Quadrupole oscillation of a single-vortex Bose-Einstein condensate: evidence for Kelvin modes

We study the two transverse quadrupole modes of a cigar-shaped Bose-Einstein condensate with a single centered vortex. We show that the counterrotating mode is more strongly damped than in the absence of a vortex, whereas the corotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counterrotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the vortex line.     

Experimental observation of Beliaev coupling in a Bose-Einstein condensate

We report the first experimental observation of Beliaev coupling between collective excitations of a Bose-Einstein condensed gas. Beliaev coupling is not predicted by the Gross-Pitaevskii equation and so this experiment tests condensate theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode show that the Beliaev process transfers energy to a lower-lying mode and then back and forth between these modes, unlike Landau processes which lead to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between the two scissors modes.     

Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates

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.     

Experimental observation of the tilting mode of an array of vortices in a dilute Bose-Einstein condensate

We have measured the precession frequency of a vortex lattice in a Bose-Einstein condensate of Rb87 atoms. The observed mode corresponds to a collective motion in which all the vortices in the array are tilted by a small angle with respect to the z axis (the symmetry axis of the trapping potential) and synchronously rotate about this axis. This motion corresponds to excitation of a Kelvin wave along the core of each vortex and we have verified that it has the handedness expected for such helical waves, i.e., precession in the opposite sense to the rotational flow around the vortices.     

Vortex reconnection in a swirling flow

Processes of vortex reconnection on a helical vortex, which is formed in a swirling flow in a conical diffuser, have been studied experimentally. It has been shown that reconnection can result in the formation of both an isolated vortex ring and a vortex ring linked with the main helical vortex. A number of features of vortex reconnection, including the effects of asymmetry, generation of Kelvin waves, and formation of various bridges, have been described.     

Dissipation of vortex disturbances in a vibrationally nonequilibrium diatomic gas

The influence of the vibrational relaxation on suppression of the Kelvin??Helmholtz instability in an evolving shear layer of a vibrationally nonequilibrium diatomic gas is studied numerically on the basis of equations of two-temperature aerohydrodynamics. Planar waves with the maximum growth rates, which were computed within the framework of a linearized system of equations of inviscid two-temperature gas dynamics, are used as the initial disturbances. It is shown that relaxation of the nonequilibrium vibrational mode at excitation levels, which can be obtained in diatomic gases in nozzle flows, in underexpanded jets, or in flows with moderate laser pumping, is accompanied by noticeable suppression of vortex disturbances. The associated relative enhancement of dissipation of kinetic energy of a large vortex structure averaged over its ??lifetime?? reaches approximately 13 %.     

Kelvin waves cascade in superfluid turbulence

We study numerically the interaction of four initial superfluid vortex rings in the absence of any dissipation or friction. We find evidence for a cascade of Kelvin waves generated by individual vortex reconnection events which transfers energy to higher and higher wave numbers k. After the vortex reconnections occur, the energy spectrum scales as k(-1) and the curvature spectrum becomes flat. These effects highlight the importance of Kelvin waves and reconnections in the transfer of energy within a turbulent vortex tangle.     

Beliaev damping of quasiparticles in a Bose-Einstein condensate

We report a measurement of the suppression of collisions of quasiparticles with ground state atoms within a Bose-Einstein condensate at low momentum. These collisions correspond to Beliaev damping of the excitations, in the previously unexplored regime of the continuous quasiparticle energy spectrum. We use a hydrodynamic simulation of the expansion dynamics, with the Beliaev damping cross section, in order to confirm the assumptions of our analysis.     

Universal mechanism of dissipation in Fermi superfluids at ultralow temperatures

We show that the vortex dynamics in Fermi superfluids at ultralow temperatures is governed by the local heating of the vortex cores creating the heat flux carried by nonequilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of ^{3}He-B, the temperature of the vortex cores is estimated to be of the order 0.2 T(c). The dispersion of Kelvin waves is derived, and the heat flow generated by Kelvin cascade is shown to have a value close to that experimentally observed.     

Kelvin-wave cascade on a vortex in superfluid 4He at a very low temperature

A study by computer simulation is reported of the behavior of a quantized vortex line at a very low temperature when there is continuous excitation of low-frequency Kelvin waves. There is no dissipation except by phonon radiation at a very high frequency. It is shown that nonlinear coupling leads to a net flow of energy to higher wave numbers and to the development of a simple spectrum of Kelvin waves that is insensitive to the strength and frequency of the exciting drive. The results are likely to be relevant to the decay of turbulence in superfluid 4He at very low temperatures.     

