is there any anyone doing experiments?
BEC experiments are done in ultra-high vacuum and a BEC contain a very small number of atoms.
So the density is extremely small.
This question is a bit puzzling. For example, would you consider liquid He4 a "BEC" condensate? I would say that that BEC has a density larger than air.
On the other hand, as f95toli has mentioned you can also get it less than air in many of these atomic gas BEC.
So the question is like asking if "gasses" have smaller or larger density than air. The answer: it depends on the gas! The same applies here.
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