Quantum Optomechanics on Multiple Mass Scales

非常精确地测量机械物体的位置在基础研究和技术设备中有几种应用。例如，在原子力显微镜（AFM）中，激光用于读取表面上微观悬臂扫描的位置，具有足够的精度来测量亚纳米尺度上的表面变化（小于百万分之一米的千分之一-小数点后9个零）。在一个完全不同的尺寸尺度上，激光被用来读取干涉引力波（GW）探测器的公斤级反射镜的位置，精度达到亚原子计（小于一米的百万分之一——小数点后18个零）。尽管这些设备占用非常不同的尺度，但它们由相似的原理和精确位置测量的限制联合起来。原子力显微镜（AFM）的悬臂，GW探测器的反射镜，以及其他大量的机械振荡器，它们被用作量子信息科学的工具，计时器，频率标准，或其他精密传感器，它们有一个共同点。它们都寻求在量子力学允许的最佳精度下运行。当使用激光测量一个机械物体的位置时，由光子的离散性质引起的光的量子涨落限制了人们能做得多好。这项工作探讨了在实验室实验中位置测量的这些量子限制，这些实验跨越微克到克尺度的机械振荡器，其目标是开发技术，以改善一般的位置测量，但也有特定的应用于GW探测器。激光干涉仪引力波天文台（LIGO）旨在探测由超新星爆炸、中子星和黑洞碰撞等剧烈宇宙事件发出的gw。由于GWs与电磁辐射完全不同，直接探测GWs有望打开一扇通往宇宙的新窗口，并为研究仅用光“看不见”的宇宙现象提供机会。来自天体物理源的GW会引起时空的微观扭曲，这种扭曲可以通过干涉仪来测量，干涉仪的镜子悬挂成摆，以将其与GW附近的所有其他影响隔离开来。臂长的变化，通常是1e-19米（质子大小的1/10000 !），是通过非常精确地测量从每4公里长的干涉仪臂反射的激光的干涉图案来检测的。由光子的离散性质引起的光的量子涨落限制了GW探测器的灵敏度。由于光的随机量子波动，所谓的散粒噪声限制了干涉图样的精度，从而限制了GW信号的测量。类似地，辐射压力噪声限制了干涉仪镜面的灵敏度，因为当激光从干涉仪镜面反射时，被传递到镜面的光子的波动动量“踢”。提出的实验方案包括：利用克和微克尺度的机械振荡器进行腔光力学实验，旨在研究几种辐射压力诱导的现象，包括直接观测量子辐射压力（反作用）噪声，这有望成为高级LIGO的主要限制噪声源；光机械诱导透明度的观察与操作观察有源压缩——一种产生光压缩态的有希望的替代方法；宏观物体的基态冷却；达到并超过自由粒子标准量子极限，这将允许直接测试量子不破坏测量技术。本研究的主要目的是进一步了解量子体制下的光力学系统，重点关注与GW探测器最相关的特征。同样吸引人的是，在宏观机械振荡器系统中，由于光镜耦合而探索量子相关的基本物理的前景。

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.