Yeesh nothing worse than typing a lengthy reply when server reset happens lol. So instead of retyping everything I'm going to cheat and pull key lines from articles I posted
Essentially if I understand your question correctly when you obtain a bose Einstein condensate. The atoms become blurry and overlap, They essentailly become indistinguishable from one another. You are correct in that ther is no way to separate them until you release them from the trap or allow them to warm up the period of time they allowed in one experiment is 0.1 s but I wouldn't describe it as preference but rather indistinquishable. Some articles and youtube videos state they lose all information and think they are every boson I don't agree with that statement.
Below are all lines cut and pasted from the articles above that pertain directly to your question
We can rarely observe the effects of quantum mechanics in the behaviour of a macroscopic amount of material. In ordinary, so-called bulk matter, the incoherent contributions of the uncountably large number of constituent particles obscure the wave nature of quantum mechanics, and we can only infer its effects. But in Bose condensation, the wave nature of each atom is precisely in phase with that of every other. Quantum-mechanical waves extend across the sample of condensate and can be observed with the naked eye. The sub- microscopic thus becomes macroscopic.
New Light on Old Paradoxes
The creation of Bose-Einstein condensates has cast new light on long- standing paradoxes of quantum mechanics. For example, if two or more atoms are in a single quantum-mechanical state, as they are in a condensate, it is fundamentally impossible to distinguish them by any measurement. The two atoms occupy the same volume of space, move at the identical speed, scatter light of the same colour and so on.
Nothing in our experience, based as it is on familiarity with matter at normal temperatures, helps us comprehend this paradox. That is because at normal temperatures and at the size scales we are all familiar with, it is possible to describe the position and motion of each and every object in a collection of objects. The numbered Ping-Pong balls bouncing in a rotating drum used to select lottery numbers exemplify the motions describable by classical mechanics.
At extremely low temperatures or at small size scales, on the other hand, the usefulness of classical mechanics begins to wane. The crisp analogy of atoms as Ping-Pong balls begins to blur. We cannot know the exact position of each atom, which is better thought of as a blurry spot. This spot-known as a wave packet-is the region of space in which we can expect to find the atom. As a collection of atoms becomes colder, the size of each wave packet grows. As long as each wave packet is spatially separated from the others, it is possible, at least in principle, to tell atoms apart. When the temperature becomes sufficiently low, however, each atom's wave packet begins to overlap with those of neighbouring atoms. When this happens, the atoms "Bose - condense" into the lowest possible energy state, and the wave packets coalesce into a single, macroscopic packet. The atoms undergo a quantum identity crisis: we can no longer distinguish one atom from another.
essentially not only are they indistinquishable from one another they also have the same wave length at the lowest possible energy state
"The Bose-Einstein condensate is a rare example of the uncertainty principle in action in the macroscopic world. "
as far as the the above line means is best described by the method they trap the condensate to image the condensate they turn off the trap.
this is a line from one of the articles I posted. If I recall the posts it was the first article.
" What does
the uncertainty principle tell us about this? It says that
if you know really well where a quantum object is, you
can’t really know how fast it’s going; and on the other
hand, if you know less well where the object is, you can
have a better idea of how fast it’s going. If the object is
bunched up in coordinate space, it will be spread out in
momentum space, and vice versa. We actually get a
demonstration of the uncertainty principle at work
when we turn off the trap, let the atoms fly apart, and
take a picture of their momentum distribution. Sure
enough, the cloud, which was initially squeezed up in
the axial direction in coordinate space, is now more
spread out in that direction. So this is quantum mechanics
at large. "
Hope this helps
