  We investigate the properties of a distinguishable single excited state
impurity pinned in the center of a trapped Bose-Einstein condensate (BEC) in a
one-dimensional harmonic trapping potential by changing the bare mass of the
impurity and its interspecies interaction strength with the BEC. 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 obtain 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 the condensate wave function remains present during a
time-of-flight (TOF) 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, we found out that the generation of gray
bi-soliton or gray quad-solitons (four-solitons) depends on the bare mass of
the excited-impurity in a harmonic trap.
