These notes are part of the five lessons given in Les Houches on october 2008 for the cold atom and BEC predoc school. Why a lesson about trapped ions in such a school? There is no BEC, no degenerate gas, no Mott transition with trapped ions...but there are optical clocks among the most accurate in the world, there is phase transition from liquide to crystal, there are cold molecules to study cold reactions and most famous of all, there is the realisation of quantum gates, the bricks of quantum computer. Furthermore, experiments done with trapped ions have inspired and initiated several breakthroughs with neutral atoms because with such a system, “your hands are free”, the trap keeps the ion(s) for you and you can try many different laser interaction protocoles. Here are the basics that, I hope, will help you understand why experiments with trapped ions can be so interested
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