Nanoelectromechanical resonators and nanoconfinement in quantum fluids

Modern nanofabrication techniques have led to tremendous advances in many fields of physics. In particular, new superfluid phases of helium-3 have recently been discovered in engineered geometries that sculpture the order parameter of the topological superfluid on the nanometer scale. Detailed studies are required to reveal the physical properties of the new superfluid phases, and to identify the mechanisms that stabilize them. Recently, nanomechanical sensors for superfluid helium-4 have also emerged. They are promising tools for studying, for instance, the fast dynamics of quantized vortices. Incorporating nanoelectromechanical resonators to a superfluid environment pose several challenges involving acoustic dissipation, interaction with nearby surfaces, nonlinearity, and understanding of the device-fluid interactions in mesoscopic objects. In this thesis, low-frequency nanoelectromechanical resonators for studying the superfluids helium-4 and helium-3 are developed. To minimize the effect of walls, freestanding aluminum devices are fabricated on an opening in the substrate. The devices are characterized in vacuum, in helium-4 gas, and in superfluid helium-4. Good understanding of the device-intrinsic properties such as tunneling two-level systems is achieved, and device-fluid interactions are found to be in good agreement with the theories derived for macroscopic objects. Additionally, we use nuclear magnetic resonance spectroscopy to study the polar phase of superfluid helium-3, stabilized between oriented strands of nanometer-scale diameter and spacing. We show that the stability of the polar phase against scattering from non-magnetic impurities is protected by an extension of the Anderson theorem, albeit the system is an unconventional p-wave state with anisotropic gap. We verify experimentally that the superfluid gap in the polar phase has a cubic temperature dependence, which is a direct consequence of the Dirac nodal line in the spectrum of the Bogoliubov quasiparticles. The confining strands pin vortices strongly, allowing us to measure the density of vortices created in the transition to the superfluid state. We show that an applied bias field suppresses the number of vortices created by the Kibble-Zurek mechanism, providing a shortcut to adiabaticity in this system. The uncovered intrinsic properties of the nanoelectromechanical sensors aid in the design of new devices, and the good understanding of the device-fluid interactions demonstrated in the thesis pave way for future experiments, for instance on vortex dynamics. In helium-3, studies on vortex dynamics enable probing the properties of the fermionic vortex-core-bound states, including the elusive Majorana zero mode. In future, nanoengineered sensors and nanoengineered confinement of helium-3 could be combined, allowing for example experiments on dynamics of the synthetic electromagnetic and gravitational fields.