Coherent molecular bound states of bosons and fermions near a Feshbach resonance

We analyze molecular bound states of atomic quantum gases near a Feshbach resonance. A simple, renormalizable field theoretic model is shown to have exact solutions in the two-body sector, whose binding energy agrees well with observed experimental results in both Bosonic and Fermionic cases. These solutions, which interpolate between BEC and BCS theories, also provide a more general variational ansatz for resonant superfluidity and related problems.

Figure 1

Binding energy $E_b$ vs the magnetic field $B$ for the ${}^{85}\mathrm{Rb}$ experiment [2]. The parameter values are taken from the subsequent high-precision measurements on the same system [21]: $B_0=155\mathrm{G}$ and $a_{bg}=-443a_0$, where $a_0$ is the Bohr radius. In addition, we take ${\chi }_0=2.84\times {10}^{-4}{\mathrm{m}}^{3∕2}∕\mathrm{s}$ and $\Delta \mu =-2.23{\mu }_B$ [23], where ${\mu }_B$ is the Bohr magneton. The solid line is our theoretical result, Eq. (7), while the dashed line is the result of Eq. (8). The circles are the experimental data of Ref. 21.

Figure 2

Binding energy $E_b$ vs $B$ for the ${}^{40}\mathrm{K}$ experiment [4], where $B_0=224$ G and $a_{bg}=174a_0$. In addition, we take ${\chi }_0=1.12\times {10}^{-4}{\mathrm{m}}^{3∕2}∕s$ and $\Delta \mu =1.27{\mu }_B$ [23]. The solid line is our theoretical result, while the circles and the error bars are the experimental data from Fig. 5 of Ref. 4.