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. The apparatus consists of a straight vibrating wire immersed in liquid
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/2
m3, 0, and +h/2
m3, where h is Planck's constant and
m3 is the mass of the
3He atom. This experiment confirms that superfluid
3B is a Cooper-paired superfluid with a macroscopic quantum wave function.
An object can move through a superfluid without resistance provided that its speed is below a critical value; higher speeds result in the formation of vortices, which are small volumes of normal fluid and superfluid that rotate and dissipate energy. Although the dynamics of these vortices are considered to be crucial in understanding superfluidity, the strong and complex interactions of the superfluid, dissipative forces, and surface effects in most superfluids (such as liquid helium) all combine to obscure observations.
The difference between normal systems and superfinid systems is perhaps most strikingly manifested in their current flow. Superfluid current flow displays very special features, both in its structure and in its response to external probes. We now focus our attention on these characteristic “superfluid” properties at zero-temperature. The generalization of the theory to finite temperatures is postponed until Chapter 6 . Two fundamental features of superfluid flow are the following: Superfluid flow is irrotational This property may be viewed in a number of ways. In the language of a two-fluid model, it is expressed by the equation: ∇ × v s = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429495717/2cc6e3e4-f702-48c8-b407-59783ef3d6a6/content/eq89_v2.tif"/> where v s is the superfluid velocity, which we shall define more precisely in Chapter 5 . More conveniently, we may say that it is impossible to set up rotational currents on a macroscopic scale in a superfluid. It follows that when a transverse probe is applied to the fluid, the latter does not respond. For example, let us imagine a simple experiment, in which a bucket of helium is rotated at a constant angular velocity ω . In a frame of reference which rotates along with the walls, the fluid feels a Coriolis force, which acts as a transverse probe applied to the system. A normal liquid would respond to such a probe; at equilibrium, the liquid would be dragged by the walls and rotate at the same angular velocity ω . In a homogeneous superfluid at T = 0, the liquid does not respond to the 50 Coriolis force; it stays at rest while the walls are rotating. In an actual superfluid, we shall see that matters are more complicated, in that vortices may appear in the rotating bucket. As a result, one does not encounter the dramatic manifestation of superfluid behavior predicted for a homogeneous superfluid. Nevertheless, the above fictitious experiment is conceptually very important, as it illustrates an essential feature of superfluids, namely their rigidity against transverse probes. The physical importance of such a concept is even more obvious in superconductors, since in that case it corresponds to the Meissner effect. Superfluid flow is resistance free: when a superfluid flows in a thin capillary, it is not slowed down by the walls. The flow thus persists without any pressure head applied to the end of the capillary.
We consider the dynamics of a supersolid state that is based on Leggett's idea of local phase flow around the atomic sites of the solid. This leads to a local microscopic superfluid velocity that is not Galilean and is defined only relative to the solid and a
T=0 superfluid fraction ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}<1$ (with $\ensuremath{\rho}$ being the macroscopic mass density). Landau's excitation-based argument for superfluids---that at temperature
T=0 the normal fluid mass density ${\ensuremath{\rho}}_{N}$ is zero---should apply to supersolids. Together these two arguments imply that at low
T there is a missing mass density. We attribute this to a supersolid density ${\ensuremath{\rho}}_{L}$, with ${\ensuremath{\rho}}_{L}\ensuremath{\equiv}\ensuremath{\rho}\ensuremath{-}{\ensuremath{\rho}}_{S}\ensuremath{-}{\ensuremath{\rho}}_{N}$ and a momentum-bearing supersolid velocity
vLi. We derive the macroscopic dynamical equations for this system with three momentum-bearing macroscopic velocities
(vLi,vNi,vSi) using Onsager's irreversible thermodynamics. For slow spatial variations,
vSi accelerates along the negative gradient of the chemical potential or mass, like for an ordinary superfluid, and
vNi is subject to drag against
vLi with a characteristic drag time $\ensuremath{\tau}$. There are three contributions to the acceleration of
vLi: drag against
vNi, along the negative gradient of the chemical potential or mass, and due to the forces of lattice elasticity. For high-frequency motion relative to the drag time $\ensuremath{\tau}$, ${\ensuremath{\rho}}_{L}$ moves independently of ${\ensuremath{\rho}}_{N}$. The normal modes for such a system have a crossover frequency below which the normal fluid velocity
vNi is dragged into motion with
vLi (so the theory reduces to the
vSi,vNi theory of Andreev and Lifshitz) and above which the normal fluid velocity
vNi is an independent variable. For an isotropic lattice we study the transverse and longitudinal responses. A frequency-dependent rotational inertia experiment is predicted to show, at frequencies that are low relative to $\ensuremath{\tau}$, that ${\ensuremath{\rho}}_{L}$ and ${\ensuremath{\rho}}_{N}$ move together but that at high frequencies ${\ensuremath{\rho}}_{L}$ moves much more than ${\ensuremath{\rho}}_{N}$.
In Fermi superfluids, such as superfluid (3)He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction, which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction, the internal dynamics of the superfluid component becomes more important compared with the damping and coupling effects from the normal component. As a result profound changes in superfluid dynamics are observed: the temperature-dependent transition from laminar to turbulent vortex motion and the decoupling from the reference frame of the container at even lower temperatures.