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arXiv:1206.1825 · Modern Physics Letters B

CROW INSTABILITY IN UNITARY FERMI GAS

Sandeep Gautam

Published May 16, 2013• 5 citations
arXivHTMLPDF

Abstract

In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrödinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex–antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex–antivortex pair into multiple vortex rings and ultimately into sound waves.

DOI
10.1142/s0217984913500978

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•Jan 1, 2001•13 citations
In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrödinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex–antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex–antivortex pair into multiple vortex rings and ultimately into sound waves.
We show theoretically that elongated vortex-antivortex dipoles can be created controllably in trapped Bose-Einstein condensates, using known experimental techniques. Vortex dipoles of sufficient length are unstable and cascade into slow vortex rings which ultimately decay via sound emission. This instability of antiparallel vortex line elements, which self-generates Kelvin waves on vortex loops in trapped atomic gases, may play a role in bridging the Kelvin-wave and Kolmogorov-Richardson cascades of quantum turbulence.
Abstract We study the formation and dynamics of shock waves initiated by a repulsive potential in a superfluid unitary Fermi gas by using the order-parameter equation. In the theoretical framework, the regularization process of shock waves mediated by the quantum pressure term is purely dispersive. Our results show good agreement with the experiment of Joseph et al (2011 Phys. Rev. Lett. 106 150401 ). We reveal that the boxlike-shaped density peak observed in the experiment consists of many vortex rings due to the transverse instability of the dispersive shock wave. In addition, we study the transition from a sound wave to subsonic shock waves as the strength of the repulsive potential increases and show a strong qualitative change in the propagation speed of the wavefronts. For a relatively small strength of the repulsive potential, the propagation speed decreases below the sound speed with the increase of the strength as a scaling behavior. For a large strength where the shock waves are formed by colliding two spatially separated clouds, the speed is still smaller than the sound speed, but remains almost unchanged as the strength increases, which can be interpreted as the same expansion speed of the proliferation of the vortex rings originated from the transverse instability.
We follow the time evolution of a superfluid Fermi gas of resonantly interacting ^{6}Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a vortex ring, which, in turn, breaks to finally leave behind a single solitonic vortex. In intermediate stages, we find evidence for an exotic structure resembling the Φ soliton, a combination of a vortex ring and a vortex line. Direct imaging of the nodal surface reveals its undulation dynamics and its decay via the puncture of the initial soliton plane. The observed evolution of the nodal surface represents dynamics beyond superfluid hydrodynamics, calling for a microscopic description of unitary fermionic superfluids out of equilibrium.
In classical inviscid fluids, antiparallel vortices perturbed by Kelvin waves exhibit the Crow instability, where the mutual interaction of the Kelvin modes renders them dynamically unstable. This results in the approach and reconnection of the vortices, leading to a cascaded decay into ever-smaller vortex loops. Through mean-field simulations we study the Crow instability of quantum vortex lines in a superfluid whose atoms are subject to the anisotropic, long-ranged dipole-dipole interaction. We observe that the direction of dipole polarization plays a crucial role in determining the dynamically favored Kelvin modes. The subsequent rate of the instability is linked to the mediation of the vortex curvature by the effective dipole-dipole interaction between the vortices themselves. The vortex curvature is strongly suppressed and modes of lower wavenumber are preferred when the dipole polarization is parallel to the vortices, whereas the curvature is maximized for polarizations along the vortices' separation axis. For polarizations along the binormal axis, modes of higher wavenumber are favorable but the instability rate is considerably inhibited. This paves the way to a deeper understanding of vortex reconnections, vortex loop cascades and turbulence in dipolar superfluids.
The Gross-Pitaevskii (GP) equation admits a two-dimensional solitary wave solution representing two mutually self-propelled, anti-parallel straight line vortices. The complete sequence of such solitary wave solutions has been computed by Jones and Roberts (J. Phys. A, 15, 2599, 1982). These solutions are unstable with respect to three-dimensional perturbations (the Crow instability). The most unstable mode has a wavelength along the direction of the vortices of the same order as their separation. The growth rate associated with this mode is evaluated here, and it is found to increase very rapidly with decreasing separation. It is shown, through numerical integrations of the GP equation that, as the perturbations grow to finite amplitude, the lines reconnect to produce a sequence of almost circular vortex rings. 1