Hi all,
This is a pure curiosity question. Obviously, Superfluid helium has to do with BECs (in particular, it is implicitly suggested by Feynman in his famous lectures). However, my idea of a BEC is that it is like a Maser, or a matter Laser, right ? So in principle, all the bosons in the BEC have the same QM state vector, don't they ? But in superfluid helium, we can see a thin film climbing up and down the walls of the beaker, which shows that at least some particles don't have the same momentum as everyone else in the beaker. So is superfluid helium really a BEC ? And if not, is it because it is in a quite dense state, whereas most BECs are obtained in a low density gaseous state ?
The short answer is yes, it is. As you correctly stated in a BEC most of the bosons occupy the lowest quantum state possible, I don't see the connection to the Maser, though.
Actually, superfluidity is for bosons what supra conductivity is for fermions and they are both consequences of Bose-Einstein-Condensation.
I can recommend also the wikipedia page on this for further reading - there you'll find quite a nice summary:
https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate
Thanks for your answer. About the maser, it's my mistake. I meant the equivalent of a Laser (L for Light) but for Matter (M). However given the complete meaning of the acronym Laser, this would not make sense actually XD. I just meant that it is a state where all particles are in the same state.
So you don't really address the key point of my question, which was about the fact that all particles don't seem to all have the same momentum (therefore they are not all in the same state) in a superfluid helium sample.
Oh, sorry - I missed that.
The particles in a BEC are usually in the same momentum state (i.e. the ground state). This is the minimum momentum (although, it's still finite). As the momentum should be 3-D, I guess, you can 'shift' components of the momentum vector from one spatial direction to the other without changing the absolute value of the p-vector. However, to be honest, this is more an educated guess on my side - the question is indeed a good one (meaning that I'm not sure, if I can provide the full answer). :)
I think the connection between BEC and superfluidity is not that obvious. The theory of superfluidity by Landau makes no mention of the statistics of the particles (Bose or Einstein), as was often noticed. It does not mean though that BEC are not superfluid: they are, as a consequence of Bogoliubov theory and of the finite speed of zero momentum phonons (because of the weak interaction between particles).. Incidentally, what you call BEC is not superfluid without interactions because the low momentum excitation have zero speed, as is well known too. Superfluidity requires that zero energy fluctuations have finite speed (or a gap) and that the temperature is less than a critical value. This is correct for interacting bosons, like Helium 4 but also for fermions like Helium 3, but there things are more complex than what is described by the original Landau theory because of a complex relation between the order parameter and the spin of the particles, but it remains within the general framework of this theory. About the Maser, I believe it is a kind of non equilibrium system that can hardly be understood with equilibrium theories. The frictionless flow (all particles not having the same momentum) you refer to is well explained by Landau theory.
Yves Pomeau
Thank you very much for your answers (sorry for the delay, I was away). I recognize the discussion has nothing to do with the Maser, it was just an acronym misunderstanding from my younger years, thank you for finally correcting it.
I understand I have to turn to Landau theory to get the subtleties involved.
Cheers