A distinguishable single excited-impurity in a Bose-Einstein condensate

We investigate the properties of a distinguishable single excited state impurity pinned in the center of a trapped Bose-Einstein condensate in a one-dimensional harmonic trapping potential by changing the bare mass of the impurity and its interspecies interaction strength with flic Bose-Einstein condensate. We model our system by using two coupled differential equations for the condensate and the single excited-impurity wave function, which we solve numerically. For equilibrium, we find that an excited-impurity induces two bumps or dips on the condensate for the attractive-or repulsive-interspecies coupling strengths, respectively. Afterwards, we show that the excited-impurity induced imprint upon flic condensate wave function remains present during a time-of-flight expansion after having switched off the harmonic confinement. We also investigate shock-waves or gray-solitons by switching off the interspecies coupling strength in the presence of harmonic trapping potential. During this process, wc found that the generation of gray bi-soliton or gray quad-solitons (four-solitons) depend on the bare mass of the excited-impurity in a harmonic trap.