Interplay of Gravity and Quantum Mechanical Superpositions

两个最基本的和得到充分验证的物理学理论是广义相对论和量子力学，广义相对论描述了引力，量子力学描述了我们已知的其他三种基本力。我们仍然没有找到一个一致的引力量子力学理论。量子力学和引力的统一是一段时间以来人们非常渴望的前景。随着量子场论实现了量子力学和狭义相对论的统一，广义相对论在某种程度上也是量子的已被视为必然。为了确定这是否是一种危险的测试方法，人们已经提出来了，但是还没有找到明确的答案。考虑到这一点，该项目将寻求，除其他外，帮助回答引力，至少在其低能量极限下，是否本质上是量子的。有些人已经开始质疑引力是否本质上是量子实体，提出了它是否可以是一个经典场/背景与量子力学愉快地共存的可能性。如果引力真的是经典的，那么我们将面临的最引人注目的竞技场，也许是预测处于特殊量子态的物质（比如处于高度离域叠加态的物质）作为引力源时的引力场。为此，该项目的广泛目标将是设计实验，将介观物体的量子叠加态与引力耦合，或将它们用作引力源，并通过这些实验推断引力的量子性质。我们还将研究这些实验的潜力，使精确的加速度测量和重力测量，并使引力定律和牛顿常数的确定在短距离内。目前的项目将寻求（i）扩展上述引力加速度测量的建议，压缩态和其他工程非经典量子态的叠加，以便优化测量精度为给定的能量投资。(ii)将上述建议扩展到介观体系的宏观边界，以探索量子体系和引力之间的边界。特别是，从纳米半径珠外推到微米半径珠，这可以作为可测量的引力场的起源，将被检查。为此，将采用一种新的方法，通过非均匀电场通过晶体各向异性耦合到自旋态来分裂空间位置。(iii)本文将从理论上计算一个系统在一个空间区域中的不同能量-动量态的叠加态由于与它引力耦合的周围系统的存在和涨落而引起的退相干。(iv)通过使一个探测质量接近另一个处于高度非经典状态的质量，我们将研究牛顿常数G的精度，以及对牛顿定律在短距离下的潜在修正，例如来自额外维度的修正，可以确定。(v)将这些研究扩展到两个干涉仪系统，以包括两体纠缠，进一步探索引力如何解决一个高度量子化的大质量系统。我们将考虑高度非高斯状态下两个质量的相互作用（由项目早期建立的方法学准备），以产生某种形式的“无漏洞”引力量子性质的测试。

The two most fundamental and well-verified theories of physics are General Relativity,which describes gravity, and Quantum Mechanics, which describes the other threefundamental forces known to us. A consistent quantum mechanical theory of gravity stilleludes us. The unification of quantum mechanics and gravity has been a greatly desiredprospect for some time. With the unification of quantum mechanics and special relativitybeing achieved with Quantum Field Theory, it has been seen as inevitable for GeneralRelativity to also be, at some level, quantum in nature. To determine if this is the casenumerous tests have been proposed -- however no definitive answers have beenfound. With this in mind this project will seek, among other things, to help answer whethergravity, at least in its low energy limit, is fundamentally quantum in nature.Some have started to question whether gravity is fundamentally a quantum entity, raisingthe possibility of whether it could be a classical field/background happily co-existing withquantum mechanics. Perhaps the most striking arena where we will suffer if gravity isindeed classical is to predict the gravitational field when matter in peculiarly quantumstates, say in highly delocalized superpositions, acts as the source of gravity. To this end,the broad aim of this project will be to design experiments which couple quantumsuperpositions of states of mesosocpic objects to gravity, or use them as sources of gravityand through that infer about the quantum nature of gravity. We will also investigate thepotential of these experiments to enable both precision accelerometry and gravimetry andto enable the determination of gravitational force law and Newton's constant over shortdistances.The current project will seek to(i) Extend the above gravitational accelerometry proposals for superpositions ofsqueezed states and other engineered non-classical quantum states so as tooptimize the precision of measurements for a given investment of energy. (ii) Extend the above proposals up to the macroscopic boundary of the mesoscopicregime to explore the boundary between the quantum regime and gravity. Inparticular, the extrapolation from nano-meter radii beads to micro-meter radiibeads, which can serve as the origin of measurable gravitational fields, will beexamined. For this purpose, a new way to split the spatial position throughinhomogeneous electric fields coupling to spin states through crystalanisotropies, will be used. (iii) A theoretical calculation of the decoherence of a superposition of distinctenergy-momentum states of a system in one region of space due to the presenceand fluctuations of other surrounding systems that couple gravitationally to itwill be made. (iv) By bringing a probe mass in proximity to another mass in a highly non-classicalstate, we are going to investigate the precisions to which the Newton's ConstantG, and potential corrections to Newton's law for short distances, stemming, forexample from extra dimensions, could be determined. (v) Expand these investigations to two interferometer systems in order to includebipartite entanglement to further explore how gravity addresses a highlyquantum, massive system. We will consider the interactions of two masses inhighly non-Gaussian states (prepared by methodologies founded earlier in theproject) to generate some form of 'loophole free' tests for the quantum natureof gravity.