STABILIZATION OF DETERMINISTICALLY CHAOTIC SYSTEMS BY INTERFERENCE AND QUANTUM MEASUREMENTS - THE IKEDA MAP CASE

We propose a method which can effectively stabilize fixed points in th e classical and quantum dynamics of a phase-sensitive chaotic system w ith feedback. It is based on feeding back a selected quantum subensemb le 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 realiza tion involves a trapped ion interacting with laser fields.