Physical Review Letters

Precession of a single vortex line in superfluid B3

Rena J. Zieve, Yu. M. Mukharsky, J. D. Close, J. C. Davis, R. E. Packard

Published Mar 2, 1992• 38 citations

Abstract

This paper reports the discovery of a new vortex phenomenon in superfluid $^{3}\mathit{B}$. A single filament of quantized vortex line precesses as a solid body around a wire extending along the axis of a cylinder. The precession frequency equals the angular velocity of the apparatus at which the presence of a single quantum of circulation minimizes the system's free energy. The period of precession is related to the circulation quantum and the dimensions of the apparatus. Thus a measurement of the precession period is an accurate determination of the quantum unit. We find \ensuremath{\kappa}=(1.020\ifmmode\pm\else\textpm\fi{}0.03)h/2${\mathit{m}}_{3}$, where ${\mathit{m}}_{3}$ is the mass of the $^{3}\mathrm{He}$ atom.

DOI: 10.1103/physrevlett.68.1327

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Physical Review Letters

Precession of a single vortex line in superfluid B3

Rena J. Zieve, Yu. M. Mukharsky, J. D. Close, J. C. Davis, R. E. Packard

Published Mar 2, 1992• 38 citations

Publisher

Abstract

This paper reports the discovery of a new vortex phenomenon in superfluid

^{3}\mathit{B}

. A single filament of quantized vortex line precesses as a solid body around a wire extending along the axis of a cylinder. The precession frequency equals the angular velocity of the apparatus at which the presence of a single quantum of circulation minimizes the system's free energy. The period of precession is related to the circulation quantum and the dimensions of the apparatus. Thus a measurement of the precession period is an accurate determination of the quantum unit. We find \ensuremath{\kappa}=(1.020\ifmmode\pm\else\textpm\fi{}0.03)h/2

{\mathit{m}}_{3}

, where

{\mathit{m}}_{3}

is the mass of the

^{3}\mathrm{He}

atom.

DOI: 10.1103/physrevlett.68.1327

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Klaus W. Schwarz

The dynamical behavior of a quantized vortex partially attached to a wire is studied theoretically, with the aim of interpreting recent experiments on quantized circulation in superfluid $^{3}\mathrm{B}$ . The geometry considered consists of a thin wire running parallel to the axis of a circular cylinder enclosing the wire. The circulation is assumed to run part way up the wire, and then to enter the fluid as a free vortex which eventually terminates on the outer wall. It is found that such a vortex achieves a state of steady precession around the wire, accompanied by a steady unwinding motion down the wire due to frictional effects. For an off-center wire, both the precession rate and the unwinding rate develop oscillatory components. Various particulars, such as the effects of friction, of moving the wire off center, and of pinning, are investigated. Excellent agreement is obtained between experiment, analytical theory, and numerical calculations.The dynamical behavior of a quantized vortex partially attached to a wire is studied theoretically, with the aim of interpreting recent experiments on quantized circulation in superfluid $^{3}\mathrm{B}$. The geometry considered consists of a thin wire running parallel to the axis of a circular cylinder enclosing the wire. The circulation is assumed to run part way up the wire, and then to enter the fluid as a free vortex which eventually terminates on the outer wall. It is found that such a vortex achieves a state of steady precession around the wire, accompanied by a steady unwinding motion down the wire due to frictional effects. For an off-center wire, both the precession rate and the unwinding rate develop oscillatory components. Various particulars, such as the effects of friction, of moving the wire off center, and of pinning, are investigated. Excellent agreement is obtained between experiment, analytical theory, and numerical calculations.

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Vortices with spontaneously broken axisymmetry in B3

M.M. Salomaa, Григорий Ефимович Воловик

This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid $^{3}\mathit{B}$ : Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating $^{3}\mathit{B}$ at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid $^{3}\mathit{B}$: Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating $^{3}\mathit{B}$ at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.

Physical Review LettersJan 27, 1986158 citations

This paper reports the discovery of a new vortex phenomenon in superfluid

^{3}\mathit{B}

{\mathit{m}}_{3}

, where

{\mathit{m}}_{3}

is the mass of the

^{3}\mathrm{He}

atom.

The dynamical behavior of a quantized vortex partially attached to a wire is studied theoretically, with the aim of interpreting recent experiments on quantized circulation in superfluid

^{3}\mathrm{B}

. The geometry considered consists of a thin wire running parallel to the axis of a circular cylinder enclosing the wire. The circulation is assumed to run part way up the wire, and then to enter the fluid as a free vortex which eventually terminates on the outer wall. It is found that such a vortex achieves a state of steady precession around the wire, accompanied by a steady unwinding motion down the wire due to frictional effects. For an off-center wire, both the precession rate and the unwinding rate develop oscillatory components. Various particulars, such as the effects of friction, of moving the wire off center, and of pinning, are investigated. Excellent agreement is obtained between experiment, analytical theory, and numerical calculations.

We report the first observation of quantized circulation in superfluid

^{3}\mathit{B}

. The apparatus consists of a straight vibrating wire immersed in liquid

^{3}\mathrm{He}

, which is cooled by a rotating nuclear demagnetization cryostat. The experiment is carried out at about 250 \ensuremath{\mu}K. The superfluid at this temperature is in the ballistic quasiparticle regime. Circulation around the wire is found to be stable only when it takes on the values -h/2

{\mathit{m}}_{3}

, 0, and +h/2

{\mathit{m}}_{3}

, where h is Planck's constant and

{\mathit{m}}_{3}

is the mass of the

^{3}\mathrm{He}

atom. This experiment confirms that superfluid

^{3}\mathit{B}

is a Cooper-paired superfluid with a macroscopic quantum wave function.

We report the generation of a quantized vortex in superfluid

^{3}\text{H}\text{e-B}

. Oscillating objects can generate vortices due to breaking of Cooper pairs in superfluid

^{3}\text{H}\text{e}

, resulting that the threshold velocity for vortex generation is higher than the pair-breaking velocity. Using very-low-frequency vibrating wires with smooth surfaces, however, we find that the threshold velocity of vortex generation is lower than the pair-breaking velocity. The threshold velocity remains constant with decreasing

^{3}\text{H}\text{e}

pressure until the pair-breaking velocity equals the vortex-generation threshold velocity at a low pressure. These results indicate that another mechanism that is independent of pressure generates vortices for the low-frequency vibrating wire in superfluid

^{3}\text{H}\text{e}

. The threshold velocity observed in experiments turns out to be nearly equal to the velocity of the instability of the vortex lines attached to the wire, which is characterized by only the circulation quantum.

This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid

^{3}\mathit{B}

: Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating

^{3}\mathit{B}

at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.