It is known (see, e.g. Wikipedia) that the transition to Bose-Einstein condensate occurs below critical temperature: $$ T_c \approx 3.3125 \, \frac{\hbar^2 n^{2/3}}{m k_B} $$ where $n$ is the particle density in the system.
It is obvious that higher particle densities $n$ correspond to higher critical temperature $T_c$.
Nevertheless, it is always stressed that Bose-Einstein condensation has been achieved with ultra low density quantum gases (1/100000 of the density of normal air).
So my question is: Why? Which is the obstacle that prevents experimentalists from trying to Bose-Condense denser gases?
