Probing the Upper Limit of Nonclassical Rotational Inertia in Solid Helium 4

We study the effect of confinement on solid He-4's nonclassical rotational inertia fraction (NCRIF) in a torsional oscillator by constraining it to narrow annular cells of various widths. The NCRIF exhibits an observed maximum value of 20% for annuli of similar to 100 mu m width. Samples constrained to porous media or to larger geometries both have smaller NCRIF, mostly below similar to 1%. In addition, we extend the blocked-annulus experiment of Kim and Chan to solid samples with large supersolid fractions. Blocking the annulus suppresses the nonclassical decoupling from 17.1% to below the limit of our detection of 0.8%. This result demonstrates the nonlocal nature of the supersolid phenomena. At 20 mK, NCRIF depends on velocity history showing a closed hysteresis loop in different thin annular cells.