Editing Resolved sideband cooling (section)

=== Example: cooling of {{chem|Ca|+}} ions ===

[[File:Internal structure of Ca 40 ion with zeeman splitting.png|thumb|right|Relevant {{chem|Ca|+}} structure and light: blue - Doppler cooling; red - sideband cooling path; yellow - spontaneous decay; green - spin polarization <math>\sigma^-</math> pulses]]
The energy levels relevant to the cooling scheme for {{chem|Ca|+}} ions are the S<sub>1/2</sub>, P<sub>1/2</sub>, P<sub>3/2</sub>, D<sub>3/2</sub>, and D<sub>5/2</sub>, which are additionally split by a static magnetic field to their Zeeman manifolds. Doppler cooling is applied on the dipole S<sub>1/2</sub> - P<sub>1/2</sub> transition (397&nbsp;nm), however, there is about 6% probability of spontaneous decay to the long-lived D<sub>3/2</sub> state, so that state is simultaneously pumped out (at 866&nbsp;nm) to improve Doppler cooling. Sideband cooling is performed on the narrow quadrupole transition S<sub>1/2</sub> - D<sub>5/2</sub> (729&nbsp;nm), however, the long-lived D<sub>5/2</sub> state needs to be pumped out to the short lived P<sub>3/2</sub> state (at 854&nbsp;nm) to recycle the ion to the ground S<sub>1/2</sub> state and maintain cooling performance. One possible implementation was carried out by Leibfried et al.<ref name = leibfried /> and a similar one is detailed by Roos.<ref name = roos /> For each data point in the 729&nbsp;nm absorption spectrum, a few hundred iterations of the following are executed:
* the ion is Doppler cooled with 397&nbsp;nm and 866&nbsp;nm light, with 854&nbsp;nm light on as well
* the ion is spin polarized to the S<sub>1/2</sub>(m=-1/2) state by applying a <math>\sigma^-</math> 397&nbsp;nm light for the last few moments of the Doppler cooling process
* sideband cooling loops are applied at the first red sideband of the D<sub>5/2</sub>(m=-5/2) 729&nbsp;nm transition
* to ensure the population ends up in the S<sub>1/2</sub>(m=-1/2) state, another <math>\sigma^-</math> 397&nbsp;nm pulse is applied
* manipulation is carried out and analysis is carried out by applying 729&nbsp;nm light at the frequency of interest
* detection is carried out with 397&nbsp;nm and 866&nbsp;nm light: discrimination between dark (D) and bright (S) state is based on a pre-determined threshold value of fluorescence counts
Variations of this scheme relaxing the requirements or improving the results are being investigated/used by several ion-trapping groups.