  A weak continuous quantum measurement of an atomic spin ensemble can be
implemented via Faraday rotation of an off-resonance probe beam, and may be
used to create and probe nonclassical spin states and dynamics. We show that
the probe light shift leads to nonlinearity in the spin dynamics and limits the
useful Faraday measurement window. Removing the nonlinearity allows a
non-perturbing measurement on the much longer timescale set by decoherence. The
nonlinear spin Hamiltonian is of interest for studies of quantum chaos and
real-time quantum state estimation.
