What is the advantage of making a BEC in space? The NASA Cold Atom Laboratory, which I believe is slated to launch this year, has the goal of putting a Bose Einstein Condensate (BEC) apparatus on the ISS. What is the advantage of doing this? Naively, I might think that the only difference is the lack of gravity, which could be duplicated by applying the appropriate vertical force from light or magnetic fields to a terrestrial system.
This previous question suggests that one of the goals is to reach lower temperatures, but it is unclear to me why that would be true and whether there are any other motivations to the project.
 A: One reason that microgravity may be beneficial for reaching a lower temperature for laser-cooled atoms may be the following. In many ultracold atom experiments, usually after initial laser cooling, ultracold temperature is obtained by evaporative cooling (i.e. remove hot atoms from your sample, and they take away extra thermal energy, thereby cooling the sample overall), which is done in a tight  confining potential to have high elastic collision (and thus thermalization) rate. Then the sample can be adiabatically decompressed into a shallower trap, reducing the temperature even more. However, as you make final confining potential shallower/flatter, the gravitational potential will eventually dominate. This is one way gravity can be a limit on the temperature of the trapped ultracold atomic gas.
Another benefit of microgravity, especially for atomic fountain clocks, is a longer interrogation time. Because gravity is weak, atoms that are tossed up vertically take much longer time to return back to the original position, and the resulting longer interrogation time reduces the frequency uncertainty of your atomic clock further. 
EDIT: I think the answer to the question you have linked gives a similar answer as I have written in my first paragraph, and that answer also contains a link to the research resulting in the coldest temperature achieved by the gravito-magnetic trap for ultracold atoms (by Wolfgang Ketterle). Also, as dolan has nicely explained, there are limits to how you can compensate gravity using magnetic gradients (e.g. non-zero curvature, state selectivity, etc.)
A: Apparently it's potentially possible to detect gravitional waves using a BEC in low gravity, as this extract from Gravitional Waves and BECs shows:

If a gravity wave should pass through while a BEC is separated, then one of the clouds will travel further than the other thanks to the stretching of space. That will be detectable as a shift in the locations of the fringes. The actual implementation of such a scheme is far more subtle than what I have described, but the essence of the experiment remains the same.
So you can imagine that there is a lot of interest in testing general relativity at very small scales. For instance, a BEC may allow us to see whether gravity and acceleration really are indistinguishable—something called the universal equivalence principle. This basically involves taking BECs, putting them in free fall, and seeing if BECs made from different atomic species fall at different rates. 

They have tried this on a small scale on the Vomit Comet, using the plane's trajectory to reduce gravity, so taking the experimental equipment for a much longer spell in low /zero g would be the next step.
