Beliaev damping of gapped excitations in a two-component Bose-Einstein condensate

We investigate the Beliaev damping of gapped excitations in a homogenous two -component Bose-Einstein condensate with Rabi coupling and find different damping behavior of gapped excitations in two quantum phases. In the paramagnetic phase, due to constraints imposed by the Z 2 symmetry and energy -momentum conservation, the only damping channel available, that of decaying into one phonon and one new gapped mode, cannot occur unless the group velocity of the gapped modes surpasses the sound speed. Conversely, in the ferromagnetic phase, three distinct decay channels exist. Once the momentum of the excitations falls below a critical threshold, only one of these channels, that of decaying into two gapless modes, is activated, and the damping rate remains finite even at zero momentum.