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Stable circulation in superfluid [sup 3]He-A

Rena J. Zieve, Yury Mukharsky, J. D. Close, John C. Davis, R. E. Packard

Published Oct 1, 1992• 0 citations
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Abstract

The authors present evidence of stable nonzero circulation in superfluid [sup 3]He-A around a 16[mu]m diameter wire. The measurements are made on a rotating cryostat at T [approx] 0.15[Tc]. Circulation affects the splitting of the wire's normal modes, which changes the beat frequency in the emf across the wire as it vibrates in a magnetic field. The different beat frequencies at 14 and at 21 bar suggest that circulation is present at 21 bar. Furthermore, at 21 bar the beat frequency is a linear function of rotation velocity, as is expected if circulation is trapped around the wire. At 14 bar no effect of rotation is observed. The authors propose that at 21 bar the ground state texture has nonzero circulation of order h/2m[sub 3].

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The authors present evidence of stable nonzero circulation in superfluid [sup 3]He-A around a 16[mu]m diameter wire. The measurements are made on a rotating cryostat at T [approx] 0.15[Tc]. Circulation affects the splitting of the wire's normal modes, which changes the beat frequency in the emf across the wire as it vibrates in a magnetic field. The different beat frequencies at 14 and at 21 bar suggest that circulation is present at 21 bar. Furthermore, at 21 bar the beat frequency is a linear function of rotation velocity, as is expected if circulation is trapped around the wire. At 14 bar no effect of rotation is observed. The authors propose that at 21 bar the ground state texture has nonzero circulation of order h/2m[sub 3].
We report the first observation of quantized circulation in superfluid 3B^{3}\mathit{B}3B. The apparatus consists of a straight vibrating wire immersed in liquid 3He^{3}\mathrm{He}3He, 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/2m3{\mathit{m}}_{3}m3​, 0, and +h/2m3{\mathit{m}}_{3}m3​, where h is Planck's constant and m3{\mathit{m}}_{3}m3​ is the mass of the 3He^{3}\mathrm{He}3He atom. This experiment confirms that superfluid 3B^{3}\mathit{B}3B is a Cooper-paired superfluid with a macroscopic quantum wave function.
This paper provides a brief description of recent experiments measuring the fluid circulation in 3He. In the B phase, the circulation around a 16 ~m diameter wire is found to be quantized in units of h/2m~. Possible future experiments are also described. It is widely believed that quantized circulation is a fundamental property of any superfluid system [1]. The fluid circulation must be quantized in units of h/nm, where m is the mass of the individual atoms in the fluid and n is an integer that depends on the microscopic process responsible for the macroscopic quantum state. For the case of 4He, the interacting atoms experience a Bose condensation into the superfluid state and n = 1. This fact has been demonstrated in several different types of experiments [1].
The parabolic superfluid meniscus has been seen for states in which only (1) the normal or (2) the superfluid component of 3{}^{3}3He- BBB rotates. A reduced, temperature-dependent meniscus (1) was formed at small speeds $\ensuremath{\Omega}\ensuremath{\lesssim}0.21$ rad ///s. A deeper-than-expected meniscus (2) was observed after a rapid halt of the cryostat, when the normal fluid stops during a short relaxation time, followed by slow decay of the superfluid circulation. The depth of the meniscus (2) was explained by a reactive radial force between the rotating superfluid and the stationary normal liquid.
The authors have made high resolution magnetic resonance measurements of the {sup 3}He normal Fermi liquid Larmor frequency. At high temperatures, the Larmor frequency is temperature independent. At lower temperatures the authors observe a negative shift from this value that is approximately proportional to the inverse temperature, increasing to a maximum shift of order 1/10{sup 6} at the superfluid transition temperature ({approx} 1mK). The dependence of this shift on pressure (over the range 0.3 to 28.8 bar) and magnetic field, (0.04 and 0.12 T) is discussed.
We report the generation of a quantized vortex in superfluid 3He-B^{3}\text{H}\text{e-B}3He-B. Oscillating objects can generate vortices due to breaking of Cooper pairs in superfluid 3He^{3}\text{H}\text{e}3He, 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 3He^{3}\text{H}\text{e}3He 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 3He^{3}\text{H}\text{e}3He. 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.
We have observed the distortion of the gap and associated excitation spectrum in superfluid 3B^{3}\mathit{B}3B with increasing magnetic field up to the first-order transition to the A phase at a temperature of Tc{\mathit{T}}_{\mathit{c}}Tc​/T of about 7 (\ensuremath{\le}140 \ensuremath{\mu}K at P=0). The pair-breaking critical velocity of a vibrating-wire resonator is monitored as a function of field. By plotting the critical velocity we can follow changes in the B-phase excitation spectrum with increasing magnetic field, which are in excellent agreement with the calculations of Ashida and Nagai. The sudden transition to the A phase at the critical field is clearly seen.