Anharmonic effects on a phonon-number measurement of a quantum-mesoscopic-mechanical oscillator

D. H. Santamore, Hsi-Sheng Goan, G. J. Milburn, M. L. Roukes
2004 Physical Review A. Atomic, Molecular, and Optical Physics  
We generalize a proposal for detecting single phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum
more » ... imited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the readout oscillator.
doi:10.1103/physreva.70.052105 fatcat:st3kapzhabdrzafnkvxbevtnuq