Quantum Transport and Nonlinear Interactions in Hybrid, Electronic, Photonic and Mechanical Systems

Abstract

Hybrid devices based on semiconducting quantum circuits with integrated microwave photonics are promising for implementing quantum transducers, in which single electrons control photonic quantum states. To combine electronic with photonic degrees of freedom on-chip, quantum dots coupled to microwave photon cavities provide a novel family of coherent quantum devices. A fundamental property of the microscopic world described by quantum mechanics is the theory of nonlocality which is at the heart of quantum communication and computing in various physical implementations. An intriguing ex- ample of quantum delocalization is interference in the motion of a single electron. Our theoretical work suggests a realistic setup to generate entanglement between two spatially separated microwave cavities using quantum delocalized electrons that flow through a parallel double quantum dot connected between two electrodes. To prove the generation of entangled photons, we use a diagrammatic perturbative expansion based on Keldysh Green’s functions, going beyond the theoretical studies that exist in the literature. Another source for photon pairs with non-classical behavior are parametric oscillators. The occurring two-photon coherent states are essential in quantum optics and of enormous interest for applications in quantum communication since their noise properties are close to those of a minimum-uncertainty state, i.e. a squeezed state. We develop the theoretical basis to explain the phenomenon of persistent response and other nonlinear phenomena obtained in an experiment where membrane resonators are driven in an ultra-strong regime. We show that they are caused by the nonlinear, internal interactions between higher-order flexural modes and higher-order overtones of the driven mode, where one mode is acting as a parametric drive onto another mode. Furthermore, we consider the interaction of two parametrically driven and nonlinear coupled Duffing resonators, obtaining nonlinear phenomena like a bifurcation.