Scientific Report - BEC

Quantum Monte Carlo methods 28Figure 4: (color online). Phase diagram as a function of polarizationand interaction strength. In terms of the Fermi wavevector k F =(3π 2 n) 1/3 fixed by the total density n = N/V one has: 1/k F a =1/k F ↑ aat P =0and1/k F a =2 1/3 /k F ↑ a at P = 1. On the BCS side of theresonance our determination of the critical polarization is not reliable.state (b) and state (c) are separated by second order phase transitions.Critical temperature of interacting Bose gases in two and three dimensionsThe theoretical determination of the superfluid transition temperature in homogeneous,interacting Bose systems is a fine example of a many-body problem that can be quantitativelyaddressed only by “exact” numerical techniques. This fact is well understood inthe case of strongly interacting quantum fluids, such as liquid 4 He, but at first glance issurprising in the case of dilute gases. However, in three dimensions (3D) the presence ofany finite interaction changes the universality class of the transition from the Gaussiancomplex-field model, corresponding to the ideal gas Bose-Einstein condensation (BEC)temperature Tc 0, to that of the XY model. Thus, the critical temperature T c can notbe obtained from Tc0 perturbatively. In two dimensions (2D) the superfluid transition,which belongs to the Berezinskii-Kosterlitz-Thouless (BKT) universality class, is inducedby interaction effects and there is no unperturbed critical temperature to startwith.In a 3D weakly repulsive gas the critical temperature shift is fixed by the s-wavescattering length a (a >0), which characterizes interatomic interactions at low temperature[12, 13],[]T c = Tc0 1+c(an 1/3 ) . (5)