  As helium-4 is cooled below 2.17 K it undergoes a phase transition to a
fundamentally new state of matter known as a superfluid which supports flow
without viscosity. This type of dissipationless transport can be observed by
forcing helium to travel through a narrow constriction that the normal liquid
could not penetrate. Recent experiments have highlighted the feasibility of
fabricating smooth pores with nanometer radii, that approach the truly one
dimensional limit where it is believed that a system of bosons (like helium-4)
may have startlingly different behavior than in three dimensions. The one
dimensional system is predicted to have a linear hydrodynamic description known
as Luttinger liquid theory, where no type of long range order can be sustained.
In the limit where the pore radius is small, Luttinger liquid theory would
predict that helium inside the channel behaves as a sort of quasi-supersolid
with all correlations decaying as power-law functions of distance at zero
temperature. We have performed large scale quantum Monte Carlo simulations of
helium-4 inside nanopores of varying radii at low temperature with realistic
helium-helium and helium-pore interactions. The results indicate that helium
inside the nanopore forms concentric cylindrical shells surrounding a core that
can be described via Luttinger liquid theory and provides insights into the
exciting possibility of the experimental detection of this intriguing low
dimensional state of matter.
