Editing Resolved sideband cooling (section)

== Experimental implementations ==

For resolved sideband cooling to be effective, the process needs to start at sufficiently low <math>\bar n</math>. To that end, the particle is usually first cooled to the Doppler limit, then some sideband cooling cycles are applied, and finally, a measurement is taken or state manipulation is carried out. A more or less direct application of this scheme was demonstrated by Diedrich et al.<ref name=diedrich /> with the caveat that the narrow quadrupole transition used for cooling connects the ground state to a long-lived state, and the latter had to be pumped out to achieve optimal cooling efficiency. It is not uncommon, however, that additional steps are needed in the process, due to the atomic structure of the cooled species. Examples of that are the cooling of {{chem|Ca|+}} ions and the Raman sideband cooling of {{chem|Cs}} atoms.

=== 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.

=== Example: Raman sideband cooling of {{chem|Cs}} atoms ===

A [[Raman cooling#Two photon Raman process|Raman transition]] replaces the one-photon transition used in the sideband above by a two-photon process via a virtual level. In the {{chem|Cs}} cooling experiment carried out by Hamann et al.,<ref name=hamann /> trapping is provided by an isotropic [[optical lattice]] in a magnetic field, which also provides Raman coupling to the red sideband of the Zeeman manifolds. The process followed in <ref name=hamann /> is:
* preparation of cold sample of <math>10^6</math> {{chem|Cs}} atoms is carried out in [[optical molasses]], in a [[magneto-optic trap]]
* atoms are allowed to occupy a 2D, near resonance lattice
* the lattice is changed adiabatically to a far off resonance lattice, which leaves the sample sufficiently well cooled for sideband cooling to be effective ([[Lamb Dicke regime|Lamb-Dicke regime]])
* a magnetic field is turned on to tune the Raman coupling to the red motional sideband
* relaxation between the hyperfine states is provided by a pump/repump laser pair 
* after some time, pumping is intensified to transfer the population to a specific hyperfine state
* lattice is turned off and [[time of flight]] techniques are employed to perform Stern-Gerlach analysis