Quantum Limits on Measurement and Control

This lecture covers the fundamental concepts of quantum limits on measurement and control, focusing on interferometric position measurement, noise in displacement measurement, and coupling to a thermal reservoir. It also discusses ultracoherent mechanical transducers, membrane resonators in a phononic shield, and the observation of quantum-mechanical radiation-pressure fluctuations in an interferometer. The instructor explores the implications of noise in interferometric displacement measurement, the coherence revolution in optomechanics, and the entanglement of optical modes mechanically. The lecture concludes with discussions on measurement-based quantum control, feedback cooling to the quantum ground state, and the state of play in membrane force sensing and imaging.