The superfluid phases of helium-3 ((3)He) are predicted to be strongly influenced by mesoscopic confinement. However, mapping out the phase diagram in a confined geometry has been experimentally challenging. We confined a sample of (3)He within a nanofluidic cavity of precisely defined geometry, cooled it, and fingerprinted the order parameter using a sensitive nuclear magnetic resonance spectrometer. The measured suppression of the p-wave order parameter arising from surface scattering was consistent with the predictions of quasi-classical theory. Controlled confinement of nanofluidic samples provides a new laboratory for the study of topological superfluids and their surface- and edge-bound excitations.

The B phase of superfluid 3He is a three-dimensional time-reversal invariant topological superfluid, predicted to support gapless Majorana surface states. We confine superfluid 3He into a thin nanofluidic slab geometry. In the presence of a weak symmetry-breaking magnetic field, we have observed two possible states of the confined 3He-B phase manifold, through the small tipping angle NMR response. Large tipping angle nonlinear NMR has allowed the identification of the order parameter of these states and enabled a measurement of the surface-induced gap distortion. The results for two different quasiparticle surface scattering boundary conditions are compared with the predictions of weak-coupling quasiclassical theory. We identify a textural domain wall between the two B phase states, the edge of which at the cavity surface is predicted to host gapless states, protected in the magnetic field.

It was found that two different spin states of the A-like phase can be obtained in aerogel sample. In one of these states we have observed the signal of the longitudinal NMR, while in another state no trace of such a signal was found. The states also have different properties in transverse NMR experiments. Longitudinal NMR signal was also observed in the B-like phase of 3 He in aerogel.

The influence of confinement on the phases of superfluid helium-3 is studied using the torsional pendulum method. We focus on the transition between the A and B phases, where the A phase is stabilized by confinement and a spatially modulated stripe phase is predicted at the A–B phase boundary. Here we discuss results from superfluid helium-3 contained in a single 1.08-μm-thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A phase, in comparison to bulk or when confined in aerogel, with evidence for a non-monotonic pressure dependence. This suggests that an intrinsic B-phase nucleation mechanism operates under confinement. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase.