Quantum-limited imaging of a nanomechanical resonator by spatial mode sorting

We explore the use of a spatial mode sorter to image a nanomechanical resonator, with the goal of studying the quantum limits of active imaging and extending the toolbox for optomechanical force sensing. In our experiment, we reflect a Gaussian laser beam from a vibrating nanoribbon and pass the reflected beam through a commercial spatial mode demultiplexer (Cailabs Proteus-S). The intensity in each demultiplexed channel depends on the mechanical mode shapes and encodes information about their displacement amplitudes. As a concrete demonstration, we monitor the angular displacement of the ribbon’s fundamental torsion mode by illuminating in the fundamental Hermite-Gauss mode (HG00) and reading out in the HG01 mode. We show that this technique permits readout of the ribbon’s torsional vibration with a precision near the quantum limit.