Fundamental science and technology with levitated cavity optomechanics

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Technical advances allowing extremely fine measurement and control of the motion of mechanical oscillators, using light, have led to several recent scientific breakthroughs. Notable examples are due to the LIGO observatory, a kilometre scale optomechanical system capable of measuring dis-placements 1000 times smaller than the dimension of a nucleus. Awarded the 2017 Nobel prize for the first detection of gravitational waves, LIGO -one of the most sensitive instruments ever built- continues to deliver extraordinary results, including the detection in 2020 of the effects of quantum fluctuations on the motion of a ten kilogram mass.Though on much smaller scales, cavity micro-optomechanical systems might be viewed as table-top analogues since they employ similar physical principles and have adapted several of the technical strategies of LIGO to reduce measurement back action and instrumental noises down to near the Heisenberg scale. These laboratory-scale optomechanical systems are themselves yield-ing important advances including, in the last few months, the demonstration of quantum entanglement between two oscillating membranes, a key quantum resource for measurement and sensing in both fundamental physics and applications.Remarkably, within the active field of optomechanics, nano-particles levitated in a optical field are generating considerable excitement, with three independent recent demonstrations of cooling of one degree of freedom of its centre-of-mass motion from room temperature (300 Kelvin) to within less than a quantum above its lowest possible energy (microK). Levitation in vacuum forms a nano-oscillator that is extremely well isolated making it ideal for quantum-limited measurement of ultra weak forces. They offer possibilities for applications that range from commercial sensors to quantum technologies to studies of fundamental physics, including the search for exotic states of matter.We are proposing to pioneer many-particle and many-body regimes of levitated cavity optomechanics, taking the field in a new direction and capitalising on the unique scalability of to multiple identical and fully controllable nano-oscillators. Beyond basic science or quantum technology, a core objective is to develop control of the orientation of nonspherical nanoparticles for diffraction imaging. Thus the project opens the way to ranging from many-body quantum dynamics in a novel regimes to practical applications in nanoparticle characterisation.We will achieve this goal by building on our expertise in this area including proof-of-principle experiments performed for this proposal that demonstrate the viability of the new coherent scattering-based strategies. Specifically, we will use a tightly coupled experimental and theoretical approach, that aims to realise full quantum control over all motional degrees of freedom of the single particle as our point of departure. This includes not only 3D translational but also rotational and librational motion of a single particle. We will develop protocols for generation and measurement of correlations between the motion of 2 or more particles and implement and investigate 1D and 2D arrays of identical levitated particles within a cavity.