Phonon-Number-Sensitive Electromechanics.

We use the strong intrinsic nonlinearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micromechanical oscillator vibrating at 25 MHz. The qubit and the oscillator are coupled electrostatically at a rate of approximately 2π×22  MHz. In this far off-resonant regime, the qubit frequency is shifted by 0.52 MHz per oscillator phonon, or about 14% of the 3.7 MHz qubit linewidth. The qubit behaves as a vibrational energy detector and from its line shape we extract the phonon number distribution of the oscillator. We manipulate this distribution by driving number state sensitive sideband transitions and creating profoundly nonthermal states. Finally, by driving the lower frequency sideband transition, we cool the oscillator and increase its ground state population up to 0.48±0.13, close to a factor of 8 above its value at thermal equilibrium. These results demonstrate a new class of electromechanics experiments that are a promising strategy for quantum nondemolition measurements and nonclassical state preparation.