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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. 

The physics of exceptional points leads to very high sensitivity because the perturbation of an exceptionally degenerate state is highly sensitive to a system’s perturbation. This property is indeed not shared with nondegenerate systems, and it relies in the fractional power expansion (Puiseux series) describing the perturbation of eigenvalues and eigenvectors. We discuss how this property is met in systems made of coupled resonators and with coupled modes in waveguides, whose eigenvalues are the resonant frequencies and the wavenumbers, respectively. We will also discuss the experimental implementation of this principle in unstable nonlinear systems to build extremely sensitive saturated oscillators.