Superfluid 3He in rotation
Experiments on vortices in rotating superfluid 3He have revealed phenomena which have not been observed in any other quantum liquid and have implications in fields beyond low-temperature physics. In 3He-A, vorticity may be supported by a continuous winding of the order parameter which gives rise to the observed continuous coreless vortices with two flow quanta. Exotic vortices with half-integer circulation quanta may also exist in this phase. In 3He-B, an abrupt change in the vortex-core structure has been explained theoretically as a topological phase transition involving half-quantum vortices. NMR experiments on rotating 3He-B have revealed that the cores of vortices observed possess spontaneously broken parity, manifested by their ferromagnetic superfluid cores.
Vortices and NMR in rotating3He-B
The core structure of singly quantized vortices in3He-B is studied in the Ginzburg-Landau regime. For zero magnetic field, variational estimates indicate a core anisotropy; the gap is suppressed along the component of n in the plane perpendicular to the vortex axis within a core of radius ∼6ξ. For large fields (∼300 Oe) parallel to the vortex axis, a similar transverse anisotropy occurs, but its azimuthal direction is degenerate to leading order. The effective coupling constant λ in a rotating system arises from the kinetic energy of the flow, with anisotropy contributions smaller by two orders of magnitude. Predictions about the transverse NMR are compared with the observed resonances; detection of the corresponding longitudinal modes could help confirm the theoretical description.
Order parameters and energies of analytic and singular vortex lines in rotating3He-A
AbstractWe present the expressions of the generalized Ginzburg-Landau (GL) theory for the free energy and the supercurrent in terms of thed vector, the magnetic fieldH, and operators containing the spatial gradient and the rotationΩ. These expressions are then specialized to the Anderson-Brinkman-Morel (ABM) state. We consider eight single-vortex lines of cylindrical symmetry and radiusR=[2mΩ/ℏ]−1/2: the Mermin-Ho vortex, a second analytic vortex, and six singular vortices, i.e., the orbital and radial disgyrations, the orbital and radial phase vortices, and two axial phase vortices. These eight vortex states are determined by solving the Euler-Lagrange equations whose solutions minimize the GL free energy functional. For increasing field, the core radius of the
$$\hat l$$
 texture of the Mermin-Ho vortex tends to a limiting value, while the core radius of the
$$\hat d$$
 texture goes to zero. The gap of the singular vortices behaves likerα forr → 0, where α ranges between
$$\sqrt {1/2} $$
 and
$$\sqrt {9/2} $$
. The energy of the radial disgyration becomes lower than that of the Mermin-Ho vortex for fieldsH≥6.5H*=6.5×25 G (atT=0.99Tc and forR=10L*=60 µm, orω=2.9 rad/sec). ForR → 2ξT(ξT is the GL coherence length) orω →ωc2 (upper critical rotation speed), the energies of the singular vortices become lower than the energies of the analytic vortices. This is in agreement with the exact result of Schopohl for a vortex lattice atΩc2. Finally, we calculate the correction of order (1 -T/Tc) to the GL gap for the axial phase vortex.