Generation of squeezed states of nanomechanical resonators by reservoir engineering

An experimental demonstration of a nonclassical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary resonator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5-0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10(4) to 10(5) and for support temperatures of Tapproximate to25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed state via measurements of the excited state population. Furthermore, by extending this measurement procedure a complete quantum state tomography of the resonator state can be performed. This provides a universal tool to detect a large variety of different states and to prove the quantum nature of nanomechanical systems.