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We study laser cooling of two ions that are trapped in a harmonic potentialand interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime isshown to work analogously to sideband cooling of a single ion. Outside theLamb-Dicke regime, the incommensurable frequencies of the two vibrational modesresult in a quasi-continuous energy spectrum that significantly alters thecooling dynamics. The cooling time decreases nonlinearly with the linewidth ofthe cooling transition, and the effect of trapping states which may slow downthe cooling is considerably reduced. We show that cooling to the ground stateis possible also outside the Lamb-Dicke regime. We develop the model and useQuantum Monte Carlo calculations for specific examples. We show that a rateequation treatment is a good approximation in all cases.Comment: 13 pages, 10 figure

Laser cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit