Quantum-limited imaging of a nanomechanical resonator with a spatial mode sorter

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). The intensity in each demultiplexed channel depends on the mechanical modeshapes 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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>HG</a:mi> <a:mn>00</a:mn> </a:msub> </a:math> ) and reading out in the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>HG</b:mi> <b:mn>10</b:mn> </b:msub> </b:math> mode. We show that this technique permits readout of the ribbon’s torsional vibration with a precision near the quantum limit. Our results highlight new opportunities at the interface of quantum imaging and quantum optomechanics.