Nonlinear nanomechanical resonators for quantum optoelectromechanics

We present a scheme for tuning and controlling nanomechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a regime of optomechanics where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser-driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields make it possible to control the motional state of the nanoresonator at the single-phonon level. Some applications of this platform have been presented previously [S. Rips, M. Kiffner, I. Wilson-Rae, and M. J. Hartmann, New J. Phys. 14, 023042 (2012); S. Rips and M. J. Hartmann, Phys. Rev. Lett. 110, 120503 (2013)]. Here we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.