly-Glaberson (DG) instability causes the amplification of Kelvin waves on vortex lines in superfluid 4 He and 3 He-B at finite temperatures due to mutual friction between vortex lines and the normal fluid component. In this letter, we theoretically show that the DG instability is possible in atomic Bose-Einstein condensates even at T = 0 K without the normal component. The DG instability in atomic condensates can lead to observe the dispersion relation of Kelvin waves, vortex reconnections and quantum turbulence.
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.
We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.
We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose–Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin–Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system’s boundary is found to dominate.
Spontaneous pattern formation out of homogeneous media is one of the well-understood examples of hydrodynamic instabilities in classical systems, which naturally leads to the question of its manifestation in quantum fluids. Bose-Einstein condensates (BECs) of atomic gases have been an ideal platform for studying many-body quantum phenomena, such as superfluidity, and simultaneously providing an opportunity to broaden our understanding of classical hydrodynamics into quantum systems. In this review, we introduce a range of experimental studies on the pattern formation in quantum fluids of atomic gases under external driving, including Faraday waves in one and two dimensions, surface patterns, and counterflow instabilities in a mixture of superfluids. The pattern formation in the quantum system can be understood through the parametric amplification process, where an unstable dynamical mode can be exponentially amplified, similar to classical systems. Remarkably, the governing equations for surface excitations of trapped BECs can be mathematically equivalent to those of shallow water, indicating a universal description of the hydrodynamic instability across classical and quantum domains. However, the condensates, as superfluids, also possess fundamental quantum characteristics, such as quantized vorticity and a distinct dissipation channel. These unique features showcase many-body fragmentation under strong modulation and the generation of vortices in the nonlinear regime, which could offer a pathway to the study of quantum turbulence. Furthermore, the coexistence of long-range phase coherence and density modulation in driven condensates could provide unexplored features, such as those seen in supersolid-like sound modes, within nonequilibrium settings.
The dynamics of quantized vortices in weakly interacting superfluids are often modeled by a nonlinear Schrödinger equation. In contrast, we show that quantized vortices in fact obey a non-Hamiltonian evolution equation, which enhances dispersion along the vortex line while introducing a gain mechanism. This allows the vortex medium to support a helical shock front propagating ahead of a dissipative soliton. This dynamic relaxes localized curvature events into Kelvin wave packets. Consequently, a beyond local induction model provides a pathway for decay in low-temperature quantum turbulence.