Classical to quantum simulations of superfluid helium in a quasi 2D crystalline Josephson junction array

Porous two-dimensional (2D) materials provide a natural weak link to connect superfluid reservoirs, thus realizing an atomic equivalent of a superconducting Josephson junction array. Traditionally, such materials, when formed by excising holes in a 2D substrate, feature pores that are either too big or are relatively small in number, which requires a large superfluid coherence length within a narrow window of the lambda point in order to observe Josephson physics. An alternative "ground-up" approach is to consider crystalline 2D materials that naturally contain void spaces of sufficiently large size. In this work, we numerically investigate the properties of such a material, referred to as polyfantrip, as a benchmark for experimental efforts to build a superfluid interference device. Using classical simulations of gas flow through polyfantrip, we validate the experimentally observed high permeance of this nanoporous material. At low temperatures we demonstrate the inability for liquid helium to classically flow through polyfantrip. Finally, we perform path integral Monte Carlo simulations of polyfantrip separating two superfluid reservoirs. By studying winding number fluctuations, we investigate the ability for helium atoms to quantum mechanically tunnel through membrane.