Interference control of coherent perfect absorption in a driven three-level atom inside the cavity with parametric amplification

We investigate coherent perfect absorption (CPA) and electromagnetically induced transparency (EIT) in a cavity QED system that includes a degenerate optical parametric amplifier (OPA). We derive the condition for CPA and identify two distinct regimes controlled by the control laser. When the control laser is resonant and induces EIT, DQI suppresses CPA, thereby making the system a near-perfect transmitter. When the control laser is detuned, DQI again suppresses CPA, but now the system acts as a near-perfect reflector. In the EIT regime, increasing OPA strength enhances both transmitted and intracavity intensities. At the optimal detuning of the reflector regime, the input light is reflected, and the intracavity intensity drops to zero.