Understanding Gravity at the Smallest Scale

在微观距离下理解重力的本质是基础物理学中最重要的开放性问题之一。尽管广义相对论为描述大尺度上的引力效应提供了一个经过充分验证的框架，但它不能始终如一地描述量子效应普遍存在的小尺度上的引力。量子引力理论的发展是基础物理学的中心目标，它对我们理解粒子物理学和似乎弥漫在宇宙中的“暗能量”的神秘本质有着广泛的影响。许多试图为引力提供一致的微观框架的理论（例如，那些涉及额外维度的理论）预测，引力可能在亚毫米距离上偏离熟悉的平方反比定律。由于引力相互作用在微观距离上的强度很小，这种偏差在实验上很难测量。这个项目代表了这样做的一种尝试。与此同时，虽然这个计划的直接科学目标显然是现代物理学发展的核心，但对这项技术的全面研究应该丰富许多其他科学技术领域。利用激光束在真空中捕获和控制小物体的能力正在被探索，用于量子控制、量子计算和小力探测的一般领域。此外，这项工作还需要详细了解微球和构成吸引子的材料之间的剩余电磁相互作用，可以想象，这一领域的进展可能会使测量表面特性的新技术成为可能，这些表面特性是原子力显微镜等探针还无法探测到的。最后，参与该项目的学生（研究生和本科生）将在许多科学和技术领域接受非常全面的培训。以前在这些距离尺度上的测量采用了源自人体大小的设备的技术，其中使用机械弹簧作为力传感器。在这个项目中，我们建议开发一种全新的技术，利用激光的光场来限制和测量微米（或最终，亚微米）尺寸的石英纳米球的运动。这项技术利用了光学镊子的现代发展，光学镊子在生物学和聚合物科学方面取得了重大进展。通过捕获激光的主动反馈，将纳米球限制在真空中并冷却到低温，纳米球可以与室温环境解耦，显著降低热噪声源和振动噪声源。纳米球在光阱的谐波电位中振荡，通过研究微球的运动可以测量其与几微米外的吸引子质量的相互作用。使用光场代替机械弹簧提供了更大的灵活性。可以通过仔细选择用于吸引子的材料和用适当的屏蔽层涂覆吸引子来减轻背景。我们已经将5微米直径的微球冷却到mK温度，并证明了力灵敏度为10^-17 N/sqrt（Hz）。我们最近在《物理学快报》上发表了一篇论文，表明纳米球可以很容易地放电，并为具有非常小的分数电荷的粒子的存在设定了新的限制。在这个项目的过程中，我们期望能够研究卡西米尔效应，一般来说，纳米球和吸引子之间的剩余电磁相互作用，并进行第一次竞争性重力测量。

Understanding the nature of gravity at microscopic distances is one of the most important open problems in fundamental physics. Although General Relativity provides an extremely well-tested framework for describing gravitational effects at large distances, it cannot provide consistently a description of gravity at small scales where quantum effects are prevalent. The development of a quantum theory of gravity is a central goal of fundamental physics, with broad implications for our understanding of particle physics and the mysterious nature of the "dark energy" that appears to permeate the universe. Many theories attempting to provide a consistent microscopic framework for gravity (e.g., those involving extra dimensions) predict that gravity could deviate from the familiar inverse square law at sub-millimeter distances. Such deviations are extremely difficult to measure experimentally due to the small strength of gravitational interactions at microscopic distances. This project represents an attempt to do this. At the same time, while the direct scientific goals of this program are clearly central to the development of modern physics, the general investigation of the technique should enrich many other fields of science and technology. The ability to trap and control small objects in vacuum using laser beams is being explored for applications in quantum control, quantum computing and in the general area of detection of small forces. In addition the work will require the detailed understanding of residual electromagnetic interactions between the microspheres and the materials composing the attractors, and it is conceivable that progress in this area may enable new techniques for measuring properties of surfaces that are not yet accessible by probes such as Atomic Force Microscopes. Finally, the students (graduate and undergraduate) exposed to the project will receive a very complete training in many areas of science and technology.Previous measurements at these distance scales have employed techniques derived from human-size devices in which mechanical springs are used as force sensors. We propose in this project to develop a drastically new technique, using the light field of a laser to confine and measure the motion of micron (or, eventually, submicron) size quartz nanosphere. This technique takes advantage of the modern development of optical tweezers, which has produced significant advances in biology and polymer science. By confining the nanospheres in vacuum and cooling them to low temperatures through active feedback of the trapping laser, the nanospheres can be decoupled from the room temperature environment, significantly reducing thermal and vibrational noise sources. The nanosphere oscillates in the harmonic potential of the optical trap, and its interaction with attractor masses positioned several microns away can be measured by studying the motion of the microsphere. The use of a light field in lieu of a mechanical spring affords much greater flexibility. Backgrounds can be mitigated through careful selection of the materials used for the attractors and the coating of the attractors with appropriate shielding layers. We have already cooled 5 micro-meter diameter microspheres to mK temperatures and demonstrated force sensitivities of 10^-17 N/sqrt(Hz). We have recently published a paper in Phys Rev Lett showing that the nanospheres can be easily discharged and setting a new limit on the existence of particles with very small fractional charges. In the course of this project we expect to be able to study the Casimir effect and, in general, residual electromagnetic interactions between the nanospheres and the attractors and perform a first competitive gravity measurement.