Hybrid Microwave Resonator-Nanoscale Conductor Systems

Abstract: Entanglement is a fundamental aspect of quantum computation and quantum information processes. In this work, we analyse the entanglement of two microwave resonators when connected to a semiconductor double quantum dot. The two-mode squeezing operation is a commonly used tool in entanglement creation and, based on this, we utilise the related two-mode two-photon Jaynes-Cummings model in the theoretical description. We derive the Hamiltonian starting from circuit quantum electrodynamics, and consider it as an open quantum system described by the Gorini-Kossakowski-Sudarshan-Lindblad equation. Applying a mean-field approximation in the model, the Hamiltonian becomes quadratic, enabling the use of symplectic and phase space methods. In this framework, we derive the continuous differential Lyapunov equation as the equation of motion for the microwave resonators. The mean-field equations are not solvable analytically in the general case, and instead numerical methods are employed. Using the Duan criterion, we can calculate how the entanglement of the two resonators depends on the system. It is found, among other things, that the driving of the resonators generates entanglement within the mean-field system. We also find a good analytical approximation for the populations of the resonators.