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Rotational properties of superfluid Fermi-Bose mixtures in a tight toroidal trap

We consider a mixture of a Bose-Einstein condensate, with a paired Fermi superfluid, confined in a ring potential. We start with the ground state of the two clouds, identifying the boundary between the regimes of their phase separation and phase coexistence. We then turn to the rotational response of the system. In the phase-separated regime, we have center of mass excitation. When the two species coexist, the spectrum has a rich structure, consisting of continuous and discontinuous phase transitions. Furthermore, for a reasonably large population imbalance it develops a clear quasi-periodic behaviour, in addition to the one due to the periodic boundary conditions. It is then favourable for the one component to reside in a plane-wave state, with a homogeneous density distribution, and the problem resembles that of a single-component system.