Direct Imaging of Spatially Modulated Superfluid Phases in Atomic Fermion Systems

It is proposed that the spatially modulated superfluid phase, or the Fulde-Ferrell-Larkin-Ovchinnikov state could be observed in resonant fermion atomic condensates which are realized recently. We examine optimal experimental setups to achieve it by solving the Bogoliubov–de Gennes equation for both idealized one-dimensional and realistic three-dimensional cases. The spontaneous modulation of this superfluid is shown to be directly imaged as the density profiles either by optical absorption or by Stern-Gerlach experiments.

Figure 1

(a) The spatial profiles of the pairing field $\Delta (r,z)$ and (b) the total density $\rho (r,z)$ for the population difference $\delta n=0.15$ and ${\Delta }_0/{\epsilon }_F=0.35$. (c) The cross section of $\Delta (r,z)$ at $r=0$ is shown for various population differences $\delta n$.

Figure 2

(a) Stereographic view of the magnetization $m(r,z)$, and (b) its columnar density profile along the $z$ axis for $\delta n=0.15$. (c) The columnar magnetization profiles $m(z)$ for various $\delta n=0.07,0.15,0.32$. The arrows indicate the positions of the zeros of $\Delta (r=0,z)$, which is displayed in Fig. 1. The number of the zeros is 1 ($\delta n=0.07$), 3 ($\delta n=0.15$), and 5 ($\delta n=0.32$).

Figure 3

(a)  The local density of state profiles $N_{\uparrow }(r=0,z,E)$ and (b) $N_{\downarrow }(r=0,z,E)$ at $r=0$ for the population difference $\delta n=0.15$ and ${\Delta }_0/{\epsilon }_{\mathrm{F}}=0.35$. The large empty region in the center in both figures corresponds to the energy gap.