Considering the geometry of our devices (see Fig. 2) and assuming the homogeneous magnetic field B = Bŷ, the gen-035409-9

We have found an experimental evidence for the existence of the Dirac nodal line in the quasiparticle spectrum of the polar phase of superfluid 3 He. The polar phase is stabilized by confinement of 3 He between nm-sized cylinders. The temperature dependence of the gap, measured via frequency shift in the NMR spectrum, follows expected ∝ T 3 dependence. The results support the Fomin extension of the Anderson theorem to the polar phase with columnar defects: perfect columnar non-magnetic defects do no perturb the magnitude of the gap in the polar phase. The existence of the node line opens possibilities to study Bogoliubov Fermi surfaces and flat-band fermions in the polar phase.

Suspended aluminium nanoelectromechanical resonators have been fabricated, and the manufacturing process is described in this work. Device motion is driven and detected with a magnetomotive method. The resonance response has been measured at 4.2 K temperature in vacuum and low pressure 4 He gas. At low oscillation amplitudes the resonance response is linear, producing Lorentzian line shapes, and Q-values up to 4400 have been achieved. At higher oscillation amplitudes the devices show nonlinear Duffing-like behavior. The devices are found to be extremely sensitive to pressure in 4 He gas. Such device is a promising tool for studying properties of superfluid helium.

The formation of topological defects in continuous phase transitions is driven by the Kibble-Zurek mechanism. Here we study the formation of single-and half-quantum vortices during transition to the polar phase of 3 He in the presence of a symmetry-breaking bias provided by the applied magnetic field. We find that vortex formation is suppressed exponentially when the length scale associated with the bias field becomes smaller than the Kibble-Zurek length. We thus demonstrate an experimentally feasible shortcut to adiabaticity-an important aspect for further understanding of phase transitions as well as for engineering applications such as quantum computers or simulators.

We have used nanoelectromechanical resonators to probe superfluid 4 He at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant contributions to damping and the shift of the resonance frequency: tunneling two-level systems at the lowest temperatures, ballistic phonons and rotons at few hundred mK, and laminar drag in the two-fluid regime below the superfluid transition temperature as well as in the normal fluid. Immersing the nanoelectromechanical resonators in fluid increases their effective mass substantially, decreasing their resonance frequency. Dissipationless superflow gives rise to a unique possibility to dramatically change the mechanical resonance frequency in situ, allowing rigorous tests on different damping models in mechanical resonators. We apply this method to characterize tunneling two-level system losses and magnetomotive damping in the devices.