Controllable optical bistability with perfect photon absorption

We propose a scheme for controlling nonlinear coherent perfect absorption (CPA) in a three-level \Lambda-type atom-cavity system. Generally, the normally nonlinear CPA and the bistable CPA can be attained at the different frequencies of an input probe field. With a coherent control field coupling one of the ground states and the excited state of the atoms, two types of CPA can be attained at the same frequency. Besides, for the bistable CPA, the highest output-input ratio of the high stable state and the low stable state is approximately 1, and the bistable region is controllable with the control field. The controllable bistable CPA may have potential applications in optical bistable switching and optical logic devices