A Quantum Non-demolition measurement of Fock states of mesoscopic mechanical oscillators

Abstract

We investigate a scheme that makes a quantum non-demolition measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two elastic beam bending modes. The non-linear coupling between the two modes shifts the resonant frequency of the readout oscillator proportionate to the excitation of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We show that in an appropriate regime this measurement approaches a quantum non-demolition measurement of the phonon number of the system oscillator. As phonon energies in micromechanical oscillators become comparable to or greater than the thermal energy, the individual phonon dynamics within each mode can be resolved. As a result it should be possible to monitor jumps between Fock states caused by the coupling of the system to the thermal reservoirs.