How does one produce a condensate?

Question

In physics textbooks, one learns about Bose-Einstein condensate and it is all about taking thermodynamic limits. Of course, in real life, infinite systems do not exist. So, picture the following scenario. We consider a system of $N \gg 1$ identical particles in a huge box and we fix a low temperature $T$. The more particles you consider in your system, the more particles go to the ground state energy (since, theoretically, the thermodynamic limit has to be taken in such a way that the density $\rho$ is fixed, so the number of particles should also increase). Taking $N$ sufficiently large for the parameters of the experiment, one starts to see Bose-Einstein condensate.

My question is: is this a reasonable way to get a condensate? I mean, fix the temperature, and increase the number of particles so it becomes large enough to exhibit a condensate, for a fixed chosen density $\rho$. In this case, is it possible to estimate how large $N$ should be to start seeing a condensate?

Answer 1

Mathematically Bose-Einstein condensate is easier analyzed in the Grand canonical ensemble (with variable number of particles), but working in a canonical ensemble with the fixed number of particles is also possible. See, e.g., this recent question Trying to derive Bose-Einstein Condensation using the canonical ensemble

So the possible experimental approach is confining a collection of bosonic atoms with large but finite $N$, and gradually cooling it (i.e., lowering temperature) - see Laser cooling.