  The study of polaron of an open quantum system plays an important role in
both verifying the effectiveness of approximate many-body theory and predicting
novel quantum phenomenone in open quantum systems. In a pioneering work, Piazza
et al have proposed a Fermi-polaron scheme with a lossy impurity [54], which
exhibits a novel long-lived attractive polaron branch in the quantum Zeno
limit. However, we would also run into a counterpart problem that an impurity
scatters with an open quantum bath exciting polarons, which is what we focus in
on. In this work, we conclude the molecular state under the two limits of
vanishing small and infinite large dissipation intensity as well as the reason
why the dissipation range leads to the decrease of the gap between the
molecular state and molecule-hole continuum in the former case by means of
analytically research. The spectrum functions of molecular and polaron states
with different dissipation range and loss rate are investigated. We find the
spectral signals of molecular and polaron states will both diffuse firstly and
then revives as the dissipation is on the raise. Moreover, it is shown that the
attractive and repulsive polarons show different response to the increasing
dissipation range in our model. At last, we exhibit the polaron energy,
residue, effective mass and two-body decay for mass balanced and imbalanced
systems. Our results might be useful for future cold atom experiment on open
quantum systems.
