Interplay of Gravity and Quantum Mechanical Superpositions

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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.