Half quantum vortex in superfluid $^3$He-A phase in parallel plate geometry

The study of quantum vortex dynamics in He II holds great promise to refine quantum-fluid models. Bose-Einstein condensates, neutron stars or even superconductors exhibit quantum vortices, whose interactions are a key element of dissipation in these systems. These quantum objects have their velocity circulation around their core quantized and, in He II, a core as thin as a helium atom. They have been observed experimentally by indirect means, such as second sound attenuation ...

In superfluid $^3$He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially-modulated superfluid stripe phase has been proposed. We confined $^3$He in a 1.1 $\mu$m high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the forma...

The quantized vortex state appearing in the recently discovered new states in hcp 4He since their discovery is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state and its transition into the supersolid (SS) state. Its features are described. The historical expla- nations for the SS state in quantum solids such as solid 4He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as va- cancies, inte...

The experimental investigation of superfluid turbulence in 3He-B is generally not possible with the techniques which have been developed for 4He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in 3He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition betw...

We present an experimental study on the interaction and dynamics of half-quantum vortices (HQVs) in an antiferromagnetic spinor Bose-Einstein condensate. By exploiting the orbit motion of a vortex dipole in a trapped condensate, we perform a collision experiment of two HQV pairs, and observe that the scattering motions of the HQVs is consistent with the short-range vortex interaction that arises from nonsingular magnetized vortex cores. We also investigate the relaxation dyna...

We have performed numerical calculations of the structure of the single-quantum vortex in superfluid $^3$He-A. The GPU-accelerated large-scale numerical simulation is performed in the Ginzburg-Landau model and resolves length scales of both coherence-length-sized hard core and dipolar-length-sized soft core of the vortex. The calculations support previously suggested qualitative structure of the vortex, recently named as eccentric fractional skyrmion, and provide numerical va...

The possible stable singular vortex (SV) and half-quantum vortex (HQV) of the superfluid $^3$He-A phase confined in restricted geometries are investigated. The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics. The energetics between those vortices is carefully examined using the standard Ginzburg-Landau (GL) functional with a strong-coupling correction. The Fermi liquid effect, whi...

We discuss the configurations in which singly and doubly quantized vortex lines may coexist in a rotating superfluid. General principles of energy minimization lead to the conclusion that in equilibrium the two vortex species segregate within a cylindrical vortex cluster in two coaxial domains where the singly quantized lines are in the outer annular region. This is confirmed with simulation calculations on discrete vortex lines. Experimentally the coexistence can be studied ...

We consider a thin film of superfluid ${}^3$He under conditions that stabilize the A-phase. We show that in the presence of a uniform superflow and an external magnetic field perpendicular to the film, the spin degrees of freedom develop a nonuniform, helical texture. Our prediction is robust and relies solely on Galilei invariance and other symmetries of ${}^3$He, which induce a coupling of the orbital and spin degrees of freedom. The length scale of the helical order can be...

In a rotating two-phase sample of 3He-B and magnetic-field stabilized 3He-A the large difference in mutual friction dissipation at 0.20 Tc gives rise to unusual vortex flow responses. We use noninvasive NMR techniques to monitor spin down and spin up of the B-phase superfluid component to a sudden change in the rotation velocity. Compared to measurements at low field with no A-phase, where these responses are laminar in cylindrically symmetric flow, spin down with vortices ex...