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Abstract In this thesis we investigate the optical bistability (OB) and how to control it in the system of double quantum wells coupled by tunneling. For this sake, we introduce the quantum systems and their dynamics and manifest the dierence between closed and open quantum systems. Throughout this study, we conned our work to studying the closed systems interacting with the electromagnetic eld. In order to model such an interaction, we mentioned the two-level and three-level system as a manifestation of the laser-matter interaction giving rise to many optical phenomena in the system, amongst them is the electromagnetically induced transparency (EIT) which is mentioned in Chapter 2. The semiconductor band structure is covered in order to introduce the physics of quantum wells and to show how they will respond to the electromagnetic elds. Throughout this thesis, we study and model one of the important optical phenomena, optical bistability (OB), in two asymmetric quantum wells coupled through tunneling. Rather than controlling the OB by monochromatic laser eld, we use a trichromatic laser eld and simulate the e ect of the system parameters including the sidebands on the hysteresis cycle that emerges in the system. |