  We investigate the behavior of a harmonically trapped system consisting of an
impurity in a dilute ideal Bose gas after the boson-impurity interaction is
suddenly switched on. As theoretical framework, we use a field theory approach
in the space-time domain within the T-matrix approximation. We establish the
form of the corresponding T-matrix and address the dynamical properties of the
system. As a numerical application, we consider a simple system of a weakly
interacting impurity in one dimension where the interaction leads to
oscillations of the impurity density. Moreover, we show that the amplitude of
the oscillations can be driven by periodically switching the interaction on and
off.
