Cavity optomechanics is showing promise for studying quantum mechanics in large systems. However, smallness of the radiation-pressure coupling is a serious hindrance. Here we show how the charge tuning of the Josephson inductance in a single-Cooper-pair transistor can be exploited to arrange a strong radiation pressure -type coupling g0 between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high g0. Contrary to the recent proposals for exploiting the non-linearity of a large radiation pressure coupling, the main non-linearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity. PACS numbers: 42.50.Wk,81.07.Oj,73.23.Hk,85.25.Cp arXiv:1311.3802v2 [cond-mat.mes-hall] 7 Apr 2014
We consider the response of a nanomechanical resonator interacting with an
electromagnetic cavity via a radiation pressure coupling and a cross-Kerr
coupling. Using a mean field approach we solve the dynamics of the system, and
show the different corrections coming from the radiation pressure and the
cross-Kerr effect to the usually considered linearized dynamics.Comment: 6 pages, 9 figure
The experimental observation of quantum phenomena in mechanical degrees of freedom is difficult, as the systems become linear towards low energies and the quantum limit, and thus reside in the correspondence limit. Here we investigate how to access quantum phenomena in flexural nanomechanical systems which are strongly deflected by a voltage. Near a metastable point, one can achieve a significant nonlinearity in the electromechanical potential at the scale of zero point energy. The system can then escape from the metastable state via macroscopic quantum tunneling (MQT). We consider two model systems suspended atop a voltage gate, namely, a graphene sheet, and a carbon nanotube. We find that the experimental demonstration of the phenomenon is currently possible but demanding, since the MQT crossover temperatures fall in the millikelvin range. A carbon nanotube is suggested as the most promising system.
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