Optical bistability in sideband output modes induced by squeezed vacuum

We consider $N$ two-level atoms in a ring cavity interacting with a broadband squeezed vacuum centered at frequency $\omega_{s}$ and an input monochromatic driving field at frequency $\omega$. We show that, besides the central mode (at $\o$), many other {\em sideband modes} are produced at the output, with frequencies shifted from $\omega$ by multiples of $2(\omega -\omega_{s})$. Here we analyze the optical bistability of the two nearest sideband modes, one red-shifted and the other blue-shifted.