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

TL;DR

This study constructs a phase diagram for a trapped $^{87}$Rb Bose gas using macroscopic parameters, revealing new features of the BEC transition and suggesting it may be a third-order phase transition.

Contribution

It introduces a novel macroscopic parameter $ ext{Pi}$ to characterize the BEC phase transition without relying on local density approximation.

Findings

Identification of new features in the phase diagram related to BEC transition

Proposal that BEC may be a third-order phase transition

Development of a thermodynamic description based on macroscopic parameters

Abstract

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.