Probing the Upper Limit of Nonclassical Rotational Inertia

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