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We investigate the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) andhomogeneous Sarma superfluid states in alkaline-earth-like $^{173}$Yb atomicgases near an orbital Feshbach resonance at zero temperature with populationimbalances in both the open and closed channels (or bands). We find that inhomogeneous space by adjusting the open-channel Zeeman energy $h_o$, both theSarma and Fulde-Ferrell superfluid states are greatly enhanced by thespin-exchange interaction while the closed-channel Zeeman energy $h_c$ remainssmall. In the presence of an external harmonic trap, the trapped gas features ashell structure of separated phases, where the Sarma phase leaves detectablevalley structure in the columnar-integrated momentum distribution, and theFulde-Ferrell state acquires enhanced spatial anisotropy. As both signaturescan be easily detected in time-of-flight images, our findings are helpful torealize and detect the long-sought FFLO and Sarma superfluid states at the sametime in experiments.

Enhanced Fulde-Ferrell-Larkin-Ovchinnikov and Sarma superfluid states near an orbital Feshbach resonance