Does superfluidity imply BEC? (+ other BEC questions)

[nonequilibrium]

Hello, I have to do a basic presentation about BEC (for a course on "Scientific Communication") and I had a question or two:

How come there are many youtube clips of superfluidity and none of BECs? Is it wrong to consider superfluid 4He as a weakly-interacting BEC? (as I understand, a BEC is actually only applicable for an ideal (quantum) gas? But the theory was broadened to weakly interacting systems?) This is what I read anyway, but I see the cooling temperatures are also much lower for BECs, or is that just for the ideal gas-type BECs?

Also, is it possible to create superfluid H20? (as its spin adds up to an integer?)

And is the thought process of creating a BEC (for 4HE) the following: we cool the atoms down, the wave function for each 4HE gets bigger (due to momentum -> 0), and due to the sum of the spin of an atom being an integer, each atom is beginning to look like the wave function of a boson, and then all the atoms can fall into each other due to properties of bosons?
(if so, why doesn't it work for atoms with spin-sum of half an integer on the condition that the number of atoms is even, so that the total spin-sum is again an integer?)

Thank you!

 

[DrDu]

Well, superfluidity in 4-He is much easier to observe than BEC's in some traps with laser-cooling. However, 4-He cannot be described as a weakly interacting gas, it's a liquid.

I think all BEC's created up to now are only metastable with respect to a condensation into a solid. Due to the dipole moment of H2O it might be difficult to stabilize a metastable BEC of water molecules.

To your last question. Yes, in principle also particles of half integer spin can pair up and then form a superfluid. That happens e.g. in superfluid 3-He.

 

[nonequilibrium]

Thank you. Regarding your first note: then is it wrong to use 4-He as an example of a BEC? Anyway, it does seem correct to say it is an example of bose-einstein statistics, correct (because it shows that bosons can "team up" to form a new state of matter with weird qualities as superfluidity)? If so, then what is the remaining difference with a BEC?

 

[JustinLevy]

This is a bit tough, because it depends on how picky you want to be. Since He4 helium atoms are bosons, calling superfluid He4 an example of Bose-Einstein Condensation (BEC) is getting a large part of the idea correct and I think is fine for trying to describe science ideas to the public (which seems to be your course?). As far as "simplifying" for the public goes, this one I feel is quite minor.

To show the power of this (ie. how little it is "simplifying" the idea), let me note that your expectations from this picture of superfluid He4 are correct:

if so, why doesn't it work for atoms with spin-sum of half an integer on the condition that the number of atoms is even, so that the total spin-sum is again an integer?

It does occur. For example He3 (a fermion atom), can pair up and these pairs which are then bosons can "bose condense". This is essentially what allows He3 to go superfluid.

Is it wrong to consider superfluid 4He as a weakly-interacting BEC?

Well, the He4 are not weakly interacting. It is a fluid. Actually, the only thing preventing it from being a solid is the low mass of He4 (and thus high "zero point energy"). The kinetic energy can only be reduced so far.

(as I understand, a BEC is actually only applicable for an ideal (quantum) gas? But the theory was broadened to weakly interacting systems?) This is what I read anyway, but I see the cooling temperatures are also much lower for BECs, or is that just for the ideal gas-type BECs?

I just checked wikipedia, and I'm guessing you got this from there.

This issue is the derivation of Bose-Einstein statistics assumes non-interacting states. Depending on your level of physics knowledge, you can see that in the derivation here:
http://en.wikipedia.org/wiki/Bose–Einstein_statistics

As with most physics, this is actually an approximation for almost everything. Obviously that doesn't mean it is worthless. In some cases the interactions neglected in the approximation are so small, it is not even worth discussing beyond a throw away comment.

Where I disagree with wikipedia a bit, is their implications of what they mean by interactions. Look at the derivation of BE statistics. As long as we can list the energy levels of single excitations of the system, and these energy levels are "non-interacting" enough to allow description of all (relevant) excitations of the system (ie. we can get the energy quite well from: excitation energy = number of 1st excitations * first excitation energy + number of second excitations * second excitation energy ... etc.), then we should be able to use Bose-Einstein statistics well for the statistics of this system. And futhermore be able to discuss BEC well.

Such decomposition works well for most large systems, even if the interactions of the individual "particles" is fairly strong. That is why the main ideas of BEC still work so well for guiding the intuition with He4 and He3 superfluidity.

Also, is it possible to create superfluid H20? (as its spin adds up to an integer?)

Due to how they cool gasses for BECs, it is _incredibly_ hard to cool molecules in this manner (even many atoms have too many transitions to be helpful ... that is why most groups focus on specific types of atoms). So yes, merely from your argument there (that it is a boson), it may be theoretically possible, but very far from practical.

And to follow up on a previous comment, the dipole moment alone can't rule it out, as there are groups working on atoms with magnetic dipole moments. I sat through a talk, but don't remember the details unfortunately.

 

[nonequilibrium]

Thank you for the detailed reply! It helps a lot!