Fig. 1: Experimental cell confining ³He.

a Nanofabricated sample cell, cut away to show cavity in lower silicon wafer, bonded to upper wafer. The support posts shown maintain cavity height D under different liquid pressures. The cavity is filled through a fill line via a sintered heat exchanger and cooled through the column of ³He within it. Small volumes of bulk liquid at each end of the cavity provide markers for the bulk superfluid transition T_c0, and eliminate thermometry errors due to temperature gradients. The NMR coil set around the sample is shown in Supplementary Fig. 1. Suitable small magnetic field gradients are used to resolve the NMR response of different regions of the cell, see ‘Methods’. b, c NMR signatures of superfluid transition in cavity and bulk markers, for two different surface boundary conditions, at ³He pressure of 2.46 bar. ³He-A in the cavity shows a negative frequency shift whereas the bulk markers show positive frequency shift; \({\Delta}f_{\mathrm{A}}^{{\mathrm{bulk}}}\) and \({\Delta}f_{\mathrm{B}}^{{\mathrm{bulk}}}\) refer to the calculated bulk superfluid frequency shifts of ³He-A and ³He-B, respectively, see Supplementary Note 2. The T_c suppression observed with a surface boundary layer of solid ⁴He is eliminated by the addition of ⁴He to create a superfluid ⁴He film at the surface. The white horizontal bands show the measured T_c and T_c0 including the uncertainties in temperature determination, see ‘Methods’. d Schematic illustration of the tuning of surface scattering conditions, parametrised by specularity coefficient S, by surface plating atomically smooth silicon with a ⁴He film. The green circles represent ⁴He atoms, the orange is liquid ⁴He, and the arrows indicate the flux of incoming and outgoing ³He quasiparticles.