Imaging-based Quantum Optomechanics

In active imaging protocols, information about a landscape is encoded into the spatial mode of a scattered photon. A common assumption is that the landscape is rigid; however, in principle it can be altered by radiation pressure, a concept that has found fruitful application in the field of quantum optomechanics. Here we explore active imaging of a mechanical resonator with an eye to generalizing the concept of radiation pressure backaction to spatially multimode light. As a thought experiment, we consider imaging the flexural modes of a membrane by sorting the spatial modes of a laser reflected from its surface. We show that backaction in this setting arises from spatial photon shot noise, an effect that cannot be observed in single-mode optomechanics. We also derive the imprecision-backaction product for coherent illumination in the limit of purely spatial backaction, revealing it to be equivalent to the standard quantum limit for purely dispersive, single-mode optomechanical coupling. Finally, we show that optomechanical correlations due to spatial backaction can give rise to two-mode entangled light. In conjunction with high-\(Q\) nanomechanics, our findings point to new opportunities at the interface of quantum imaging and optomechanics, including sensors and networks enhanced by spatial mode entanglement.