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Abstract
There has recently been considerable interest in the study of mechanical oscillators in the quantum regime. Coupled electromagnetic cavities have proven useful for the measurement and control of these mechanical modes. Recent experiments have demonstrated the cooling of a macroscopic mechanical oscillator to its quantum ground state via the back-action of a coupled electromagnetic cavity mode. Such experiments are motivated by the possibility of fundamental tests of the limits of quantum mechanics, for coherent interfaces for quantum information processing, and for enhanced sensing.
In this thesis we study the preparation and detection of multimode entangled states of mechanical oscillators using coupled electromagnetic cavity modes as a resource for control. It is shown that the entangled steady-states persist with experimentally accessible parameters, and they may be detected by monitoring the cavity output spectrum.
In particular, the research presented here describes a system composed of three mechanical oscillators coupled to three electromagnetic cavity modes. The electromagnetic cavity modes may take the form of optical cavities or microwave circuits.
Via appropriate driving of the coupled cavity modes, we show how highly-entangled states of three mechanical oscillators can be prepared. In an adiabatic limit in which the electromagnetic cavity modes are damped rapidly compared with other system
parameters, the operators describing the dissipation of the three mechanical oscillators can take the form of the nullifiers that define a continuous-variable cluster state in quantum information processing. Using this so-called reservoir engineering scheme, we describe how the mechanical oscillators can be prepared in a highly entangled steady-state.
The effect of uncontrollable dissipation of the mechanical modes into local thermal environments has also been accounted for. The entanglement properties of the steady-state are evaluated, and the impact of the mechanical motion on the spectrum
of fluctuations of the coupled electromagnetic cavity modes is determined. The bipartite entanglement between mechanical oscillators is quantified using the logarithmic negativity and the genuine tripartite mechanical entanglement is quantified using the Gaussian Rényi-2 entanglement entropy.