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.