BEC phase diagram of a $^{87}$Rb trapped gas in terms of macroscopic thermodynamic parameters

We measure the phase diagram of a $^{87}$Rb Bose gas in a harmonic trap in terms of macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables as size of the cloud ${\cal V}$, number of atoms $N$ and temperature $T$, a novel parameter $\Pi = \Pi(N,{\cal V},T)$ is introduced to characterize the overall pressure of the system. We construct the phase diagram ($\Pi$ vs $T$) identifying new features related to Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters, provide us with properties that do not need the local density approximation. An unexpected consequence of this analysis is the suggestion that BEC appears as a continuous third-order phase transition instead of being a second-order one.
Comment: 11 pages, 4 figures