# Population dynamics in sideband cooling of trapped ions outside the Lamb-Dicke regime. (arXiv:1809.02848v2 [physics.atom-ph] UPDATED)

We present the results of simulations of optical sideband cooling of atomic
ions in a trap with a shallow potential well. In such traps, an ion cannot be
Doppler cooled near to the Lamb-Dicke regime ($\eta^2(2n+1) \ll 1$). Outside
the Lamb-Dicke regime, the sideband cooling dynamics are altered by the
existence of various Fock states where the cooling becomes very slow. A calcium
ion trapped in our Penning trap realises such a situation, hence single stage
cooling is inefficient to prepare the ion in the motional ground state. For
these systems, it is necessary to study the cooling dynamics in detail and we
show that it is possible to implement an optimised cooling sequence to achieve
efficient ground state cooling. We also present the simulated cooling dynamics
of two ions trapped in a Penning trap, where the presence of an additional
motional mode requires a complicated cooling sequence in order to cool both
axial modes to the ground state simultaneously. Additionally we investigate
sideband heating of a single ion in a Penning trap.