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Superfluid $^4$He as a rigorous test bench for different damping models in nanoelectromechanical resonators

We have used nanoelectromechanical resonators to probe superfluid $^4$He at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant contributions to damping and the shift of the resonance frequency: tunneling two level systems at the lowest temperatures, ballistic phonons and rotons at few hundred mK, and laminar drag in the two-fluid regime below the superfluid transition temperature as well as in the normal fluid. Immersing the nanoelectromechanical resonators in fluid increases their effective mass substantially, decreasing their resonance frequency. Dissipationless superflow gives rise to a unique possibility to dramatically change the mechanical resonance frequency in situ, allowing rigorous tests on different damping models in mechanical resonators. We apply this method to characterize tunneling two-level system losses and magnetomotive damping in the devices.