Formation of fermionic molecules via interisotope Feshbach resonances

We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For ${}^6\mathrm{Li}$ a consistent description can be given. We discuss theoretical uncertainties for the position of the wide ${}^6\mathrm{Li}$ Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the ${}^6\mathrm{Li}\text{−}{}^7\mathrm{Li}$ system, and their importance for different types of crossover superfluidity models is discussed.

Figure 1

(Color online) Dependency of the wide-resonance position $B_0$ on $C_6$, according to the second analysis (see text). The shaded area indicates the associated uncertainty. The curve indicated with A (B) is obtained making use of the exchange energy according to [11] ( [12] ).

Figure 2

(Color online) Energy of the dressed (quasi-)molecular state as obtained with a full coupled-channels calculation (dots), with respect to the $\mid f_1,m_{f_1}⟩\otimes \mid f_2,m_{f_2}⟩=1∕2,1∕2⟩\otimes 1∕2,-1∕2⟩$ threshold. The straight line is the bare closed-channel energy ${ϵ}_b\left(B\right)$, and the energy of the dressed state according to our model is indicated by the curved line. Inset: corresponding background value of the scattering length as a function of the magnetic field $B$.

Figure 3

(Color online) Two thresholds for the ${}^6\mathrm{Li}\text{−}{}^7\mathrm{Li}$ system, which show the coincidence of two Feshbach resonances. Inset: scattering length as a function of magnetic field, for the two coinciding Feshbach resonances.