# Traps for Bose Einstein Condensate

I was just wondering about the role and effects of the trap in formation of BE condensate. In this respect if we have two potential, one small harmonic potential of energy E/10 and length L/100 inside a larger harmonic potential of energy E and Length L. Where is the BEC likely to be formed out of these two potentials ? This is just a hypothetical problem that came to mind. Can anyone share their insights regarding this ? Thanks in advance.

A BEC is formed when the de Broglie wavelength of the atoms $$\lambda_{\text{dB}}$$ are on the order of the interparticle separation ($$\sim 1/n$$, where $$n$$ is the density, so particles/volume). This is expressed in a dimensionally correct form as: $$D = n\lambda_{\text{dB}}^3,$$ known as the "degeneracy parameter", which quantifies phase-space density (position * momentum). BEC occurs when $$D \sim 1$$.
$$\lambda_{\text{dB}} \propto 1/\sqrt{T}$$, so going in temperature makes $$D$$ up. But going denser also make $$D$$ go up.