Nonlinear interaction of two photons with a one-dimensional atom: Spatiotemporal quantum coherence in the emitted field

The nonlinear photon-photon interaction mediated by a single two-level atom is studied theoretically based on a one-dimensional model of the field-atom interaction. This model allows us to determine the effects of an atomic nonlinearity on the spatiotemporal coherence of a two-photon state. Specifically, the complete two-photon output wave function can be obtained for any two-photon input wave function. It is shown that the quantum interference between the components of the output state associated with different interaction processes causes bunching and antibunching in the two-photon statistics. This theory may be useful for various applications in photon manipulation, e.g., quantum information processing using photonic qubits, quantum nondemolition measurements, and the generation of entangled photons.