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arXiv:cond-mat/9708226 · Physical Review Letters

Critical Velocity of Vortex Nucleation in Rotating Superfluid 3 He- A

V. M. H. Ruutu, Juha Kopu, M. Krusius, Ülo Parts, Bernard Plaçais, E. V. Thuneberg, W. Xu

Published Dec 22, 1997• 99 citations

Abstract

We have measured the critical velocity ${\ensuremath{\upsilon}}_{\mathrm{c}}$ at which ${}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}$ in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that ${\ensuremath{\upsilon}}_{\mathrm{c}}$ is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ in the cylinder. Slow cooldown through ${T}_{\mathrm{c}}$ in rotation yields $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ textures for which the measured ${\ensuremath{\upsilon}}_{\mathrm{c}}$'s are in good agreement with the calculated instability of the expected $\stackrel{^}{\mathbf{l}}$ texture.

DOI: 10.1103/physrevlett.79.5058

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We have measured the critical velocity

{\ensuremath{\upsilon}}_{\mathrm{c}}

at which

{}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}

in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that

{\ensuremath{\upsilon}}_{\mathrm{c}}

is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis

\stackrel{^}{\mathbf{l}}(\mathbf{r})

in the cylinder. Slow cooldown through

{T}_{\mathrm{c}}

in rotation yields

\stackrel{^}{\mathbf{l}}(\mathbf{r})

textures for which the measured

{\ensuremath{\upsilon}}_{\mathrm{c}}

's are in good agreement with the calculated instability of the expected

\stackrel{^}{\mathbf{l}}

texture.

We have used torsional oscillators, containing disk-shaped slabs of superfluid (3)He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Ω(0) is left behind after stopping rotation. The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, Ω, is parallel to l.

Nucleation of vortices in rotating superfluid by spin-up and rapid thermal quench is discussed in the framework of the time-dependent Ginzburg--Landau equation (TDGLE). An analysis of the instability in inhomogeneous rotationally-invariant system results in the expression for the critical rotational velocity. A stability analysis of multicharged vortices is presented. It is shown that they are very long-living objects with lifetime inversely proportional to the dissipation rate. It was found by numerical and analytical solution of the TDGLE that vortex nucleation by rapid thermal quench in the presence of superflow is dominated by a transverse instability of the moving normal-superfluid interface.

We have measured the resistive and reactive mutual friction coefficients in rotating superfluid ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$ at

29.3\mathrm{bars}

pressure. The results agree with those predicted from the equation of orbital hydrodynamics for two quantum continuous vortices if the previously measured value of the orbital viscosity is used. Our results put an upper limit on the orbital inertia of less than $0.005\ensuremath{\Elzxh}$ per Cooper pair. We explain our observation of history-dependent textures by noting that the ease of formation of continuous vortices depends on the relative direction of

\mathbf{l}

and the rotation axis.

We have used torsional oscillators, containing disk-shaped slabs of superfluid 3 He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating.Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity 0 is left behind after stopping rotation.The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation.When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l.A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, , is parallel to l.