6 minutes ago, swansont said:

hey’re all in the same state in a BEC (ground state of the atom, typically, and ground state of the potential well). That sounds like a minimum information condition - the entire BEC would be a single qubit.

The atoms don’t have a memory of their prior state. They would end up in a state that depended on the interaction that caused the BEC to decohere and be disrupted.

Can a BEC decohere spontaneously and without interaction with an outside system?

Is there any theoretic limit to the number of atoms that can be "assembled" and has there been any question as to whether an entangled atom (I think you can entangle atoms but I could be wrong ) can be involved in any of this?

Edit :a very quick search indicates that atoms can indeed be entangled,

eg https://www.sciencedaily.com/releases/2026/01/260126075842.htm

Edited March 13Mar 13 by geordief

4 minutes ago, geordief said:

Can the BEC decohere spontaneously and without interaction with an outside system?

No; they’re in the ground state, so energy has to be added to do that, which doesn’t happen spontaneously.

4 minutes ago, geordief said:

Is there any theoretic limit to the number of atoms that can be "assembled" and has there been any question as to whether an entangled atom (I think you can entangle atoms but I could be wrong ) can be involved in any of this?

No, the limit is practical, not theoretical. Since you know what state they’re in, entanglement isn’t involved between the atoms.

5 minutes ago, swansont said:

No; they’re in the ground state, so energy has to be added to do that, which doesn’t happen spontaneously.

No, the limit is practical, not theoretical. Since you know what state they’re in, entanglement isn’t involved between the atoms.

I was thinking of an outside atom which might have been entangled with one of the atoms before it entered the BEC..

Is that possible ,or of any possible consequence?

(Would the creation of the BEC break any prior entanglement?)

The method to obtain a BEC by using lasers would certainly do so. So will changing the state of the atom from one previously entangled from non BEC to BEC.

19 minutes ago, Mordred said:

The method to obtain a BEC by using lasers would certainly do so. So will changing the state of the atom from one previously entangled from non BEC to BEC.

Can BEC s form spontaneously?(could we ever know if they did?)

39 minutes ago, geordief said:

Can BEC s form spontaneously?(could we ever know if they did?)

Possibly, but not on earth. It would have to be someplace very cold.

Is the helium-4 superfluid state a BEC?

Edited March 13Mar 13 by KJW

29 minutes ago, KJW said:

Is the helium-4 superfluid state a BEC?

Strictly speaking, no. It's more of a mixed state, part condensate, part superfluid. The two properties are not synonymous and the relative proportions vary with temperature.

Note that the helium 4 nucleus is zero spin and therefore readily adopts condensate characteristics at a relatively high temperature. In contrast, the helium 3 nucleus is a fermion and can only take on a boson character by forming a cooper pair with another He-3 nucleus. This can only occur at much lower temperatures.

13 hours ago, sethoflagos said:

  13 hours ago, KJW said:

Is the helium-4 superfluid state a BEC?

Strictly speaking, no. It's more of a mixed state, part condensate, part superfluid. The two properties are not synonymous and the relative proportions vary with temperature.

Is this right? Or have I wrongly been assuming that the term 'condensate' referred specifically to BEC when it was being used more generally (ie for 'normal' liquid Helium)?

20 hours ago, sethoflagos said:

Strictly speaking, no. It's more of a mixed state, part condensate, part superfluid. The two properties are not synonymous and the relative proportions vary with temperature.

Helium is a liquid, which makes it a different case owing to the stronger interactions between the atoms.

The wikipedia article has a short discussion of this

https://en.wikipedia.org/wiki/Bose–Einstein_condensate

“It was quickly believed that the superfluidity was due to partial Bose–Einstein condensation of the liquid. In fact, many properties of superfluid helium also appear in gaseous condensates created by Cornell, Wieman and Ketterle (see below). Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4”

When 2 quantum objects interact does the outcome depend in some way on how each of the two objects "know" each other ?

Is that where the Uncertainty principle comes into play?

Does each object need to know both positions and momenta of the system in order to "decide" how the system evolves subsequently?

It is not just an observer who cannot measure this but the physical objects themselves have to know this for the outcome to be considered exaxtly "predetermined"..

