Controllable optical bistability of Bose–Einstein condensate in an optical cavity with Kerr medium

We study the optical bistability for a Bose-Einstein condensate of atoms in a driven optical cavity with Kerr medium. We find that both the threshold point of optical bistability transition and the width of optical bistability hysteresis can be controlled by appropriately adjusting the Kerr interaction between the photons. In particular, we show that the optical bistability will disappear when the Kerr interaction exceeds a critical value.