LAUSR

We investigate the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and homogeneous Sarma superfluid states in alkaline-earth-like $^{173}$Yb atomic gases near an orbital Feshbach resonance at zero temperature with population imbalances in both the open and closed channels (or bands). We find that in homogeneous space by adjusting the open-channel Zeeman energy $h_o$, both the Sarma and Fulde-Ferrell superfluid states are greatly enhanced by the spin-exchange interaction while the closed-channel Zeeman energy $h_c$ remains small. In the presence of an external harmonic trap, the trapped gas features a shell structure of separated phases, where the Sarma phase leaves detectable valley structure in the columnar-integrated momentum distribution, and the Fulde-Ferrell state acquires enhanced spatial anisotropy. As both signatures can be easily detected in time-of-flight images, our findings are helpful to realize and detect the long-sought FFLO and Sarma superfluid states at the same time in experiments.