Summary
The first lesson began with a summary of previous lectures. The notion of qubit, described as a fictitious spin evolving in the Bloch sphere, was recalled, as well as the description of a harmonic oscillator and the operators playing an important role in its description (quanta creation and annihilation operators, oscillator displacement in its phase space, quanta number parity operator). The interaction between a qubit and an oscillator was analyzed within the framework of Jaynes and Cummings' fully soluble model, and the properties of the "qubit plus oscillator" dressed system were recalled. Two systems implementing this simple model were described. One is the system studied in cavity electrodynamics (Rydberg atom coupled to a mode of the field in a cavity) and the other is the case of a trapped ion interacting with lasers (the qubit is realized by two internal energy levels of the ion and the oscillator is a mode of vibration of the ion in the trap). Coupling two qubits to the oscillator enables the entanglement of two atoms or ions. Conversely, coupling two field modes or two mechanical vibration modes to a qubit enables two oscillators to be entangled. Cavity electrodynamics and trapped-ion experiments performing these elementary operations were recalled.
