Observation of Bose-Einstein condensation in an atomic trap in terms of macroscopic thermodynamic parameters

To overcome the difficulties in defining pressure for a gas confined in an inhomogeneous trap, we define single macroscopic parameters that behave like pressure and volume. We measure the phase diagram of a Rb-87 Bose gas in a harmonic trap in terms of those macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables such as the trap potential V = (omega(x)omega(y)omega(z))(-1), number of atoms N, and temperature T, a parameter Pi = Pi (N, V, T) is introduced to characterize the overall macroscopic pressure of the system. We construct the phase diagram (Pi vs T) identifying the main features related to the Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters provides us with a description that does not need the local-density approximation. This procedure can be used to explore different aspects related to BEC such as the nature of the phase transition in a trapped gas.