Back-action limit of linewidth in an optomechanical oscillator

Laser cooling and amplification of mechanical modes in an optical cavity are now possible with several device geometries. Quantum back action sets the fundamental limit to cooling. It has, however, not been considered in the regenerative oscillator, wherein mechanical amplification overcomes loss, leading to self-sustained, coherent oscillations at rf and microwave rates. In these devices, the spectral purity, as measured by the phase noise, has a back-action contribution that is herein derived and evaluated in recently characterized systems. Beyond its importance as a fundamental stability limit, it can provide a way to observe quantum back action within the context of cavity optomechanics. The analysis is also applied to the case of cooling, and a pump contribution to the cooling limit is derived.