Elliptical ion traps for quantum computation

Summary form only given. The Cirac-Zoller model of quantum computation assumes that ions are confined in a linear ion trap. However, no experimental test of quantum computation or even of Raman cooling has yet been performed in a linear trap; instead the NIST group has used a miniature Paul trap in which a slight asymmetry or ellipticity is introduced to define an axis of crystallization. In this paper the case of arbitrary ellipticity is considered and two results for the crystal size and micromotion amplitude are derived. The first relation is a linear crystal stability condition, which shows that the maximum number of ions which can be confined is uniquely related to the ellipticity by a 7/3 power law. The second result shows that the micromotion in elliptical traps is far smaller than one would expect naively, specifically that the micromotion amplitude depends approximately on the 1/5 power of the number of trapped ions.