Quantum Limits on Measurement and Control of a Mechanical Oscillator

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. It offers a pedagogical approach to linear quantum measurement theory and includes a detailed guide to experimental aspects of precision interferometry. Lastly, the authors experimentally investigate the role of vacuum fluctuations in setting a fundamental limit to linear quantum feedback control. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object; further, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime. The position fluctuations of the oscillator-a glass nanostring-are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg's uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. The act of measurement not only perturbs the subject of the measurement-the mechanical oscillator-but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum - i.e., the light is squeezed. Feedback is used to manipulate a manifestation of these quantum correlations.