Theory of Hybrid Microwave–Photonic Quantum Devices

The Maxwell–Lindblad transmission line (MLT) equations are introduced as a model for hybrid photonic and microwave-electronic quantum devices. The hybrid concept has long enabled high-bandwidth photodetectors and modulators by using waveguide structures supporting microwave–optical co-propagation. Extending this technique to quantum-engineered lasers provides a route for greatly improved short-pulse and frequency comb operation, as impressively demonstrated for quantum cascade lasers. Even more, the self-organized formation of coupled microwave and optical oscillation patterns has recently enabled photonics-based ultralow-noise microwave generation. The MLT model provides a suitable theoretical description for hybrid quantum devices by combining optical and microwave propagation equations with a Lindblad-type approach for the quantum active region dynamics. A stable numerical scheme is presented, enabling realistic device simulations in excellent agreement with experimental data. Based on numerical results and analytical considerations, it is demonstrated that the functionality of the investigated hybrid quantum devices does not only rely on local coupling effects, but rather benefits from microwave-optical co-propagation, settling an ongoing debate. The MLT equations provide the basis for systematic device development and extension of the concept to other quantum-engineered hybrid devices based on, for example, quantum dot or interband cascade structures, as well as for simplified analytical models providing additional intuitive insight.