Scientific Report - BEC

Quantum Monte Carlo methods 26Figure 2: (color online). Equation of state of the normal partiallypolarized phase as a function of the concentration x for different valuesof the interaction strength.using the trial wave functionψ T (r 1 ′, ..., r N↓ , r 1 , ..., r N↑ )= ∏ i,i ′ f(r ii ′)D ↓ (N ↓ )D ↑ (N ↑ ) , (4)where i and i ′ label, respectively, ↑ and ↓ atoms. The nodal surface of the wave functionψ T is determined by the product of Slater determinants D ↑ (N ↑ )D ↓ (N ↓ ) and coincideswith the nodal surface of a two-component ideal Fermi gas. As a consequence, the wavefunction in Eq. (4) is incompatible with off-diagonal long-range order (ODLRO) anddescribes a normal Fermi gas. The results for the equation of state of the normal Fermigas are shown in Fig. 1 from which one also estimates the coefficient B in Eq. (2).The first order transition between the polarized normal and the unpolarized superfluidphase takes place at the critical concentration x c =0.44 and the coexistence curve isshowninFig.1.The density profiles obtained from the above equation of state for a gas in harmonictrap are discussed in the Section on Polarized Fermi gases in this report.Phase diagram of a polarized Fermi gas along the BCS-BEC crossoverRecent experiments, carried out on harmonically trapped configurations, investigatesuperfluidity and Bose-Einstein condensation of fermionic pairs in these systems byvarying the strength of interactions, exploring the BCS-BEC crossover, the temperatureof the gas and the degree of polarization [5]. Evidences of phase separation between asuperfluid core and a normal external shell are reported for systems close to the unitary