I What happens to the electrons in a Bose-Einstein Condensate?

[bbbl67]

TL;DR Summary

Do the electrons still orbit around the individual atomic nuclei?

When various atoms are turned into BEC's, are their electrons still arranged in their standard atomic orbitals like at higher temperatures? Or are the electrons free floating around the entire condensate? If the electrons are free-floating, then are they arranging themselves into superconductive Cooper Pairs? How close can the individual nuclei in the condensate get to each other? Do these nuclei still feel the repulsion of the protons from each other?

 

[hilbert2]

A BEC can be modeled simply by seeing the individual atoms as bosonic point particles, with some empirical interaction force between them. The interactions are of a shorter range than a Coulomb interaction between charged particles.

In other words, the internal structure of the atom is not very important here, but under those conditions it's very likely to just be in its electronic ground state.

 

[bbbl67]

A BEC can be modeled simply by seeing the individual atoms as bosonic point particles, with some empirical interaction force between them. The interactions are of a shorter range than a Coulomb interaction between charged particles.

In other words, the internal structure of the atom is not very important here, but under those conditions it's very likely to just be in its electronic ground state.

How much shorter than the Coulomb range? 50% closer, more, less?

Two electrons, such as in a Cooper pair, can form a composite boson. A Helium-4 nucleus is also a composite boson. Both would be components of a Helium atom. So would He-4 nuclei and Cooper pairs, split apart and create two independent bosons that move through each other unimpeded?

 

[hilbert2]

Cooper pairs are not needed in the theory of Bose-Einstein condensates, they are related to electrical superconductivity.

The range being shorter than in Coulomb interaction means that the interaction force drops to zero faster than proportionally to the inverse square of distance, possibly exponentially, when going further away from the atom.

 

[bbbl67]

Cooper pairs are not needed in the theory of Bose-Einstein condensates, they are related to electrical superconductivity.

The range being shorter than in Coulomb interaction means that the interaction force drops to zero faster than proportionally to the inverse square of distance, possibly exponentially, when going further away from the atom.

The reason I brought up the Cooper pairs is because they seem to create a type of boson too, and both phenomena occur at near absolute zero. So it seemed plausible that BEC's and superconductivity are somehow related?

There are certain composite bosons that are neutrally charged, such as Tritium (2 neutrons, 1 proton, and 1 electron), which makes the whole atom bosonic. There are other kinds where only the nucleus is bosonic, like anything with an even numbers of protons plus neutrons. Do BEC's work only with the whole neutrally charged bosonic atom, or just bosonic nuclei is sufficient? A bosonic nucleus would feel a lot of electrical repulsion to other nuclei.

 

[DrClaude]

BEC comes about in the theory of weakly interacting gases of identical bosons. The superfluidity of helium-4 is probably related. But nuclei of atoms cannot Bose-condense.

 

[bbbl67]

BEC comes about in the theory of weakly interacting gases of identical bosons. The superfluidity of helium-4 is probably related. But nuclei of atoms cannot Bose-condense.

So fair to say that these condensates have an overlapping electron cloud, but not overlapping nuclei?

 

[hilbert2]

So fair to say that these condensates have an overlapping electron cloud, but not overlapping nuclei?

A typical BEC is prepared from a vapor of alkali metal atoms at very low pressure, where the atoms are typically far enough from each other to have little interaction between them. So the electron clouds of the individual atoms are really close to that of a single isolated atom in vacuum, but not exactly the same because there are some interactions.

 

[bbbl67]

A typical BEC is prepared from a vapor of alkali metal atoms at very low pressure, where the atoms are typically far enough from each other to have little interaction between them. So the electron clouds of the individual atoms are really close to that of a single isolated atom in vacuum, but not exactly the same because there are some interactions.

Are BEC's in a gaseous form then? Looking at pictures of BEC's I always assumed that they might have been solid or liquid, because they looked more ordered.

 

[hilbert2]

Are BEC's in a gaseous form then? Looking at pictures of BEC's I always assumed that they might have been solid or liquid, because they looked more ordered.

The usual theory of BECs assumes that it's a very dilute gas of particles with bosonic total spin. The superfluidity of helium-4 is possibly somehow related to Bose-Einstein condensation, but it's not as simple because the atoms in liquid helium are close enough to their neighbors to interact a lot (and the electron clouds of the atoms are therefore also somewhat deformed from the shape they have in gas phase helium).

 

[bbbl67]

The usual theory of BECs assumes that it's a very dilute gas of particles with bosonic total spin. The superfluidity of helium-4 is possibly somehow related to Bose-Einstein condensation, but it's not as simple because the atoms in liquid helium are close enough to their neighbors to interact a lot (and the electron clouds of the atoms are therefore also somewhat deformed from the shape they have in gas phase helium).

So liquid helium-4 and BEC helium-4 are different?

 

[hilbert2]

So liquid helium-4 and BEC helium-4 are different?

I'm not sure what you mean with "BEC helium-4", but it seems that it's possible to attain Bose-Einstein condensation in a dilute gas of helium atoms put in an excited electronic state.

https://physicstoday.scitation.org/doi/full/10.1063/1.1381089

 

[bbbl67]

I'm not sure what you mean with "BEC helium-4", but it seems that it's possible to attain Bose-Einstein condensation in a dilute gas of helium atoms put in an excited electronic state.

https://physicstoday.scitation.org/doi/full/10.1063/1.1381089

Yeah, earlier statement by @DrClaude that BEC's come from vapor, which implies gaseous state.

 

[DrClaude]

So liquid helium-4 and BEC helium-4 are different?

Liquid helium-4 and superfluid liquid helium-4 are different (there is a phase transition between the two). Superfluid helium-4 is probably a BEC, but you need to extend the theory of Bose condensation to describe it.

 

[bbbl67]

Liquid helium-4 and superfluid liquid helium-4 are different (there is a phase transition between the two). Superfluid helium-4 is probably a BEC, but you need to extend the theory of Bose condensation to describe it.

Is there a temperature barrier which turns it into a superfluid? As I understand it, for helium to be liquid it needs to be close to absolute zero. Does it need to be even closer to absolute zero to be a superfluid, or are there other factors?

 

[hilbert2]

Is there a temperature barrier which turns it into a superfluid? As I understand it, for helium to be liquid it needs to be close to absolute zero. Does it need to be even closer to absolute zero to be a superfluid, or are there other factors?

Yes, it requires a temperature lower than melting point for liquid helium-4 to turn into a superfluid. If it's the helium-3 isotope, the temperature needs to be even lower. The mechanism of superfluidity is different for the two isotopes, because helium-3 atoms aren't bosons.

 

[DrClaude]

Helium-4:

Helium-3:

The superfluid phase in ⁴He is akin to BEC. The superfluid phase in ³He is akin to superconductivity with the formation of Cooper pairs, hence the much lower temperature.

 

[bbbl67]

Helium-4:

View attachment 282498

Helium-3:
View attachment 282499
The superfluid phase in ⁴He is akin to BEC. The superfluid phase in ³He is akin to superconductivity with the formation of Cooper pairs, hence the much lower temperature.

There is actually a solid phase for Helium?

 

[hilbert2]

I think it's possible to make anything become some kind of a solid with high enough pressure and low temperature. A liquid phase doesn't necessarily exist at all pressures, for instance carbon dioxide condenses directly to a solid if you cool it down at atmospheric pressure.