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arXiv:0909.2144 · Physical Review B

Quantum Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates

Hiromitsu Takeuchi, Naoya Suzuki, Kenichi Kasamatsu, Hiroki Saito, Makoto Tsubota

Published Mar 17, 2010• 116 citations
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Abstract

We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-type waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.

DOI
10.1103/physrevb.81.094517

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We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-type waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.
We study the dispersion relation of Kelvin waves propagating along single- and half-quantum vortices in miscible two-component Bose-Einstein condensates based on the analysis of the Bogoliubov--de Gennes equation. With the help of the interpolating formula connecting the dispersion relations in low- and high-wave-number regimes, we reveal the nontrivial dependence of the dispersion relation on the intercomponent interaction through the change in the vortex-core size of the vortical component. We also find the splitting of the Kelvin wave dispersion into gapless and gapped branches when both components have overlapping single-quantized vortices.
We explore the stability of the interface between two phase-separated Bose gases in relative motion on a lattice. Gross-Pitaevskii-Bogoliubov theory and the Gutzwiller ansatz are employed to study the short- and long-time stability properties. The underlying lattice introduces effects of discreteness, broken spatial symmetry, and strong correlations, all three of which are seen to have considerable qualitative effects on the Kelvin-Helmholtz instability. Discreteness is found to stabilize low flow velocities because of the finite energy associated with displacing the interface. Broken spatial symmetry introduces a dependence not only on the relative flow velocity but also on the absolute velocities. Strong correlations close to a Mott transition will stop the Kelvin-Helmholtz instability from affecting the bulk density and creating turbulence; instead, the instability will excite vortices with Mott-insulator-filled cores.
Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.
We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single-component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counterflowing channels, we seed a line of quantized vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behavior of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantized vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.
We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single-component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counterflowing channels, we seed a line of quantized vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behavior of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantized vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.
We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number WeWeWe, clarifying the microscopic aspects unique to the quantum fluid system. For We≲1We \lesssim 1We≲1, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to WeWeWe. When We≳1We \gtrsim 1We≳1 in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.