LAUSR

We show the existence of slow propagating phonons in quasi one dimensional Bose-Einstein condensates. The impurities are trapped inside the potential created by dark-soliton due to which the conditions to separate the three levels (qutrit), perfectly, has determined. We compute the phonon-soliton coupling and investigate the decay rates of the three level system. We derive the analytical expression of the linear susceptibility to demonstrate the phenomenon of acoustic induced transparency based on matter wave phononics. The dark-soliton qutrit with unique properties of transmission and dispersion revealing the possibility of slowing down the speed of acoustic pulse. Moreover, the present scheme could be proposed to analyze the diverse applications like quantum gates in the field of quantum information.