Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

Abstract

Abstract. The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.

Superfluid and supersolid phases in optical lattices in two dimensions

“…In what follows, all the energies will be scaled with respect to t. We also introduce two relevant physical quantities: the dipolar interaction strength a d = m e f f d 2 / 2 , with m e f f = 2 /2ta 2 the effective mass, and the dimensionless parameters Λ = λ/a and χ = a d /a. It is important to emphasize that our study includes the presence of a harmonic potential which plays a crucial role since, as it is well known, the global thermodynamics of the phase transition is qualitatively different from that of the homogeneous case [21]. A remarkable signature of this fact is that the magnitude of the coherence length can be as large as the typical confinement distance.…”

Dynamic control of the Bose–Einstein-like condensation transition in scalar active matter

“…The second line in equation (25) shows that the pressure decouples from the average volume V when below the critical volume V c , indicating that the isothermal incompressibility κ −1 = −V( ∂P ∂V ) T eff diverges at condensation. The divergence of the isothermal compressibility at criticality is indicative of ideal Bose gas behaviour [20], and has recently been observed in optical quantum gases [21] at room temperature.…”

Technical thermodynamics of an inhomogeneous gas around the Bose-Einstein transition using the global-variable method

“…Differently from the isothermal compressibility κ T for a homogeneous ideal gas, which diverges at T = T c , Reyes-Ayala and co-workers 46 have demonstrated analitically that isothermal compressibility K T of a harmonically trapped gas is continuous around the transition. However, its derivative with respect to T is discontinuous at the critical point.…”