The ability to transport energy is a fundamental property of the two-dimensional Dirac fermions in graphene. Electronic thermal transport in this system is relatively unexplored and is expected to show unique fundamental properties and to play an imp
ortant role in future applications of graphene, including opto-electronics, plasmonics, and ultra-sensitive bolometry. Here we present measurements of bipolar, electron-diffusion and electron-phonon thermal conductances, and infer the electronic specific heat, with a minimum value of 10 $k_{rm{B}}$ ($10^{-22}$ JK$^{-1}$) per square micron. We test the validity of the Wiedemann-Franz law and find the Lorenz number equals $1.32times(pi^2/3)(k_{rm{B}}/e)^2$. The electron-phonon thermal conductance has a temperature power law $T^2$ at high doping levels, and the coupling parameter is consistent with recent theory, indicating its enhancement by impurity scattering. We demonstrate control of the thermal conductance by electrical gating and by suppressing the diffusion channel using superconducting electrodes, which sets the stage for future graphene-based single microwave photon detection.
We investigate the low loss acoustic motion of superfluid $^4$He parametrically coupled to a very low loss, superconducting Nb, TE$_{011}$ microwave resonator, forming a gram-scale, sideband resolved, optomechanical system. We demonstrate the detecti
on of a series of acoustic modes with quality factors as high as $7cdot 10^6$. At higher temperatures, the lowest dissipation modes are limited by an intrinsic three phonon process. Acoustic quality factors approaching $10^{11}$ may be possible in isotopically purified samples at temperatures below 10 mK. A system of this type may be utilized to study macroscopic quantized motion and as an ultra-sensitive sensor of extremely weak displacements and forces, such as continuous gravity wave sources.
We have cooled the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven microwave frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as
3.8$pm$1.2 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath.
