Probing the upper limit of the nonclassical rotational inertia

Recently, we have used torsional oscillators to study the dependence of the nonclassical rotational inertia on sample confinement, expressed as surface to volume ratio S/V [1]. When we decreased the width of annular helium sample we observed an increase of the supersolid fraction by three orders of magnitude to 20 \% in a 150 $\mu$m wide annulus. As an extension of those measurements, we have built torsional oscillators with even smaller gaps down to 25 microns. We will give a brief description of the experimental setup and present the results of those measurements. \newline [1] A.S.C. Rittner and J.D. Reppy, Phys. Rev. Lett. \textbf{98}, 175302(2007)