Radiation Pressure Noise in Displacement Measurements of Nanomechanical Oscillators

Abstract

Optical displacement measurements play a key role in experimental tests of gravity, electromagnetism, and quantum mechanics. In a quantum-limited optical displacement measurement, photon shot noise creates fluctuations that both mask mechanical motion (imprecision noise) and impart a fluctuating force on the mechanical oscillator (radiation pressure backaction). Operation in the backaction-dominated regime is a prerequisite for ponderomotive squeezing and ground state cooling, and thus is a key motivation for the development of high-quality factor (Q) nanomechanical oscillators in the field of quantum optomechanics. In this dissertation, we chronicle our efforts to observe radiation pressure backaction with high-stress silicon nitride (Si_3N_4) nanomechanical oscillators at room temperature. The high-Q trampoline and nanoribbon resonators we employ offer a promising platform to observe radiation pressure backaction because of their low thermal noise. As such, we use them to explore the limits of free space and cavity-enhanced interferometers and optical levers. Additionally, we investigate active imaging of a mechanical oscillator, and in the process generalize radiation pressure backaction to an arbitrary mechanical mode, demonstrating it arises from photon shot noise in both time and space. Two sets of experiments will be described in detail. In the first, we cool the motion of a room temperature, high-Q Si_3N_4 trampoline resonator toward its ground state using measurement-based feedback. We reduce the occupation number of the fundamental trampoline mode from ~10^8 to ~10^3, limited by the imprecision noise of our Michelson interferometer. To remedy this, we couple the trampoline to a high-finesse optical cavity. However, a novel form of classical radiation pressure noise -- thermal intermodulation noise backaction (TINBA)-- dominates the noise in our system. We discuss mitigation strategies for TINBA, which may impede other room temperature quantum optomechanics experiments. Next, we investigate the quantum limits of angular displacement sensing with an optical lever, an overlooked topic despite a long history in fundamental and applied science. We measure the angular displacement of a high-Q Si_3N_4 nanoribbon with an imprecision 20 dB below the zero-point motion of its fundamental torsion mode, with an efficiency close to the quantum limit. To move toward the backaction-dominated regime, we demonstrate spatial optomechanical coupling between the torsion mode and a low-finesse optical cavity, where the angular displacement mediates an energy exchange between transverse cavity modes. With higher finesse, a similar experiment could enable observation of radiation pressure backaction torque. Finally, as a generalization of the optical lever, we explore the quantum limit of active imaging a mechanical oscillator. Our work connects optomechanics with quantum imaging, which analyzes encoding information in the spatial degree of freedom of an optical field, but typically ignores radiation pressure noise. We find that radiation pressure backaction, produced by optical field fluctuations in both space and time, limits the ultimate resolution in active imaging and can be used to generate entanglement between spatial modes. In combination with high-Q nanomechanical oscillators, accessing these effects could lead to a new field of imaging-based quantum optomechanics.