We consider a two-component Bose-Einstein condensate in a one-dimensionaloptical cavity. Specifically, the condensate atoms are taken to be in twodegenerate modes due to their internal hyperfine spin degrees of freedom andthey are coupled to the cavity field and an external transverse laser field ina Raman scheme. A parallel laser is also exciting the cavity mode. When thepump laser is far detuned from its resonance atomic transition frequency, aneffective nonlinear optical model of the cavity-condensate system is developedunder Discrete Mode Approximation (DMA), while matter-field coupling has beenconsidered beyond the Rotating Wave Approximation. By analytical and numericalsolutions of the nonlinear dynamical equations, we examine the mean cavityfield and population difference (magnetization) of the condensate modes. Thestationary solutions of both the mean cavity field and normalized magnetizationdemonstrate bistable behavior under certain conditions for the laser pumpintensity and matter-field coupling strength.
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