Formation of Molecules near a Feshbach Resonance in a 1D Optical Lattice

We study the molecular behavior of two atoms interacting near a Feshbach resonance in the presence of a 1D periodic potential. The critical value of the scattering length needed to produce a molecule and the binding energy at resonance are calculated as a function of the intensity of the periodic potential. Because of the nonseparability of the center of mass and relative motion, the binding energy depends on the quasimomentum of the molecule. This has dramatic consequences on the molecular tunneling properties, which become strongly dependent on the scattering length.

Figure 1

Binding energy versus inverse scattering length for different values of the laser intensity: from top to bottom, $s=20,10,5,0$ (solid line). Also shown are the asymptotic behavior for large $d/a$ (dotted line) and the binding energy in harmonic approximation (dashed line) for $s=20$.

Figure 2

Left panel: Critical value of the inverse scattering length as a function of the laser intensity for different values of quasimomentum: $Q=0$ (solid line) and $Q=q_B$ (dashed line). Right panel: Binding energy at unitarity ($d/a=0$) as a function of the laser intensity (solid line). Also shown are the harmonic approximation (dashed line) and the inclusion of anharmonic corrections (dots).

Figure 3

Binding energy dispersion as a function of quasimomentum $Q$ for fixed $s=2.5$ and for different values of the inverse scattering length: from top to bottom, $d/a=2,0,-1.17(=d/a_{\mathrm{cr}}),-1.66$. The open squares give the dispersion at $d/a=2$ evaluated from Eqs. (8, 9).

Figure 4

Bandwidth (left panel) and effective mass ratio $2m/M^{*}$ (right panel) of the molecule as a function of the inverse scattering length for $s=2.5$ (solid line). The asymptotic behavior for large positive $d/a$ is also shown (dotted line). In the left panel the dot-dashed line indicates $2{ϵ}_1(q_B/2)=0.395E_R$, while in the right panel it indicates the effective atomic mass ratio $m/m^{*}=0.83$.