Theory of quantum optomechanical systems and quantum transport

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The last five years has seen an immense amount of progress in the quest to understand and control quantum mechanical effects in small electronic circuits and small optical systems. Such effects could lead to revolutions in electronics, information processing, and in our ability to detect and measure incredibly small signals. The long term goals of this research proposal are to develop a full theoretical understanding of quantum physics in engineered structures such as superconducting quantum circuits and so-called "quantum optomechanical" systems, where light is coupled to motion of a mechanical degree of freedom (such as a vibrating nanobeam). Our research will hopefully allow us to elucidate new quantum mechanical phenomena generic to driven, dissipative systems, and provide crucial insights for current and future experiments. It will also help pave the way for new applications and new kinds of "quantum technologies". In terms of more specific goals, we will develop new tools to allow to understand optomechanical systems where the interaction between light and mechanical motion is strong even when there is just a single particle of light (photon) present. This fascinating strong-coupling regime naturally leads to behaviour very different than that predicted using classical physics, and could even lead to natural methods for preparing highly non-classical states of motion and of light (i.e. states that have no simple counterpart in classical physics). We will also explore fascinating new effects that arise when a quantum eletronic circuit is driven by microwave radiation prepared in such non-classical states.