Feshbach resonances in a nonseparable trap

We consider a pair of atoms in an arbitrary trapping potential in the presence of a magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states, taking into account possible coupling between center of mass and relative motion induced by the trap. As a specific example, we discuss the case of different atomic species in a harmonic potential, where each atom feels a different trapping frequency.

Figure 1

Energy levels in units of the relative trapping frequency $\omega$ for a K-Rb Feshbach resonance. The ratio of the trapping frequencies between K and Rb atoms is assumed to be $1.4$ as in Ref. [31]. Five molecular bound states are taken into account. The inset shows a closer view of the region where the bound states cross the trap levels.

Figure 2

Energy levels away from the K-Rb resonance. Dashed blue lines depict the uncoupled $C=0$ case, where the eigenstates can be labeled by the quantum numbers $N\ell n$. The actual eigenstates (black solid lines) are composed from them.

Figure 3

The same as in Fig. 1 but for the Li-Cs resonance, where the ratio of trapping frequencies is assumed to be $1.8$.

Figure 4

The same as in Fig. 2 but for the Li-Cs resonance. The coupling term plays a less important role than in the K-Rb case.