  We perform an extensive numerical study on the breathing dynamics of a
few-body Bose polaron setup in a one-dimensional species-selective harmonic
trap. The dynamics is triggered by a quench of the impurity trap. The
excitation of the background majority atoms is mediated via the
majority-impurity interaction. The breathing spectrum is obtained for different
numbers of majority particles, several values of the majority-component
interaction strengths and trap ratios. It is further compared to the breathing
spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for
equal post-quench traps the employed protocol allows to couple states of
different center-of-mass parity in contrast to species-symmetric trap quenches.
Among the participating eigenstates we identify one having odd center-of-mass
parity and even global parity. The breathing frequency induced by this state is
a monotonically decreasing function of the coupling parameter. Importantly, in
order to be observable it requires the entanglement between the species to be
taken into account. We demonstrate this by comparing the numerically exact
results obtained by means of the Multi-Layer Multi-Configuration Time-Dependent
Hartree Method for Mixtures to the ones of a species mean-field ansatz. The
entanglement-sensitive breathing frequency persists also for unequal
post-quench traps where the center-of-mass cannot be decoupled. Finally, we
analyze the impact of parity symmetry on the breathing dynamics by initializing
a state of odd global parity. We evidence a striking resemblance to the ground
state breathing dynamics.
