We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noises that enforce the standard quantum limit: the measurement imprecision and radiation-pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for cavity optomechanical systems.
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