Bifurcations, stability, and mode evolution in segregated condensate mixtures

We present new features of low energy Bogoliubov quasiparticle excitations of a two component Bose-Einstein condensate (TBEC) in quasi-2D geometry at zero temperature using Hartree-Fock-Bogoliubov (HFB). We, in particular, consider the TBECs of $^{133}$Cs~-$^{87}$Rb and $^{85}$Rb~-$^{87}$Rb, and show specific features in the low energy excitation spectrum as a function of the interaction strength. For $^{85}$Rb~-$^{87}$Rb TBEC, the appearance of a new zero energy mode is observed. Whereas for $^{133}$Cs~-$^{87}$Rb TBEC we report a bifurcation of the softened Kohn mode at the point of transition from miscible to immiscible domain. The lower energy mode, after the bifurcation, goes soft and becomes a new Goldstone mode of the system.