What is the largest number of bosons placed in a BEC? What is the record for the largest number of bosons placed in a Bose-Einstein condensate?
What are the prospects for how high this might get in the future?
EDIT: These guys reported 20 million atoms in 2008.  "Large atom number Bose-Einstein Condensate machines" (pdf).
EDIT 2: van der Straten's group reported 100-200 million.
https://doi.org/10.1063/1.2424439 
https://doi.org/10.1103/PhysRevA.80.043606 
https://doi.org/10.1103/PhysRevA.80.043605
But these guys don't seem to claim the largest BEC, so I wonder if there's larger.
EDIT 3: ~ 1 billion hydrogen atoms back in 2000 by Greytak et al.
https://doi.org/10.1016/S0921-4526(99)01415-5
Of course, hydrogen has only 1 nucleon while sodium (used by van der Straten et al.) has 23, so these are quite comparable in terms of mass.
 A: Superfluid helium 4 is the winner here, and by a vast margin. There's a body of literature from the 90s that attempts to estimate the fraction of helium atoms that are Bose condensed in superfluid helium 4. To quote this paper, "These works... estimate the condensate fraction to be ≈7% at saturated vapor pressure (SVP)." At a mass density of 125 g/L, this would give about $10^{24}$ condensed atoms per liter!
Note that while helium liquifies below 4K, you need to go below ~2K to get superfluid helium. The transition from liquid to superfluid is continuous, and so the amount of superfluid helium right at the transition temperature is basically zero. However below about 1K, virtually all helium atoms are in the superfluid state.
That an Avogadro's number or more of atoms can occupy the zero-momentum state of an arbitrarily large box is a pretty remarkable demonstration of Bose-Einstein condensation.
Honorable mentions

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*Regarding more conventional BECs, the largest I've come across is only slightly larger than the 1 billion you quote in your question; ­ $1.1 \pm 0.6 \times 10^9$ atoms in an earlier paper by the same authors. Most research these days works with only millions of atoms (and rarely hydrogen), so I'm not aware of any efforts to push above billions.


*Superconductors have a lot in common with Bose Einstein condensates, since in this effect pairs of fermions also condense into a macroscopic 'supercurrent.' No two fermions can occupy the same state, but if you'll accept the similarities, then there are some theoretical proposals that entire stars can form a "BEC". See e.g. Bose-Einstein Condensate general relativistic stars, though I can't speak to the correctness of this paper.
A: I would suspect the What is the largest number of bosons placed in a BEC would be the largest vat of liquid below boiling point 4He. I think 4He must be in the ground state to be a non boiling liquid and this is effectively a BEC.
