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By coupling a single-electron transistor to a high-quality factor, 19.7-megahertz nanomechanical resonator, we demonstrate position detection approaching that set by the Heisenberg uncertainty principle limit. At millikelvin temperatures, position resolution a factor of 4.3 above the quantum limit is achieved and demonstrates the near-ideal performance of(More)
Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron(More)
The coupling of mechanical and optical degrees of freedom via radiation pressure has been a subject of early research in the context of gravitational wave detection. Recent experimental advances have allowed studying for the first time the modifications of mechanical dynamics provided by radiation pressure. This paper reviews the consequences of back-action(More)
— We use first-order perturbation theory to provide a local linear relation between the circuit parameters and the poles of an RLC network. The sensitivity matrix, which defines this relationship, is obtained from the systems eigenvectors and the derivative of its eigenvalues. In general, the sensitivity matrix is related to the equilibrium fluctuations of(More)
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