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多种应用。例如，在原子力显微镜（AFM）中，激光被用来读出扫描表面的显微悬臂的位置，其精度足以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，激光被用来读出干涉引力波（GW）探测器的千克级反射镜的位置，其精度为亚attometer（小于百万分之一米的百万分之一--小数点后18个零）。尽管这些设备占据非常不同的尺度，但它们通过类似的原理和限制来统一精确的位置测量。原子力显微镜的杠杆，GW探测器的镜子，以及实际上作为量子信息科学工具的各种其他机械振荡器，作为计时器，作为频率标准，或作为其他精密传感器，都有一个共同点。它们都寻求在量子力学允许的最佳精度下运行。当使用激光来测量机械物体的位置时，由光子的离散性质引起的光的量子波动对人们的测量效果施加了限制。这项工作探讨了这些量子限制的位置测量在实验室实验中，跨越微克到克尺度的机械振荡器，与发展技术，提高位置测量一般的目标，但也与特定的应用GW探测器。激光干涉引力波天文台（LIGO）试图探测由超新星爆炸和中子星与黑洞碰撞等剧烈宇宙事件发出的引力波。由于GWs与电磁辐射完全不同，因此GWs的直接探测有望打开一扇通往宇宙的新窗口，并提供研究仅使用光“不可见”的宇宙现象的机会。来自天体物理学源的引力波会引起时空的微观扭曲，这种扭曲可以通过干涉仪来测量，干涉仪的反射镜被悬挂起来，以将它们与引力波之外的所有其他效应隔离开来。臂长的变化，通常是1 e-19米（质子大小的1/10000！），通过非常精确地测量从干涉仪的每个4公里长的臂反射的激光的干涉图案来检测。由光子的离散性质引起的光的量子波动限制GW检测器的灵敏度。由于光的随机量子波动而产生的所谓散粒噪声限制了干涉图案以及GW信号的测量精度。类似地，辐射压力噪声限制了灵敏度，这是由于当激光从干涉仪反射镜反射时，干涉仪反射镜被转移到反射镜的光子的波动动量“踢”。提出的实验方案包括使用克级和微克级机械振荡器的腔光力学实验，旨在研究几种辐射压力诱导的现象，包括直接观察量子辐射压力（反作用）噪声，预计将是一个主要的限制噪声源在先进的LIGO;观察和操纵光学机械诱导的透明度;有质动力压缩的观测，一个有前途的替代产生压缩态的光;基态冷却的宏观物体;和达到和超过自由粒子标准量子极限，这将允许直接测试量子非爆破测量技术。这项研究的主要目的是进一步了解光机械系统的量子制度，重点是最相关的GW探测器的功能。同样吸引人的是探索宏观力学振荡系统中由于光镜耦合而产生的量子关联的基本物理的前景。

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.