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 10⁴ to 10⁵ and for support temperatures of T≈25 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.