Scanning SQUID investigation of the suppression of superfluid density in mesoscopic superconducting rings

We use a scanning SQUID microscope to measure the suppression of the superconducting response of quasi-1D rings specifically designed to exhibit phase winding fluctuations below Tc.~ Extremely high flux sensitivity as well as a positionable sensor capable of measuring many individual rings and subtracting the background in situ make scanning SQUID ideal for this measurement.~ The physical ring parameters are carefully controlled during fabrication to reduce the ring's superconducting phase stiffness by tuning the energy spacing of states where a uniform phase winds an integer number of times around the ring.~ When the energy difference between adjacent phase winding states is approximately equal to the temperature, the superfluid density is suppressed by the contribution of multiple states to the response. ~ We present susceptibility data and a theoretical framework that demonstrate how these fluxoid fluctuations suppress the ring's diamagnetism below Tc.