  The interplay between measurement and quantum correlations in many-body
systems can lead to novel types of collective phenomena which are not
accessible in isolated systems. In this work, we merge the Zeno-paradigm of
quantum measurement theory with the concept of polarons in condensed-matter
physics. The resulting quantum-Zeno Fermi-polaron is a quasi-particle which
emerges for lossy impurities interacting with a quantum-degenerate bath of
fermions. For loss rates of the order of the impurity-fermion binding energy
the quasi-particle is short lived. However, we show that in the strongly
dissipative regime of large loss rates a long-lived polaron branch re-emerges.
This quantum-Zeno Fermi-polaron originates from the nontrivial interplay
between the Fermi-surface and the surface of the momentum region forbidden by
the quantum Zeno projection. The situation we consider here is realized
naturally for polaritonic impurities in charge-tuneable semiconductors and can
be also implemented using dressed atomic states in ultracold gases.
