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We propose a scheme which can effectively restore fixed points in the quantumdynamics of repeated Jaynes-Cummings interactions followed by atomic statemeasurements, when the interaction times fluctuate randomly. It is based onselection of superposed atomic states whose phase correlations tend to suppressthe phase fluctuations of each separate state. One suggested realizationinvolves the convergence of the cavity field distribution to a single Fockstate by conditional measurements performed on two-level atoms with fluctuatingvelocities after they cross the cavity. Another realization involves a trappedion whose internal-motional state coupling fluctuates randomly. Its motionalstate is made to converge to a Fock state by conditional measurements of theinternal state of the ion.Comment: RevTeX, 5 pages, four (EPS) figures automatically included through  epsfig. Physical Review A 1998 (accepted for publication) Two references  added to Ref. [8]. No other change. Final version which will appear in  Physical Review

Trapping-state restoration in the randomly driven Jaynes-Cummings model by conditional measurements