A Continuous Quantum Non-Demolition Measurement of the Energy of a Nano-Mechanical Resonator

The primary difficulty in performing a continuous Quantum Non-Demolition (QND) measurement of the energy of a nano-mechanical resonator is that of devising an easily realizable non-linear coupling. Here we show that it is possible to perform such a QND measurement with only a linear coupling to the resonator. Using this technique we show that that the resonator energy can be monitored by coupling it to a trapped ion in an optical cavity