We investigate classically and quantum-mechanically the coherent interaction between a single mode of the electromagnetic field and a stream of two-level atoms under the assumptions that only one atom at a time is coupled to the field and that the interaction times are all equal. This is a quantum-optics analog of a coherently kicked harmonic oscillator. We find that the classical system always evolves toward a marginally stable steady state at the threshold of type-1 intermittency, independently of the initial state of inversion of the atoms. But there are infinitely many such steady states, and which one is reached may depend sensitively on the initial conditions. In contrast, in the case of inverted atoms the quantized system usually does not reach a steady state: The intrinsic quantum fluctuations of the field almost always force it eventually to grow past the classical fixed points. A notable exception occurs under conditions such that the sequence of inverted atoms injected into the cavity leads to the preparation of a highly excited Fock state of the cavity mode.
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