How to choose which atoms to cool using optical cooling technology? Which atoms are easiest to cool down to very low temperatures (e.g. mK)? Which quantities does one need to look at?
My very naive guesses so far are:


*

*Their mass: the heavier they are they least likely they'll keep moving around.

*Their interaction energy? 

 A: Laser Cooling using Rubidium.  I am sure you have gone through the Wikipedia related articles, but I can't see the reason why these particular atoms are used explained there. Unfortunately the extract below only deals with Rb, although K is immediately  above Rb in the periodic table, (so I won't win a Nobel prize for guessing it has many of the same properties as Rb).

Rubidium was a later arrival on the laser-cooling scene, but took off in popularity when it was realized that the diode lasers used for CD players worked in the near-infrared, at a wavelength very close to that needed to laser cool rubidium. That brought laser cooling within reach of a huge range of labs– rather than dropping a couple hundred thousand dollars on a dye laser system, you could spend maybe ten grand on the complete laser system, with money left over for vacuum hardware.
In addition to being enabled by cheap lasers, rubidium turns out to have a bunch of nice properties, particularly for people doing BEC experiments. It’s got hyperfine structure, meaning you need a repumping laser, but the frequency difference is relatively easy to manage, and that allows you to do “dark spot” traps to bump up the atom number. The number of atoms you can get in a condensate, and the energy of those atoms, depend on the collisional properties of the atoms in question, and those work out very nicely for rubidium– the “scattering length” that characterizes the collision for rubidium-87 is moderately large and positive, and by happy coincidence is nearly the same for two different magnetically trappable states, and between those states, so they’ve been able to do all sorts of fun two-species experiments. The collisional properties are also vastly better than those of cesium, so laser-cooled rubidium samples have found lots of applications in “clocks,” and for comparisons of time standards of different types.
Rubidium was the system for the first dilute-vapor BEC, earning Cornell and Wieman their share of the 2001 Nobel Prize. They’ve kind of gone back and forth with the Ketterle group at MIT ever since for “coolest recent BEC experiment,” with the JILA team being the first to see vortices in a condensate (one of the signatures of superfluid behavior), and all sorts of two-species stuff because there are two trappable states that will happily coexist. The Bose condensation of rubidium-85 was also pretty impressive, because 85Rb by itself has a negative scattering length which prevents the formation of a stable condensate, but they were able to change the collisional properties using a Feshbach resonance, opening the door for a lot of other experiments using those resonances.
These days the laser situation is less rosy than it was in the early 1990’s– the electronics inductry has moved on to different laser technologies, so the only people who still buy 780nm lasers are atomic physicists, and there aren’t enough of us to support a robust market for cheap lasers. But there are more commercial suppliers of complete laser systems these days, so it’s not all that bad. If you were going to set up a generic ultracold-atom system from scratch to allow a wide range of possible experiments, rubidium is still probably the atom of choice.

