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.