Fig. 2: Elastic scattering from ⁴He confined inside MCM-41.

a Experimental S(Q, 0) from helium confined to Ar pre-plated pores with an incident wavevector Q_in of 2.5 Å⁻¹ at T = 1.6 K. The presented data is for the completely filled pore with (13 mmol g⁻¹) with the scattering from the Ar and boundary layer helium (8.68 mmol g⁻¹) subtracted (see Supplementary information for the raw data). The shown uncertainties are the statistical errors after the subtraction. The light blue line is a fit of two Gaussians to the scattering centered around 2.1 Å⁻¹ originating from the second and third layers of helium in the pores. The purple line is a fit to a Gaussian centered at 1.6 Å⁻¹ which we attribute to helium at the pore center. b–e show the results of quantum Monte Carlo simulations for the structure of ⁴He confined inside a smooth Ar pre-plated nanopore at T = 1.6 K. b shows the radially averaged density-density correlation function \({g}_{2}(r)=\left\langle \rho (r)\rho (0)\right\rangle\) in units of the density ρ = N/(πR²L) with N the total number of particles inside a pore of length L and radius R for the four filling fractions highlighted in Fig. 1. c The resulting static structure factor for all atoms in the pore. d The projected density-density correlations for separations measured along the pore for only those atoms in the central core of the fully filled pore along with a fit to the low energy prediction from Tomonaga-Luttinger liquid theory (solid line). The resulting core-only structure factor in e shows a peak at 2k_F = 2πρ_1D (indicated by a vertical dashed line) where ρ_1D = N/L. The lighter blue vertical line (also in a) corresponds to the separation which minimizes the bulk ⁴He–⁴He interaction potential that controls the structure in the strongly adsorbed outer layers.