  We propose a method which can effectively stabilize fixed points in the
classical and quantum dynamics of a phase-sensitive chaotic system with
feedback. It is based on feeding back a selected quantum sub-ensemble whose
phase and amplitude stabilize the otherwise chaotic dynamics. Although the
method is rather general, we apply it to realizations of the inherently chaotic
Ikeda map. One suggested realization involves the Mach-Zender interferometer
with Kerr nonlinearity. Another realization involves a trapped ion interacting
with laser fields.
