Abstract

By a full quantum model, absorption of a weak probe beam is investigated in a closed inverted Y four-level system which is coupled with two electromagnetic fields. The dynamical equations of its density matrix elements are achieved by applying the interaction Hamiltonian in interaction picture. We show the existence of electromagnetically induced transparency phenomena in the steady state. This effect is appeared even for the decreasing one of the coupling photons number down to zero. In this case the quantum vacuum state can cause the electromagnetically induced transparency for the probe beam. In the full quantum method, the absorption of a corresponding three-level  $Lambda$-type system is achieved where one of the coupling fields, in inverted Y four-level system, is set to the vacuum state. But the absorption of a corresponding three-level Ladder system is not achieved where other coupling field is set to be in the vacuum.  It is due to the coupling of vacuum state with atomic levels.