Quantum Optomechanics on Multiple Mass Scales

Measuring the position of mechanical objects very precisely has several applications in fundamental research as well as in technological devices. In atomic force microscopes (AFM), for example, lasers are used to read out the position of a microscopic cantilever scanning over a surface, with sufficient precision to measure surface variations on the sub-nanometer scale (less than a thousandth of a millionth of a meter--9 zeros past the decimal place). On a completely different size scale, laser light is used to read out the positions of kilogram-scale mirrors of interferometric gravitational wave (GW) detectors with sub-attometer precision (less than a millionth of a millionth of a millionth of a meter--18 zeros past the decimal place). Even though these devices occupy very different scales, they are united by similar principles and limitations to precision position measurement. AFM cantilevers, the mirrors of GW detectors, and indeed a large variety of other mechanical oscillators used as tools of quantum information science, as time keepers, as frequency standards, or as other precision sensors have one thing in common. They all seek to operate at the best precision that quantum mechanics allows. When using laser light to measure the position of a mechanical object, the quantum fluctuations of the light, arising from the discrete nature of photons, imposes a limit on how well one can do. This work explores these quantum limits to position measurement in laboratory experiments that span micro-gram to gram scale mechanical oscillators, with the goal of developing techniques for improving position measurements in general, but also with specific applications to GW detectors.

The Laser Interferometer Gravitational-wave Observatory (LIGO) seeks to detect GWs emitted by violent cosmic events such as supernova explosions and collisions of neutron stars and black holes. Since GWs are completely distinct from electromagnetic radiation, direct detection of GWs is expected to open a new window into the Universe and provide opportunities to study cosmic phenomena that are "invisible" using light alone. GWs from astrophysical sources cause microscopic distortions of spacetime that can be measured by an interferometer whose mirrors are suspended as pendulums to isolate them from all other effects beside the GW. The changes in arm length, typically of order 1e-19 meters (1/10000 the size of a proton!), are detected by very precise measurement of the interference pattern of the laser light reflected from each 4 kilometer long arm of the interferometer. Quantum fluctuations of the light arising from the discrete nature of photons limit the sensitivity of GW detectors. The so-called shot noise, due to the random quantum fluctuations of the light, limits the precision with which the interference pattern, and hence the GW signal, can be measured. Similarly, radiation pressure noise limits the sensitivity due to the interferometer mirrors being "kicked" by the fluctuating momentum of the photons that is transferred to the mirrors when the laser light reflects from them. The proposed experimental program comprises cavity optomechanics experiments with gram- and micro-gram scale mechanical oscillators are aimed at studying several radiation pressure induced phenomena, including direct observation quantum radiation pressure (backaction) noise that is expected to be a major limiting noise source in Advanced LIGO; observation and manipulation of optomechanically induced transparency; observation of ponderomotive squeezing, a promising alternative for generation of squeezed states of light; ground state cooling of macroscopic objects; and reaching and surpassing the free-particle Standard Quantum Limit, which would allow for direct tests of quantum non-demolition measurement techniques. The main purpose of this research is to further the understanding of optomechanical systems in the quantum regime focusing on the features most relevant to GW detectors. Equally attractive is the prospect of exploring the fundamental physics of quantum correlations due to light-mirror couplings in a macroscopic mechanical oscillator system.