We analyze a scheme for controlling coherent photon absorption by cavity electromagnetically induced transparency (EIT) in a three-level atom-cavity system. Coherent perfect absorption (CPA) can occur when time-reversed symmetry of lasing process is obtained and destructive interference happens at the cavity interfaces. Generally, the frequency range of CPA is dependent on the decay rates of cavity mirrors. When the control laser is settled, the smaller cavity decay rate causes the wider frequency range of CPA, and the input intensity is larger to satisfy CPA condition for a given frequency. While the cavity parameters are determined, Rabi frequency of the control laser has little effect on the frequency range of CPA. However, with EIT-type quantum interference, the CPA mode is tunable by the control laser. This means the CPA with given frequency and intensity of an input laser can be manipulated as the coherent non-perfect absorption (CNPA). Moreover, with the relative phase of input probe lasers, the probe fields can be perfectly transmitted and/or reflected. Therefore, the system can be used as a controllable coherent perfect absorber or transmitter and/or reflector, and our work may have practical applications in optical logic devices.
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