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

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.publishe

Quantum-correlated photons generated by nonlocal electron transport

Since the realization of high-quality microwave cavities coupled to quantum dots, one can envisage the possibility to investigate the coherent interaction of light and matter in semiconductor quantum devices. Here we study a parallel double quantum dot device operating as single-electron splitter interferometer, with each dot coupled to a local photon cavity. We explore how quantum correlation and entanglement between the two separated cavities are generated by the coherent transport of a single electron passing simultaneously through the two different dots. We calculate the covariance of the cavity occupations by use of a diagrammatic perturbative expansion based on Keldysh Green's functions to the fourth order in the dot-cavity interaction strength, taking into account vertex diagrams. In this way, we demonstrate the creation of entanglement by showing that the classical Cauchy-Schwarz inequality is violated if the energy levels of the two dots are almost degenerate. For large level detunings or a single dot coupled to two cavities, we show that the inequality is not violated