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

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.

This proposal is concerned with the physics of two very different light-matter systems: random lasers and superconducting qubits. Concerning random lasers, the dynamical and statistical complexity of the optical response of these systems and our lack of understanding of it are currently hindering the development of applications. The main potential beneficiaries from the basic research suggested here are applied physics and engineering laboratories, which academic but geared towards applications, and the optoelectronics/photonics industry. Random lasers are easy to manufacture, form into different shapes, can be of micron size and are relatively cheap. Several applications for these systems have recently been suggested as disparate as temperature sensing and medical diagnostics, all of which will benefit from a quantum theory for these lasers, without which it is hard to predict how their temporal and spatial coherence properties will depend on the device parameters. I would like to stress that such a theory does not exist today, and this is exactly the point where the impact of our research can be maximal, although one has to calibrate the anticipation of impact to the fact that this is still a basic science proposal. Therefore, a possible scenario is that companies, working in collaboration or inspired by applied physics or engineering research groups will try to develop one of the numerous applications that have been suggested in recent years in the academic literature. To summarize, I estimate that a quantum theory for these systems would enhance the chances that these efforts will actually take place. If we turn to quantum engineering with superconducting qubits, it is clear from the onset that one of the strongest motivations for experimenting with them stems from their potential usefulness as future computational elements, with a huge potential impact on the high-tech industry. Superconducting qubits are leading candidates in solid state quantum computing architectures, with most potential to transfer to industry. In fact at least two large companies in the U.S., IBM and BBN already have decided to put their stakes in this direction and are employing research teams. A basic condition to move forward with applications is improving our understanding the control of quantum systems, a largely open question today, with relevance for other competing qubit architectures in quantum information science and other devices. However, our current theoretical understanding of controllability and of the optimal control landscape are very limited, with most applications and analysis done for the very different field of quantum chemistry on steering chemical reactions to affect the desired products. Therefore, progress on the question of optimal control will bear direct impact on all these efforts of quantum engineering, by simply indicating what tasks we can expect our circuits to perform with high fidelity. Beneficiaries in the industry and applied research groups will also gain from efficient algorithms, since as in all modern engineering fields, simulations form an integral part of a the tools for developing new products. If we take as a concrete example quantum algorithms, there is need for developing the pathway to larger scale integration of registers of several qubits, since it is clear that in 2-5 years we will have these registers fully functional in solid state architecture. However, current computational modeling is way behind, with even large Linux computing clusters not being able to fully model a chip of 3-4 transmon qubits. In this proposal I plan to spend a significant amount of time developing generic codes that will be able to effectively simulate large circuits.