Bose-Einstein Condensate

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A question occurred to me concerning the Bose-Einstein condensate:
When you have a quantum gas of bosons at a low temperature you obtain a Bose-Einstein condensate where some bosons are in the same state. When you consider the two bosons with the same state, they should behave like one boson, shouldn't they? Because when you have an interaction you shouldn't have any preferences to one of the bosons. So there shouldn't be a way to separate the two boson after they reached the same state? Or does the Heisenberg uncertainty principle apply here? If so, who is this done in computation? Thanks it advance!
 

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While I'm not sure how one would describe the uncertainty princliple to the bose Einstein condensate, in a general way it would be an apt example of observation or measurement of the condensate in that the temperature required to form the condensate is extremely close to 0 K. That even attempts to record/measure its state causes the condensate to heat up to the point that it collapses back to a non bose-condensate. I did copy the original pdf publication issued from the University of Cambridge, Hopefully I didn't lose it when my other computer crashed If I can find it I'll post it here for viewing. I really hope I can find it in my collection.
 
  • #5
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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 seperate 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
 
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I guess I didn't explain my problem very well. In a BE condensate you have indistinguishable bosons with identical wave functions. The problem is now, how can you separate them? The separation is meant to be that the bosons get non identical wave functions. I can't really imagine how to handle that in a computation.
 
  • #7
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page 96 to 100 of the first article link posted showed a seperation using induced frequencies with the trapper page 98 covers one such seperation where two clouds were formed in the spin positions. Every article I've come across on studying the Bose Eientein condensate usually involve induced perturbations using the trap itself to study the effect. This iss another article that descibes some of the findings

http://yannickseurin.free.fr/pubs/BretinSSD04_PRL.pdf
http://www.phys.psu.edu/~dsweiss/PRA%20RC%20optical%20BEC.pdf [Broken]

Every method of studyI have ever come across has been through manipulations of the trapping method or through scattering effects there are various other articles with similar approach, as far as seperating one individual to another would have to be through the removing of the trap and monitoring the seperation though using the trap and disturbing it with frequencies or optical light will allow some seperation and study.
 
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  • #8
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I guess I didn't explain my problem very well. In a BE condensate you have indistinguishable bosons with identical wave functions. The problem is now, how can you separate them? The separation is meant to be that the bosons get non identical wave functions. I can't really imagine how to handle that in a computation.
you would simply use a so called permanent to dscribe the many-body wave function of an assembly of bosons occupying different single-particle wave functions.

Notice that 'separating' the particles in different states has nothing to do with physically making the distance between two of them bigger, or breaking up some bound state.
 

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