An important goal in all facets of quantum optics is to be able to perform precise measurements of non-linear observables. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and also provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using a linear interaction and measurement, but observation of nonlinear degrees-of-freedom, such as phonon number, remains outstanding. Here we report the observation of position-squared thermal motion of a micro-mechanical resonator by exploiting the optical non-linearity of the radiation pressure interaction. Using this measurement, we conditionally prepare classical bi-modal mechanical states of motion with feature sizes well below 100 pm. Future improvements to our approach will allow the preparation of quantum superposition states, which can be used to experimentally explor e collapse models of the wavefunction and the potential for mechanical-resonator based quantum-metrology applications.
•http://www.equs.org/ - ARC Centre of Excellence for Engineered Quantum Systems
•http://www.physics.uq.edu.au/QOlab/ - Queensland Quantum Optics Lab
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