We continue our investigations of cavity QED with time- dependent parameters. In this paper we discuss the situation where the state of the atoms leaving the cavity is reduced but the outcome is not recorded. In this case our knowledge is limited to an ensemble description of the results only. By applying the Demkov-Kunike level-crossing model, we show that even in this case, the filtering action of the interaction allows us to prepare a pre-assigned Fock state with good accuracy. The possibilities and limitations of the method are discussed and some relations to earlier work are presented.
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