Acoustic quasibound states and tachyonic instabilities from binary Bose-Einstein condensates

We consider two-component Bose-Einstein condensates (BECs) and introduce the BEC vortex in $1+2$ dimensions. We focus on two types of gapped excitations induced by the modes of two-component BECs with relative phases of $0$ and $\pi$, analogous to the massive scalar field with positive and negative mass squared, respectively. The inclusion of space-dependent Rabi coupling can induce an effective space-dependent mass term. We study superradiant instabilities resulting from the quasibound states corresponding to positive mass squared and the tachyonic instabilities arising from negative mass squared in both the frequency and time domains. These instabilities resemble two possible mechanisms that make Kerr black holes unstable in scalar-tensor gravity with the presence of matter around the black hole. Our proposed phenomena could potentially be implemented in future experiments, drawing from the success of recent analog rotating black hole implementations.