Ion traps allow us to study single quantum systems, cooled to the lowe
st vibrational state of motion within confining electric and magnetic
fields. In this article, we describe the working principles of ion tra
ps and the methods used to cool the ions (principally laser cooling).
We then discuss how these cold ions, held almost at rest in the trap,
can be used to illuminate fundamental issues of quantum mechanics: qua
ntum jumps, the quantum Zeno effect and the quantum statistics of phot
ons scattered by the ions. Finally, we describe how several ions loade
d in a trap are cooled into ordered quasi crystals.