  We consider a two-component Bose-Einstein condensate in a one-dimensional
optical cavity. Specifically, the condensate atoms are taken to be in two
degenerate modes due to their internal hyperfine spin degrees of freedom and
they are coupled to the cavity field and an external transverse laser field in
a Raman scheme. A parallel laser is also exciting the cavity mode. When the
pump laser is far detuned from its resonance atomic transition frequency, an
effective nonlinear optical model of the cavity-condensate system is developed
under Discrete Mode Approximation (DMA), while matter-field coupling has been
considered beyond the Rotating Wave Approximation. By analytical and numerical
solutions of the nonlinear dynamical equations, we examine the mean cavity
field and population difference (magnetization) of the condensate modes. The
stationary solutions of both the mean cavity field and normalized magnetization
demonstrate bistable behavior under certain conditions for the laser pump
intensity and matter-field coupling strength.
