Abstract
In the second lesson, we began to describe the methods used to manipulate ions trapped in quantum information. We analyzed the properties of the quadrupole Paul trap and showed how it is possible to separate micro- and macro-movements in the motion of ions. After giving some orders of magnitude, we described the linear Paul trap for confining a chain of ions coupled together by Coulomb interaction. We described the crystallization process in such a trap and analyzed the vibrational modes of two or three ions, then generalized to a larger number of ions. We then tackled the important problem of radiative cooling of the ions, starting with Doppler pre-cooling using a natural large-width transition. We evaluated the limiting temperature reached by this process, then described an additional "red sideband" cooling mechanism using a transition of low natural width. We also introduced the Lamb-Dicke parameter, essential for describing the coupling of trapped ions to laser radiation. Finally, we qualitatively analyzed the cooling of a collective vibration mode by action on a single ion, known as "sympathy" cooling.
