Cooling of trapped multilevel ions: A numerical analysis

Laser cooling of trapped multilevel ions is studied numerically. The ions are assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke regime). A master equation for the center-of-mass motion is used to numerically evaluate cooling rates and final temperatures for arbitrary light field configurations. The results show both well-known cooling mechanisms (Doppler cooling, sideband cooling) and effects introduced by the presence of multiple atomic levels. Quantitative results are given for a trapped ${\mathrm{Ba}}^{+}$ ion. The numerical procedure can easily be adapted for all ions used in today’s trapping experiments. © 1996 The American Physical Society.