Pion Condensation in Baryonic Matter: from Sarma Phase to LOFF Phase

We investigated two pion condensed phases in the frame of two flavor Nambu--Jona-Lasinio model at finite baryon density: the homogeneous and isotropic Sarma phase and inhomogeneous and anisotropic LOFF phase. At small isospin chemical potential $\mu_I$, the Sarma state is free from the Sarma instability and magnetic instability due to the strong coupling and large enough effective quark mass. At large $\mu_I$, while the Sarma instability can be cured via fixing baryon density $n_B$ to be nonzero, its magnetic instability implies that the LOFF state is favored than the Sarma state. In the intermediate $\mu_I$ region, the stable ground state is the Sarma state at higher $n_B$ and LOFF state at lower $n_B$