Scientific Report - BEC

Nonlinear dynamics and solitons 4210.5(kF a) −1 = −1(dashed)(kF a) −1 = 0 (solid)(kF a) −1 = +1 (dash-dotted)Δ /Δ 00−0.5−1 (a)−10 −5 0 5 1010.8n/n 00.60.40.2(b)0−10 −5 0 5 10zk FFigure 3: (a) Order parameter and (b) density for a dark soliton with(k F a) −1 =0and±1. The value (k F a) −1 = 0 (solid line) corresponds tounitarity, while (k F a) −1 = −1 (dashed) and (k F a) −1 = +1 (dot-dashed)are on the BCS and BEC side of the resonance, respectively. Both Δ(z)and n(z) are normalized to their asymptotic values far away from thesoliton.Solitons in Fermi gasesIn three dimensions a dark soliton is characterized by a real order parameter whichchanges sign at a planar node (a point node in 1D). In the BEC regime the soliton is asolution of the GP equation for the order parameter of the condensate with repulsiveinteraction. While in the BEC case the node of the order parameter causes a notchin the density distribution, in a BCS superfluid the density is almost unaffected bythe presence of the node. The situation is similar to that of vortices. As in that case,the behavior of the density along the BCS-BEC crossover is expected to be interestingand rather nontrivial, as a result of the delicate balance of coherence and nonlinearinteractions. In [12] we investigated this problem by using a mean-field theory for a 3DFermi gas at zero temperature, based on the solution of the Bogoliubov - de Gennes(BdG) equations [13].As shown in Fig. 3b, we found the occurrence of a deep depletion of the density at