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Observing a physical quantity without disturbing it is a key capability forthe control of individual quantum systems. Such back-action-evading orquantum-non-demolition measurements were first introduced in the 1970s in thecontext of gravitational wave detection to measure weak forces on test massesby high precision monitoring of their motion. Now, such techniques have becomean indispensable tool in quantum science for preparing, manipulating, anddetecting quantum states of light, atoms, and other quantum systems. Here weexperimentally perform rapid optical quantum-noise-limited measurements of theposition of a mechanical oscillator by using pulses of light with a durationmuch shorter than a period of mechanical motion. Using this back-action evadinginteraction we performed both state preparation and full state tomography ofthe mechanical motional state. We have reconstructed mechanical states with aposition uncertainty reduced to 19 pm, limited by the quantum fluctuations ofthe optical pulse, and we have performed `cooling-by-measurement' to reduce themechanical mode temperature from an initial 1100 K to 16 K. Future improvementsto this technique may allow for quantum squeezing of mechanical motion, evenfrom room temperature, and reconstruction of non-classical states exhibitingnegative regions in their phase-space quasi-probability distribution.

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics