Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate–unitarity crossover

We derive a generalized Gross-Pitaevskii density-functional equation appropriate to study the Bose-Einstein condensate (BEC) of dimers formed of singlet spin-half Fermi pairs in the BEC-unitarity crossover while the dimer-dimer scattering length $a$ changes from 0 to $\infty$. Using an effective one-dimensional form of this equation, we study the phenomenon of dynamical self-trapping of a cigar-shaped Fermi superfluid in the entire BEC-unitarity crossover in a double-well potential. A simple two-mode model is constructed to provide analytical insights. We also discuss the consequence of our study on the self-trapping of an atomic BEC in a double-well potential.

Figure 1

(Color online) Equienergy phase contour plot of the unitary Fermi SF. (a) Contours of different energies for $\Lambda =8$. (b) Contours of $E=10$ for different values of $\Lambda$. Energy is in units of $2\mathcal{K}$.

Figure 2

(a) Strength of nonlinearity ${\left(N/2\right)}^{3/2}U$, (b) tunneling energy $2\mathcal{K}$, and (c) their ratio $\Lambda$ (c) as functions of $N\lambda$ at unitarity. (d) The critical ${\Lambda }_c$ as function of $S\left(0\right)$ for $\theta \left(0\right)=0$ [see Eq. (18)].

Figure 3

(Color online) Population imbalance $S\left(t\right)$ vs $t$ dynamics with (a) $N\lambda =100,S\left(0\right)=0.2,\kappa =10,A=8$, (b) $N\lambda =100,S\left(0\right)=0.2,\kappa =10,A=16$, (c) $N\lambda =1000,S\left(0\right)=0.3,\kappa =10,A=16$, and (d) $N\lambda =100,S\left(0\right)=0.3,\kappa =8,A=12$ for dimer-dimer scattering length $a$ varying over the BEC-unitarity crossover.

Figure 4

Different dynamical regimes of Fermi superfluid in the BEC-unitary crossover.

Figure 5

(Color online) Time-averaged population imbalance $⟨S\left(t\right)⟩$ vs nonlinearity $aN\lambda$ for different $N\lambda$ for trap parameters $A=16,\kappa =10$ and (a) $S\left(0\right)=0.3$ and (b) $S\left(0\right)=0.6$. Different curves are generated by varying the scattering length $a$ across the BEC-unitarity crossover for $S\left(0\right)=0.3$ and 0.6, respectively, based on initial wave form (20).