Discovery and Properties of Quantized Vortices in Helium II

Donnelly, Russell J.

doi:10.1007/978-1-4613-0639-9_3

Cited by 15 publications

(28 citation statements)

References 13 publications

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“…Qualitatively, vortex knots with small knot ratio R 1 /R 0 are fast and stable, as they propagate along the z-direction without breaking. During the evolution, Kelvin waves [8] appear; such waves are visible at the last stages of cases (a), (b), (e), and (f).…”

Section: Vortex Knot Dynamicsmentioning

confidence: 95%

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Vortex knots in a Bose-Einstein condensate

2012

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We present a method for numerically building a vortex knot state in the superfluid wave-function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and stability of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how unstable vortex knots break up into vortex rings.

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Section: Vortex Knot Dynamicsmentioning

confidence: 95%

“…Vortex rings have been studied experimentally in superfluid liquid helium [8,9] and in Bose-Einstein condensates [10]. Numerical simulations have revealed that superfluid turbulence contains linked vortex lines [11], but, to the best of our knowledge, individual vortices with non-trivial topology have never been observed directly.…”

Section: Introductionmentioning

confidence: 99%

Vortex knots in a Bose-Einstein condensate

2012

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“…Due to the large number of degrees of freedom and the nonlinearity of the governing equations of motion, the problem is usually tackled statistically by introducing assumptions and closures in terms of correlators. This is the case in the seminal work of Kolmogorov in 1941 based on the idea of Richardson's energy cascade, where energy in classical fluids is transferred from large to small scales [1].Superfluids form a particular class among fluids characterised essentially by two main ingredients: the lack of dissipation and the evidence that vortex circulation takes only discrete values multiple of the quantum of circulation [2]. Superfluid examples which are routinely created in laboratories are superfluid liquid Helium (He II) and Bose-Einstein condensates (BECs) made of dilute Alkali gases.…”

mentioning

confidence: 99%

“…Superfluids form a particular class among fluids characterised essentially by two main ingredients: the lack of dissipation and the evidence that vortex circulation takes only discrete values multiple of the quantum of circulation [2]. Superfluid examples which are routinely created in laboratories are superfluid liquid Helium (He II) and Bose-Einstein condensates (BECs) made of dilute Alkali gases.…”

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confidence: 99%

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

2016

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The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then studied showing that linked rings may appear during the decay. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.The full understanding of turbulence in a fluid is one of the oldest yet still unsolved problems in physics. A fluid is said to be turbulent when it manifests excitations occurring at several length-scales. Due to the large number of degrees of freedom and the nonlinearity of the governing equations of motion, the problem is usually tackled statistically by introducing assumptions and closures in terms of correlators. This is the case in the seminal work of Kolmogorov in 1941 based on the idea of Richardson's energy cascade, where energy in classical fluids is transferred from large to small scales [1].Superfluids form a particular class among fluids characterised essentially by two main ingredients: the lack of dissipation and the evidence that vortex circulation takes only discrete values multiple of the quantum of circulation [2]. Superfluid examples which are routinely created in laboratories are superfluid liquid Helium (He II) and Bose-Einstein condensates (BECs) made of dilute Alkali gases. Here the superfluid phase is usually modelled via a complex field describing the order parameter of the system and quantised vortices appear as topological defects where the superfluid density vanishes.In three spatial dimensions those defects organise themselves into closed lines (or even open lines at the boundaries if confining sides are considered) of different configurations. Any vortex line point induces a velocity field in the superfluid which affects the motion of any object in the system including the vortex line itself. In general, even for a single closed vortex line, the dynamics are chaotic and the problem does not have analytical solutions. Superfluid turbulence regards the study of the evolution of many vortex lines, a tangle, which induce velocity field gradients in the fluid at several length scales. Different mathematical models have been devised to mimic the dynamics of a superfluid. An example is the vortex filament (VF) model based on the Biot-Savart law that relates vorticity and velocity [3]. This model is able to mimic the dynamics of dense vortex tangles due to a relatively fast numerical integration technique [4]. The VF model implicitly assumes that the superfluid density field is constant everywhere and the vortex structure is...

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“…In the superfluid systems studied until now, such as liquid Helium [1], superconductors [2], and Bose-Einstein condensates [3,4,5,6,7,8,9,10,11], a vortex line behaves as a classical object. However, placing a Bose-Einstein condensate in an optical lattice [12,13,14,15,16] leads to an unprecedented control over the system parameters, which has already enabled experimental studies on quantum phase-transitions [15,17,18], superfluidity [12,13], and number squeezing [14].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous squeezing of a vortex in an optical lattice

Martikainen¹,

Stoof²

2004

Phys. Rev. A

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We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.

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Discovery and Properties of Quantized Vortices in Helium II

Cited by 15 publications

References 13 publications

Vortex knots in a Bose-Einstein condensate

Vortex knots in a Bose-Einstein condensate

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

Spontaneous squeezing of a vortex in an optical lattice

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