In one spatial dimension, enhanced thermal and quantum fluctuations should preclude the existence of any long range ordered superfluid phase of matter.  Instead, the quantum liquid should be described at low energies by an emergent hydrodynamic framework known as Tomonaga-Luttinger liquid theory.  In this talk I will present details on some complimentary experimental and theoretical searches for this behavior in helium-4 including: (1) pressure driven superflow through nanopores, and (2) the excitation spectrum of a confined superfluid inside nano-engineered porous silica-based structures. For flow experiments, we have devised a framework that is able to quantitatively describe dissipation at the nanoscale leading to predictions for the critical velocity borne out by recent superflow measurements in nanopores.  In confined porous media, with radii reduced via pre-plating with rare gases, I will discuss ab initio simulations of phase and density correlations inside the pore that are in agreement with recent neutron scattering measurements.   Taken together, these results indicate significant progress towards the experimental observation of a truly one-dimensional quantum liquid.

This work was supported by the NSF through grants DMR-1809027 and DMR-1808440.