Breathing modes and stability of trapped two-component ultracold atoms

The breathing modes and stability of trapped two-component ultracold atoms are studied using a variational method. We consider a boson-boson, a boson-fermion, and a fermion-fermion mixture in a 3D isotropic harmonic trap and in a 1D optical lattice. When the two components are miscible, the corresponding in-phase and out-of-phase breathing mode frequencies are calculated against the value of the inter-component interaction. The stability of the two-component system is shown to have strong correlation with the behaviors of breathing modes.