We have proposed a scheme for double-beam optical bistability in a tunnel-coupled asymmetric double quantum-well driven by two optical fields circulating inside two independently unidirectional ring cavities. In contrast to the single-cavity case where single-photon saturated absorption and self Kerr-nonlinearity are dominant, the two-photon absorption and cross phase modulation can be enhanced via tunneling induced interference and have an important influence to the formation of bistability. The bistable behavior can be controlled effectively via the system parameters such as the input and detuning of control field, the detuning of the probe field, Fano interference strength and cooperation parameter. Furthermore, the proposed scheme has the ability to manipulate the outputs of two optical cavities simultaneously. Due to the flexible design of semiconductor quantum well, our scheme is more practical than atomic system, therefore it can be utilized to achieve dual all-optical switching which has application in optical communication and computing.
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