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Quantum optomechanics has led to advances in quantum sensing, optical manipulation of mechanical systems, and macroscopic quantum physics. However, previous studies have typically focused on dispersive optomechanical coupling, which modifies the phase of the light field. Here, we discuss recent advances in “imaging-based” quantum optomechanics – where information about the mechanical resonator’s motion is imprinted onto the spatial mode of the optical field, akin to how information encoded in an image. Additionally, we find radiation pressure backaction, a phenomenon not usually discussed in imaging studies, comes from spatially uncorrelated fluctuations of the optical field. First, we examine a simple thought experiment in which the displacement of a membrane resonator can be measured by extracting the amplitude of specific spatial modes. Torsion modes are naturally measured with this coupling and are interesting for applications such as precision torque sensing, tests of gravity, and measurements of angular displacement at and beyond the standard quantum limit. As an experimental demonstration, we measure the angular displacement of the torsion mode of a Si3N4 nanoribbon near the quantum imprecision limit using both an optical lever and a spatial mode demultiplexer. Finally, we discuss the potential for future imaging-based quantum optomechanics experiments, including observing pondermotive squeezing of different spatial modes and quantum back-action evasion in angular displacement measurements. 

Abstract Squeezed light has long been used to enhance the precision of a single optomechanical sensor. An emerging set of proposals seeks to use arrays of optomechanical sensors to detect weak distributed forces, for applications ranging from gravity-based subterranean imaging to dark matter searches; however, a detailed investigation into the quantum-enhancement of this approach remains outstanding. Here, we propose an array of entanglement-enhanced optomechanical sensors to improve the broadband sensitivity of distributed force sensing. By coherently operating the optomechanical sensor array and distributing squeezing to entangle the optical fields, the array of sensors has a scaling advantage over independent sensors (i.e.,$$\sqrt{M}\to M$$ $\sqrt{M}\to M$, whereMis the number of sensors) due to coherence as well as joint noise suppression due to multi-partite entanglement. As an illustration, we consider entanglement-enhancement of an optomechanical accelerometer array to search for dark matter, and elucidate the challenge of realizing a quantum advantage in this context. 

We show that a silicon nitride optomechanical membrane, acting as an accelerometer, can be used to search for dark matter.