  We derive simple models for the dynamics of a single atom coupled to a cavity
field mode in the absorptive bistable parameter regime by projecting the time
evolution of the state of the system onto a suitably chosen nonlinear
low-dimensional manifold, which is found by use of local tangent space
alignment. The output field from the cavity is detected with a homodyne
detector allowing observation of quantum jumps of the system between states
with different average numbers of photons in the cavity. We find that the
models, which are significantly faster to integrate numerically than the full
stochastic master equation, largely reproduce the dynamics of the system, and
we demonstrate that they are sufficiently accurate to facilitate feedback
control of the state of the system based on the predictions of the models
alone.

Quantum Physics