Vortex sink under conditions of a thermal choking with regard to the real properties of gases

Changes in the formulation of the problem for a vortex source and a vortex sink upon taking into account the change in the heat capacity and the adiabatic exponent for a diatomic gas (for the example of air) in response to an increase in the temperature from 300 K to a few thousands of Kelvin are discussed. A thermal choking is studied for a vortex sink, and critical values of the energy parameter are calculated. It is shown that the minimal radius of the vortex sink decreases upon a heat release. Similarity parameters including the dimensionless circulation (or mass flow), the energy parameter, and the position and thickness of the heat-release region are varied. Errors of the gas model that assumes constant heat capacities and a constant adiabatic exponent are estimated.     

Effective temperature and scaling laws of polarized quantum vortex bundles

An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A∝k−1/2, follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.     

Three-wave mixing of bogoliubov quasiparticles in a bose-einstein condensate

A dressed basis is used to calculate the dynamics of three-wave mixing between Bogoliubov quasiparticles in a Bose condensate. Because of the observed oscillations between different momentum modes, an energy splitting, analogous to the optical Mollow triplet, appears in the Beliaev damping spectrum of the excitations from the oscillating modes.     

Geometric Properties of the Maxwell Set and a Vortex Filament Structure for Burgers Equation

The inviscid limit of the stochastic Burgers equation is discussed in terms of the level surfaces of the minimising Hamilton–Jacobi function, the classical mechanical caustic and the Maxwell set and their algebraic pre-images under the classical mechanical flow map. We examine the geometry of the Maxwell set in terms of the behaviour of the pre-Maxwell set, the pre-caustic and the pre-level surfaces. In particular, contrary to the ideas of Helmholtz and Lord Kelvin, we prove that even if initially the fluid flow is irrotational, in the inviscid limit, associated with the advent of the Maxwell set a non-zero vorticity vector forms in the fluid with vortex lines on the Maxwell set. This suggests that in quite general circumstances for small viscosity there is a vortex filament structure near the Maxwell set for both deterministic and stochastic Burgers equations.      

Vortex multiplication in applied flow: A precursor to superfluid turbulence

A surface-mediated process is identified in 3He-B which generates vortices at a roughly constant rate. It precedes a faster form of turbulence where intervortex interactions dominate. This precursor becomes observable when vortex loops are introduced in low-velocity rotating flow at sufficiently low mutual friction dissipation at temperatures below 0.5Tc. Our measurements indicate that the formation of new loops is associated with a single vortex interacting in the applied flow with the sample boundary. Numerical calculations show that the single-vortex instability arises when a helical Kelvin wave expands from a reconnection kink at the wall and then intersects again with the wall.     

Experimental observation of a superfluid gyroscope in a dilute Bose-Einstein condensate

We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to Planck's over 2pi per particle, as predicted for a superfluid.     

Nonpremixed ignition of H2/air in a mixing layer with a vortex

The ignition of a laminar non-premixed H₂/air mixing layer with an embedded vortex was computationally studied with detailed chemistry and transport. The initial vortex velocity and pressure fields were specified based on the stream function of an incompressible nonviscous vortex. The fuel side is pure hydrogen at 300 K, and the oxidizer side is air at 2000 K. The vortex evolution process was found to consist of two ignition events. The first ignition occurs in a diffusion mode with chain branching reactions dominating. The second ignition takes place in the premixed mode, with more chemical reactions involved, and is significantly affected by the heat and species generated in the first ignition event. The coupling between the most reactive mixture fraction and scalar dissipation rate was verified to be crucial to the ignition delay. The effects of the vortex strength, characteristic size, and its center location were individually investigated. For all vortex cases, the ignition delay was shorter than that of the 1D case. Furthermore, the ignition delay has a nonmonotonic dependence on all the vortex parameters.     

Analytical study of the splitting process of a multiply-quantized vortex in a Bose–Einstein condensate and collaboration of the zero and complex modes

We study the dynamics of a trapped Bose–Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross–Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov–de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.     

The shear viscosity of a trapped Bose-condensed gas

By obtaining Kubo formula type and using nonequilibrium Green’s functions, we calculate the shear viscosity of a trapped Bose-condensed gas below and above the Bose-Einstein condensation temperature (T_BEC). The contributions of the interactions between condensate and noncondensate atoms and between noncondensate atoms take into account to the viscous relaxation time, by evaluating second order self-energies in Beliaev approximation.     

Scale-separation scheme for simulating superfluid turbulence: Kelvin-wave cascade

A Kolmogorov-type cascade of Kelvin waves-the distortion waves on vortex lines-plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin-wave cascade on a single vortex line. This idea is likely to be generalizable for a full-scale simulation of different regimes of superfluid turbulence. With the new scheme, we are able to unambiguously resolve the cascade spectrum exponent, and thus to settle the controversy between recent simulations of Vinen, Tsubota, and Mitani [Phys. Rev. Lett. 91, 135301 (2003)]] and recently developed analytic theory [Phys. Rev. Lett. 92, 035301 (2004)]].