For a mixture of alkali-earth atomic gas in the long-lived excited state ${}^3{P}_0$ and the ground state ${}^1{S}_0$, in addition to nuclear spin, another “orbital” index is introduced to distinguish these two internal states. In this Letter we propose a mechanism to induce Feshbach resonance between two atoms with different orbital and nuclear spin quantum numbers. Two essential ingredients are the interorbital spin-exchange process and orbital dependence of the Landé $g$ factors. Here the orbital degrees of freedom plays a similar role as the electron spin degree of freedom in magnetic Feshbach resonance in alkali-metal atoms. This resonance is particularly accessible for the ${}^{173}\mathrm{Yb}$ system. The BCS-BEC crossover in this system requires two fermion pairing order parameters, and displays a significant difference compared to that in an alkali-metal system.

• Received 24 April 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.135301