In theory, is it possible to generate a BEC with only 2 atoms? If not, what would be the lower threshold?

I have a basic understanding of BECs: you consider only 2-atom interactions, pseudopotential (delta) and the Gross–Pitaevskii equation, critical temperature...

I don't see any theoretical reason why this idea would not be possible, am I missing something? I guess that at some point of the theory $N >> 1$ was assumed for some reason, maybe to neglect some other terms in a formula, but I cannot find where.

Experimentally I understand the difficulty, since the critical temperature scales as the cubic root of the number of atoms (3D).


From the comments it's clear that the question does not make sense. Moreover, 2 bosons in the same state is not an "interesting" system as a BEC. The relevant question now is what makes the BEC interesting in comparison? Well, I think it is the fact that you can prepare a bunch (millions) of atoms from an incoherent blob in a determined quantum state at once, i.e., without having to prepare them one by one.

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    $\begingroup$ I think it depends what you actually call a BEC. Often it is defined at a "macroscopic quantum state". I don't see how you could call 2 atoms a macroscopic thing. If you say that only the energy counts and you add spin you can even do this with fermions. So having to Bosons in the same quantum state doesn't seem very special to me. $\endgroup$ – Noldig Oct 28 '15 at 15:43
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    $\begingroup$ There is nothing that stops you putting two bosonic atoms into the same state, and that would be something you couldn't do with two fermionic atoms. It's just that it won't exhibit any macroscopic properties, and those properties are what is usually considered when talking about "creating a BEC". In general you talk about "states of matter" applying to at least moderately large numbers, even though you can often (generally?) define them in microscopic ways as well. $\endgroup$ – dmckee Oct 28 '15 at 16:13
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    $\begingroup$ I would have compared it to trying to define a two atom solid or liquid, but yeah. That's the way I am thinking about this. $\endgroup$ – dmckee Oct 28 '15 at 16:34
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    $\begingroup$ @Rol To reiterate the other comments in a slightly altered form: BEC is usually defined to be a manifestation of a phase transition in a macroscopic system of interacting particles. This is quite different from the trivial "condensation" of non-interacting bosons into the same orbital. Note that in a physical atomic BEC the atoms are not "in the same state", since there are spatial correlations induced by the collisions. However at large length scales the dynamics of the condensate can be described by an order parameter which behaves in many ways like a single wavefunction. $\endgroup$ – Mark Mitchison Oct 28 '15 at 18:02
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    $\begingroup$ Note also that temperature can be a perfectly sensible quantity for two-atom systems in thermal equilibrium, so dmckee's solid or liquid analogy makes more sense here. $\endgroup$ – Mark Mitchison Oct 28 '15 at 18:04

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