Absence of Pressure-Driven Supersolid Flow at Low Frequency

Abstract

An important unresolved question in supersolid research is the degree to which the non-classical rotational inertia (NCRI) phenomenon observed in the torsional oscillator experiments of Kim and Chan, is evidence for a Bose-condensed supersolid state with superfluid-like properties. In an open annular geometry, Kim and Chan found that a fraction of the solid moment of inertia is decoupled from the motion of the oscillator; however, when the annulus is blocked by a partition, the decoupled supersolid fraction is locked to the oscillator being accelerated by an AC pressure gradient generated by the moving partition. These observations are in accord with superfluid hydrodynamics. We apply a low frequency AC pressure gradient in order to search for a superfluid-like response in a supersolid sample. Our results are consistent with zero supersolid flow in response to the imposed low frequency pressure gradient. A statistical analysis of our data sets a bound, at the 68% confidence level, of 9.6$\times 10^{-4}$ nm/s for the mass transport velocity carried by a possible supersolid flow. In terms of a simple model for the supersolid, an upper bound of 3.3$\times 10^{-6}$ is set for the supersolid fraction at 25 mK, at this same confidence level. These findings force the conclusion that the NCRI observed in the torsional oscillator experiments is not evidence for a frequency independent superfluid-like state. Supersolid behavior is a frequency-dependent phenomenon, clearly evident in the frequency range of the torsional oscillator experiments, but undetectably small at frequencies approaching zero.