Just as Feynman strongly emphasized at the end of the lecture ,paraphrasing "it is as if Nature herself doesn't know her next move"

3 hours ago, swansont said:

Helium is a liquid, which makes it a different case owing to the stronger interactions between the atoms.

The wikipedia article has a short discussion of this

https://en.wikipedia.org/wiki/Bose–Einstein_condensate

“It was quickly believed that the superfluidity was due to partial Bose–Einstein condensation of the liquid. In fact, many properties of superfluid helium also appear in gaseous condensates created by Cornell, Wieman and Ketterle (see below). Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4”

Does this seem to confirm my original post? It occurred to me last night that it implied that helium should therefore have three 'liquid' phases:

Helium I (2.7K to 4.2K @ ambient pressure) - a normal cryogenic liquid phase.

Helium II (superfluid part)

Helium II (BEC part)

'Condensate' is pretty much a wastebasket category in my industry for any liquid that has emerged from a condenser, and I've been caught out before confusing the composition of one condensate with that of another. Perhaps I'd been caught out again.

However https://en.wikipedia.org/wiki/Helium contains the following that seems to confirm that Helium II is indeed a mixed phase state, albeit a somewhat different mix to what I had in mind.

Helium II is a superfluid, a quantum mechanical state of matter with strange properties. For example, when it flows through capillaries as thin as 10 to 100 nm it has no measurable viscosity.[28] However, when measurements were done between two moving discs, a viscosity comparable to that of gaseous helium was observed. Existing theory explains this using the two-fluid model for helium II. In this model, liquid helium below the lambda point is viewed as containing a proportion of helium atoms in a ground state, which are superfluid and flow with exactly zero viscosity, and a proportion of helium atoms in an excited state, which behave more like an ordinary fluid.[101]

Why on earth did they pick 'condensation' as a name for this phase change? In the case of Helium II it leads to a decrease(!!!) in density from what one would expect. It's confusing the hell out of me and I'll bet I'm not the only one.

2 hours ago, sethoflagos said:

It's confusing the hell out of me and I'll bet I'm not the only one.

I don't understand BECs quite well enough to be confused.

4 hours ago, geordief said:

Does each object need to know both positions and momenta of the system in order to "decide" how the system evolves subsequently?

I don't have to know my legs are attached in order to run away from a tiger.

4 hours ago, sethoflagos said:

Why on earth did they pick 'condensation' as a name for this phase change? In the case of Helium II it leads to a decrease(!!!) in density from what one would expect. It's confusing the hell out of me and I'll bet I'm not the only one.

I suspect it’s because of the way the atoms collapse into the ground state when it’s formed. It’s a condensation in the energy state view, analogous to condensation wherein a physical droplet forms from vapor.

13 hours ago, sethoflagos said:

Does this seem to confirm my original post? It occurred to me last night that it implied that helium should therefore have three 'liquid' phases:

Helium I (2.7K to 4.2K @ ambient pressure) - a normal cryogenic liquid phase.

Helium II (superfluid part)

Helium II (BEC part)

'Condensate' is pretty much a wastebasket category in my industry for any liquid that has emerged from a condenser, and I've been caught out before confusing the composition of one condensate with that of another. Perhaps I'd been caught out again.

However https://en.wikipedia.org/wiki/Helium contains the following that seems to confirm that Helium II is indeed a mixed phase state, albeit a somewhat different mix to what I had in mind.

Why on earth did they pick 'condensation' as a name for this phase change? In the case of Helium II it leads to a decrease(!!!) in density from what one would expect. It's confusing the hell out of me and I'll bet I'm not the only one.

At extremely low temperatures the DeBroglie wavelengths of the individual particles overlap and form a macroscopic single wavelength.

Relevant formula

\[\lambda_{db}=\sqrt{\frac{2\pi\hbar^2}{mK_B T}}\]

As both Bose-Einstein statistics and Fermi Dirac apply the Boltzmann equation specifically Maxwell Boltzmann the mathematics will typically apply phase space. Defined by the Hamilton in the mean field approximation as a single interaction term. I have often seen this associated with the Hartree approximation to give some of the math typically involved.

Should add the Compton wavelength also becomes modified into an effective Compton wavelength using the equations in the link below

https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation

Edited March 15Mar 15 by Mordred