# What happens when Bose-Einstein Condensate exits a vacuum?

• Jason White

#### Jason White

I haven't learned about this yet in school but I'm assuming as the atoms condense down to a single wavelength the volume of the liquid would be very small. If this condensate was instantly released out of a vacuum and into normal atmospheric pressure, would the volume rapidly expand?

Secondly, since everything is brought down to match a single wave function, and the temperature is very, very, very low, would the mass also reduce significantly, or is the wavelength so small that the Energy (E=HC/f) is still large and carries the same weight through the equation E/(C^2)=m

The atoms would collide with air molecules, get energy and the BEC would break down.

would the mass also reduce significantly
The mass is independent of that. Strictly speaking, a hot gas has a tiny bit more energy and therefore more mass, but the difference is negligible (small fractions of 1 eV per particle, where the mass of a particle is billions of eV).

I haven't learned about this yet in school but I'm assuming as the atoms condense down to a single wavelength the volume of the liquid would be very small. If this condensate was instantly released out of a vacuum and into normal atmospheric pressure, would the volume rapidly expand?

Secondly, since everything is brought down to match a single wave function, and the temperature is very, very, very low, would the mass also reduce significantly, or is the wavelength so small that the Energy (E=HC/f) is still large and carries the same weight through the equation E/(C^2)=m

This is rather puzzling and doesn't make any sense.

The reason why the BE condensate is cooled down AND often done in vacuum is to maintain coherence. Otherwise, at higher temperatures and higher pressure, the thermal and scattering effects will destroy the coherence maintained by the gas molecules. It has nothing to do with "size"! Thus your question on it expanding in "normal atmosphere" is a bit strange, because even before that, you already no longer have a BE condensate. You just have an ordinary, useless volume of gas!

That question on that mass reduction, I have no idea what that is or where that came from. You seem to somehow equate low temperature with low "wavelength" of some kind. The application of the physics here is very odd.

Zz.

Well, i realize that it would no longer be a BE condensate, that's the point. The question was more so pertaining to, if there would be a rather instantaneous expansion in volume due to the extreme pressure and temperature differences. As gas cools, the volume reduces to a liquid and further to as you go to a solid (thermal expansion/contraction), i would assume it would condense even further below the lambda point. So would reversing this process cause and fast expansion of volume from liquid to gas?

As gas cools, the volume reduces to a liquid and further to as you go to a solid (thermal expansion/contraction), i would assume it would condense even further below the lambda point.
If that happens you do not get a BEC. You have to keep the density (and therefore pressure) very low to avoid condensation.

Well, i realize that it would no longer be a BE condensate, that's the point. The question was more so pertaining to, if there would be a rather instantaneous expansion in volume due to the extreme pressure and temperature differences. As gas cools, the volume reduces to a liquid and further to as you go to a solid (thermal expansion/contraction), i would assume it would condense even further below the lambda point. So would reversing this process cause and fast expansion of volume from liquid to gas?

This makes your whole question seems even more puzzling.

If all you want to know is what happen to a very cold gas when suddenly exposed to heat and high pressure, then why did you invoke a BE condensate in the first place? Why not just ask that, rather than introduce the complexity of a BE condensate into the equation? Then this becomes a classical thermodynamics problem (and does not belong in the Solid State forum).

BTW, a BE condensate need NOT be a liquid. You are already restricting yourself to LHe by mentioning the "lambda point". This makes it even more of a head-scratcher, because where do you see people producing LHe in a "vacuum" to produce a BE condensate?

There's a lot of things that don't fit properly in here.

Zz.

This makes your whole question seems even more puzzling.

If all you want to know is what happen to a very cold gas when suddenly exposed to heat and high pressure, then why did you invoke a BE condensate in the first place? Why not just ask that, rather than introduce the complexity of a BE condensate into the equation? Then this becomes a classical thermodynamics problem (and does not belong in the Solid State forum).

BTW, a BE condensate need NOT be a liquid. You are already restricting yourself to LHe by mentioning the "lambda point". This makes it even more of a head-scratcher, because where do you see people producing LHe in a "vacuum" to produce a BE condensate?

There's a lot of things that don't fit properly in here.

Zz.
The point of the question was for a hydrogen BEC. Like i said we haven't learned specifically about BEC's yet in lecture but i assumed volume reduced since temperature reduced.

1) I was under the assumption that multiple hydrogen molecules could take the state of one hydrogen molecule since their wave function would be the same, thus giving the multiple hydrogen atoms a superposition as if it was 1 atom with 1 wavelength which was the wavelength of the BEC, thus reducing the volume.

2) Under this assumption, thinking about the law of conservation of energy, i was assuming that under the equation E=HC/F that that frequency of that wave function would change to accommodate the smaller volume but larger density, thus equalling a same mass.

3) Thats why i was wondering under the assumptions that the volume would deduce to essentially 1 or a few hydrogen atoms, that when exposed to regular atmospheric pressure, it would RAPIDLY expand, and this expansion could perhaps be controlled by separating the expanding gas from the still, current BEC.

Remember that this is all theoretical and I'm not questioning current methods, I'm simply a physics and mechanical engineer major trying to think of new ways to approach the same result with different pathways in an attempt to create more usefulness.

under the assumptions that the volume would deduce to essentially 1 or a few hydrogen atoms
No that does not happen.
The increasing overlap between wavefunctions comes from expanding wavefunctions, not from a reduced volume. BECs still have a low density.

No that does not happen.
The increasing overlap between wavefunctions comes from expanding wavefunctions, not from a reduced volume. BECs still have a low density.
So essentially you're saying the volume of 1,000 liquid hydrogen atoms is the same as 1,000 BEC hydrogen atoms?

No, a typical BEC would be much larger. Typical densities are about 1012 to 1015 atoms/cm^3, corresponding to micro- to milligrams per cubic meter.

Liquid helium is different, that has a density more like ordinary liquids.

But density is different than volume. Are you saying that the BEC density is larger than a liquid Hydrogen density? Thus, wouldn't that mean that the volume would have to decrease. Unless you account for a decrease in mass from the decrease in energy through the change in thermal energy?

But density is different than volume.
Yes, but ##N=\rho V##. Low density <=> large volume (for a fixed number of particles)

Are you saying that the BEC density is larger than a liquid Hydrogen density?
I just said the BEC density is smaller by orders of magnitude. Most liquids have a density of hundreds of kilograms per cubic meter.

Unless you account for a decrease in mass
This is completely negligible.