Magnetic Feshbach resonances in collisions of nonmagnetic closed-shell ${}^1\Sigma$ molecules

Magnetic Feshbach resonances play a central role in experimental research on atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali metal molecules in the ground rovibrational state of the ground electronic ${}^1\Sigma$ state. Unlike alkali metal atoms, ${}^1\Sigma$ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for ${}^1\Sigma$ molecules may exceed 1 mG, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.

Figure 1

Hyperfine structure of the ${}^{87}$Rb${}^{133}$Cs(X ${}^1{\Sigma }^{+}$) rotational ground state. Hyperfine states considered here are highlighted (in red).

Figure 2

Elastic [upper solid (black) curves] and inelastic cross sections for two molecules in the initial states, as indicated in Fig. 1: top, $(M_{\mathrm{Rb}}=-\frac{3}{2},M_{\mathrm{Cs}}=-\frac{7}{2})$; middle, $(M_{\mathrm{Rb}}=-\frac{1}{2},M_{\mathrm{Cs}}=-\frac{7}{2})$; and bottom, $(M_{\mathrm{Rb}}=-\frac{3}{2},M_{\mathrm{Cs}}=-\frac{5}{2})$. Inelastic cross sections are shown at magnetic fields of 10 G [lower solid (red) curves], 100 G [dashed (blue) curves], and 1000 G [dotted (green) curves].

Figure 3

The effect of the nuclear quadrupole moments on the inelastic cross section for two molecules: top, in initial state $(M_{\mathrm{Rb}}=-\frac{3}{2},M_{\mathrm{Cs}}=-\frac{7}{2})$; middle, initial state $(M_{\mathrm{Rb}}=-\frac{1}{2},M_{\mathrm{Cs}}=-\frac{7}{2})$; and bottom, initial state $(M_{\mathrm{Rb}}=-\frac{3}{2},M_{\mathrm{Cs}}=-\frac{5}{2})$. Dotted black curve, full calculation; dashed (red) curve, calculation with $eQ{q}_{\mathrm{Rb}}=0$; solid (blue) curve, calculation with $eQ{q}_{\mathrm{Cs}}=0$; dot-dashed (green) curve, calculation with $eQ{q}_{\mathrm{Rb}}=eQ{q}_{\mathrm{Cs}}=0$. Calculations were performed at a magnetic field of 100 G.

Figure 4

The locations and widths ${\Delta }_B$ of magnetic Feshbach resonances for collisions of RbCs(${}^1\Sigma$) molecules in the state $(M_{\mathrm{Rb}}=\frac{3}{2},M_{\mathrm{Cs}}=\frac{7}{2})$ computed with various interaction potential strengths $\lambda$, for the basis sets $N\le 2$, $L\le 4$ (top) and $N\le 3$, $L\le 2$ (bottom).