Hybrid systems: Quantum cavities coupled to spin qubits

Recent experimental advances enable the manipulation of quantum matter by exploiting the quantum nature of light. Quantum information transfer between distant regions is one of the aims of the fields of quantum computation and quantum information. We will theoretically explore the physics of charge and spin qubits implemented in semiconductor quantum dots immersed in quantum cavities, for arbitrary coupling strength with the photon field. The aim is to couple two distant qubits and to transfer information between them through the cavity photons. First we will explore the Hamiltonian of a two level system consisting on two charge electronic states in a quantum dot and we will analyze the cavity transmission for different coupling intensities between light and matter. We will extend our analysis to couple the cavity to a two level spin qubit system. Floquet theory is the optimal tool to analyze periodic Hamiltonians in the time domain. It allows to tune the electronic, transport and dynamical properties of matter. We will explore as well other techniques as the input-output formalism to analyze the transmission through the cavity.