BEC transition of a weakly interacting ultracold Bose gas in a linear quadrupolar trap

Abstract

We discuss the thermal gas to Bose-Einstein Condensation (BEC) transition of an ultracold Bose gas in a linear quadrupolar trap with contact interatomic interactions within the Hartree-Fock (HF) approximation. We briefly review the theoretical framework of the thermodynamics of a gas confined by a non-uniform potential to show how mechanical equilibria must be formulated in term of generalized volume and pressure variables ${\cal V}$ and ${\cal P}$ that replace the usual volume and hydrostatic pressure of a uniform system. We solve for the density profile within HF as a function of temperature $T$ and molar volume $v = {\cal V}/N$. With this information, we are able to calculate all the thermodynamic properties of the system and analyze the behavior of the gas through the BEC (superfluid) transition. We find that the transition is completely smooth, showing no sign of critical behavior. We emphasize how these predictions can be readily measured with the current experimental setups.