We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of
3He confined in highly anisotropic Nafen aerogel. Superfluidity of
3He confined in Nafen is the realization of a ``nematic superfluid'' with Cooper pairs condensed into a single
p-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second ``chiral'' phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid
3He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of
3He-Nafen.
We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates simulates certain aspects of the confinement in a theory like
SU(2) quantum chromodynamics (QCD) in 2+1 space-time dimensions. By identifying the circulation of superfluid velocity as the baryon number and the relative phase between two components as a dual gluon, we identify HQVs in a single component as electrically charged particles with a half baryon number. Further, we show that only singlet states of the relative phase of two components can stably exist as bound states of vortices, that is, a pair of vortices in each component (a baryon) and a pair of a vortex and an antivortex in the same component (a meson). We then study the dynamics of a baryon and meson; a baryon is static at equilibrium and rotates once it deviates from the equilibrium, while a meson moves with constant velocity. For both baryons and mesons we verify a linear confinement and determine that they are broken, thus creating other baryons or mesons in the middle when two constituent vortices are separated by more than some critical distance, resembling QCD.
3 He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in 3 He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.