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An experimental demonstration of a non-classical state of a nanomechanicalresonator is still an outstanding task. In this paper we show how the resonatorcan be cooled and driven into a squeezed state by a bichromatic microwavecoupling to a charge qubit. The stationary oscillator state exhibits a reducednoise in one of the quadrature components by a factor of 0.5 - 0.2. Thesevalues are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$and for support temperatures of T $\approx$ 25 mK. We show that the coupling tothe charge qubit can also be used to detect the squeezed state via measurementsof the excited state population. Furthermore, by extending this measurementprocedure a complete quantum state tomography of the resonator state can beperformed. This provides a universal tool to detect a large variety ofdifferent states and to prove the quantum nature of a nanomechanicaloscillator.Comment: 13 pages,9 figure

Generation of squeezed states of nanomechanical resonators by reservoir engineering