  The interaction of matter with quantum light leads to phenomena which cannot
be explained by semiclassical approaches. Of particular interest are states
with broad photon number distributions which allow processes with high-order
Fock states. Here, we analyze a Jaynes-Cummings-type model with three
electronic levels which is excited by quantum light. As quantum light we
consider coherent and squeezed states. In our simulations we include several
loss mechanisms, namely, dephasing, cavity, and radiative losses which are
relevant in real systems. We demonstrate that losses allow one to control the
population of electronic levels and may induce coherent population trapping, as
well as lead to a redistribution of the photon statistics among the quantum
fields and even to a transfer of the photon statistics from one field to
another. Moreover, we introduce and analyze a novel quantity, the quantum
polarization, and demonstrate its fundamental difference compared to the
classical polarization. Using the quantum polarization and the third level
population, we investigate electromagnetically induced transparency in the
presence of quantum light and show its special features for the case of
squeezed light. Finally, quantum correlations between fields are studied and
analyzed in the presence of different types of losses.
