Light-Matter Systems Out of Equilibrium: from Random Lasers to Circuit Quantum Electrodynamics

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This proposal contains two subprojects about the physics of light-matter systems, both sharing a common theme and methods, but also quite different in aims and specifics. I propose to theoretically investigate the physics of two classes of artificial quantum devices: random lasers and superconducting circuits. Random lasing in a disordered photonic medium is relatively new and only partially understood phenomenon, in which the mechanisms of scattering and gain determine the lasing spectrum and directionality, and the cavity boundaries play only a secondary role. There is a strong potential for applications of random lasers, since they are easy to manufacture, shape, and are relatively cheap. The second part of the project concerns the physics of superconducting circuits, which is described by a theoretical framework called Circuit Quantum Electrodynamics (circuit QED). This is an emerging field which aims to study the implementation of superconducting qubits and circuits to quantum information processing and quantum optics, with an emphasis on methods of control of the individual components of the system. The first quantum algorithms in a solid state device have been demonstrated in these systems, and the complexity of the circuits experienced a steady growth in scale in the recent years, which is expected to continue. This proposal aims to address some of the theoretical needs of both fields which are central to their development, by which we will also explore a frontier of many-body non-equilibrium quantum theory and develop computational methods for quantum control. Non-equilibrium physics of light-matter interaction stands at the basis of both systems and therefore we propose to employ similar theoretical methods to investigate the role of quantum fluctuations in the optical nonlinear response of the two systems. In circuit QED this effort will extend existing analytical theory of superconducting qubits, and complement the proposed development of exact simulations. For random lasers we will gain insight into the temporal and spatial fluctuations of the lasing modes, as well as to the role of photonic disorder in statistical studies of random spectra.