Atom-Molecule Coexistence and Collective Dynamics Near a Feshbach Resonance of Cold Fermions

Degenerate Fermi gas interacting with molecules near a Feshbach resonance is unstable with respect to the formation of a mixed state, in which atoms and molecules coexist as a coherent superposition. A theory of this state is developed using a mapping to the Dicke model, treating the molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of the molecular field in the mixed state.

Figure 1

Phase diagram of coupled atom-molecule system obtained from Eq. (8) for ${}^{\mathrm{40}}\mathrm{K}$ system [10] at particle density $n\approx 1.8\times {10}^{13}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{3}}$, Fermi energy $E_F=0.35\mu \mathrm{K}$, and coupling strength $g^{2}n/E_F\approx 60\mu \mathrm{K}$. (The coupling was estimated using the microscopic theory of Feshbach resonance [15], applied to the conditions of the JILA experiment [10]). Inset: Effective potential schematic illustrating the behavior in the three regions.

Figure 2

Pseudospin precession (12) for fermion pair states corresponding to the soliton train (16) is shown on the Bloch sphere $r_p^{x,y,x}=\langle {\sigma }_p^{x,y,x}\rangle$. Parameters used: $b_{-}/b_{+}=0.1$, $\eta -2E_F=-b_{+}$, constant density of states. The energies above and below the Fermi level (solid and dashed curves) are chosen as indicated by arrows in the inset. Note that each state completes a full $2\pi$ Rabi cycle per soliton. Inset: Radius $r_p=(b_{+}^2-b_{-}^2)/({\omega }_p^2+b_{+}^2+b_{-}^2)$ and center $z_p=(1-2n_p){\omega }_p^2/({\omega }_p^2+b_{+}^2+b_{-}^2)$ of trajectories vs energy $\xi (p)={ϵ}_p^{(0)}-E_F$. Note the absence of particle-hole symmetry.