Eletrodinâmica Quântica de Cavidades na Faixa de Micro-ondas em Chips Semicondutores com Pontos Quânticos Definidos Eletrostaticamente

Abstract

This work presents a theoretical and computational study of light-matter interaction in circuit quantum electrodynamics (cQED) architectures based on semiconductor quantum dots. Using the density matrix formalism and the theory of open quantum systems, we employ the Lindblad master equation to model dissipative mechanisms, including energy relaxation (T1) and decoherence (T2). The theoretical framework starts from the quantization of the electromagnetic field and the Jaynes-Cummings model within the rotating-wave approximation (RWA), and is extended to the dispersive regime via the Schrieffer-Wolff transformation, yielding effective Hamiltonians and dispersive shifts. We then perform numerical simulations to characterize coherent dynamics under microwave control and to compare the obtained results with experimental benchmarks reported in the literature, with emphasis on reproducing Rabi oscillations and Ramsey interferometry. Finally, we examine the limits of validity of the RWA at stronger coupling and demonstrate the controlled preparation of dark states (decoherence-free subspaces) in the two-qubit Tavis-Cummings model.