  This paper applies results on the robust stability of nonlinear quantum
systems to a system consisting an optical cavity containing a saturated Kerr
medium. The system is characterized by a Hamiltonian operator which contains a
non-quadratic term involving a quartic function of the annihilation and
creation operators. A saturated version of the Kerr nonlinearity leads to a
sector bounded nonlinearity which enables a quantum small gain theorem to be
applied to this system in order to analyze its stability. Also, a non-quadratic
version of a quantum Popov stability criterion is presented and applied to
analyze the stability of this system.
