These Bose-Einstein Condensates really illuminate some of the fundamental physics of the universe, one particular experiment, performed by JILA, is perhaps as interesting as it is puzzling.
Take a 'traditional' BEC of 85Rb and cool it to only 3 billionths of a degree above zero, and then adjust the magnetic field which holds the condensate in place. Theoretically, the magnetic field should alter the way the wavefunction of the condensate self-interacts, making it either 'repulsive' or 'attractive'. Therefore, you should see the cloud of atoms pulse in and out as you adjust the field.
What actually happened when the experiment was performed, was that, yes, as you make the self-interaction repulsive, the cloud swells as predicted by theory; but when made attractive, the cloud does at first contract, but then suddenly explodes outwards! This 'explosion' (actually about 1500 of the atoms are heated to 200 billionths of a degree so the energy is very small) has a lot of characteristics of a supernova, leading to the coining of the term 'Bosenova'. It produces a shell of atoms, or collimated jets that expand outwards looking like photos of stellar explosions, but interestingly about half the atoms seem to vanish; they're not in the gas of the explosion, or in the remnant left behind! Most likely either the atoms are in a form that's undetectable, or have been given so much energy, they've shot out of the magnetic trap entirely. But who knows, perhaps you are confining the atoms to a state they shouldn't be in and they genuinely disappear, or quantum tunnel out of the trap or even our universe.
(Weird! I hope it doesn't turn out to be an experimental error, and I'm sure it won't; this group is good)
Recently BEC have been used to model a variation of black holes; gravastars in an attempt to use quantum mechanics to explain macroscopic objects at extreme energy scales...