Topology of Quantum Grey Soliton in Multi-Component Inhomogeneous Bose-Einstein Condensates

We study the dispersion mechanism of Lieb mode excitations of both single and multi component ultra-cold atomic Bose gas, subject to a harmonic confinement through chirp management. It is shown that in some parameter domain, the hole-like excitations lead to the soliton's negative mass regime, arising due to the coupling between chirp momentum and Kohn mode. In low momenta region the trap considerably affects the dispersion of the grey soliton, which opens a new window to observe Lieb-mode excitations. Further, we extend our analysis to binary condensate, which yields usual shape compatible grey-bright soliton pairs. The inter-species interaction induces a shift in the Lieb-mode excitations, where the pair can form a bound state. We emphasize that the present model provides an opportunity to study such excitations in the low momenta regime, as well as the formation of bound state in binary condensate.