Quantum backaction and noise interference in asymmetric two-cavity optomechanical systems

We study the effect of cavity damping asymmetries on backaction in a membrane-in-the-middle optomechanical system, where a mechanical mode modulates the coupling between two photonic modes. We show that when the energy difference between the optical modes dominates (i.e., in the adiabatic limit) this system generically realizes a dissipative optomechanical coupling, with an effective position-dependent photonic damping rate. The resulting quantum noise interference can be used to ground-state cool a mechanical resonator in the unresolved sideband regime. We explicitly demonstrate how quantum noise interference controls linear backaction effects and show that this interference persists even outside the adiabatic limit. For a one-port cavity in the extreme bad cavity limit, the interference allows one to cancel all linear backaction effects. This allows continuous measurements of position-squared, with no stringent constraints on the single-photon optomechanical coupling strength. In contrast, such a complete cancellation is not possible in the good cavity limit. This places strict bounds on the optomechanical coupling required for quantum nondemolition measurements of mechanical energy, even in a one-port device.