Abstract
The third lesson began with a description of other laser cooling methods, adapted to a few special cases ( Beryllium Raman sideband cooling and information acquisition cooling (stochastic method). We then set out to describe in detail the interaction Hamiltonian of an ion with a laser, treating the ion's motion quantically. The Hamiltonian was developed in terms of the power of the Lamb-Dicke parameter, allowing us to separate the terms responsible for central (carrier) and lateral band resonances. The former correspond to the absorption or emission of a laser photon by the ion, with no change in the number of vibrational phonons, while the latter are associated with simultaneous changes in the number of light and vibrational quanta. Interaction with the carrier enables single-qubit operations, equivalent to qubit rotation. The resonant interaction on the first sidebands is described by terms analogous to those encountered in cavity electrodynamics, hence the great similarity of ion physics to that of cavity Rydberg atoms studied in previous years. We described the phenomenon of Rabi oscillation of an ion and qualitatively analyzed the entanglement operations between qubit states of the ion and the mode of vibration. The lesson ended with a description of a two-ion entanglement experiment, including a Bell inequality measurement.
