| Summary: | <p>The constant development of mesoscopic physics demands ever more precise and fast measurement and control of nanoscale objects. In this thesis, I demonstrate a sensitive electrical measurement of a carbon nanotube mechanical resonator at radio frequency, and the observation of its coherent oscillation as a consequence of the measurement back-action. </p>
<p>A single-electron transistor is embedded in the nanotube, the conductance of which is sensitive to the resonator displacement. The measurement scheme exploits this linear transduction and amplifies the electrical signal with an impedance-matching tank circuit followed by cryogenic amplifiers. As a result, the vibration displacement can be continuously monitored at radio frequency, with a sensitivity approaching within a factor 470 of the standard quantum limit.</p>
<p>The remarkable sensitivity is accompanied with strong back-action forces from electron tunnelling which randomly perturb the mechanical states. Despite its stochastic nature, in the subsequent experiments I observed self-sustaining coherent mechanical oscillation induced by such back-action. The emergence of the coherent oscillation from a static source is reminiscent of unconventional lasing without stimulated emission. The single-electron transistor, pumped by a constant bias, plays the role of a gain medium while the resonator functions as a phonon cavity. Other analogues of laser behaviour, including injection locking, classical squeezing through anharmonicity, and frequency narrowing through feedback, were demonstrated.</p>
<p>These experiments together explored a new paradigm of electromechanics, which might facilitate future fundamental physics research as novel probes at the nanoscale.</p>
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