Cooling of trapped multilevel ions: A numerical analysis

Abstract

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 regime͒. 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 cool-ing͒ and effects introduced by the presence of multiple atomic levels. Quantitative results are given for a trapped Ba ϩ ion. The numerical procedure can easily be adapted for all ions used in today's trapping experiments.

Fabrication and heating rate study of microscopic surface electrode ion traps

“…For two level systems this is straightforward, however for multi-level dynamics the situation is more complex. In particular, dark-resonances and the strength of the repump light field(s) have significant influence on the line shape [45,46,47].…”

Optimization of Doppler Cooling of a Single 40Ca+ Ion

“…This is consistent with the study reported by Reiß el al. 8) However, the temperature of the ion does not change in the range of $50-MHz detuning of the 866 nm laser, because the 2 P 1=2 -2 D 3=2 transition is strongly saturated. Therefore, we set the detuning of the 866 nm laser to 0, and do not record the dependence of the detuning on the temperature.…”

“…The cooling rate for Doppler cooling depends on various experimental parameters, for example, the laser detunings, 8) the intensities of the cooling beams, and the magnitude of the applied magnetic fields. Proper cooling to the Doppler limit facilitates ground-state cooling in the second stage.…”

Fast Laser Cooling Using Optimal Quantum Control

“…Here γ g is the decay rate from |e to |g and from |t to |r , and γ r is the decay rate from |e to |r and from |t to |g . The slight difference between the expressions of ρ1 and ρ2 is due to the different emission dipole patterns [59].…”