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Spontaneous parametric down-conversion ͑SPDC͒ has been extensively studied for the case of a continuous wave pump. In this paper SPDC is studied for the case in which the pump is a pulse. The pump pulse acts like a clock with an uncertainty equal to its width. This makes it possible to distinguish pairs of photons born at sufficiently different depths inside the crystal with a consequent decrease in two-photon interference. We study this effect in detail for degenerate collinear type-II SPDC and degenerate type-I SPDC. It may be possible in the type-II case to eliminate the clock effect of the pump by judicious choice of materials and wavelengths.

Generating nonclassical light offers a benchmark tool for fundamental research and potential applications in quantum optics. Conventionally, it has become a standard technique to produce nonclassical light through the nonlinear optical processes occurring in nonlinear crystals. We describe this process using cold atomic-gas media to generate such nonclassical light, especially focusing on narrowband biphoton generation. Compared with the standard procedure the new biphoton source has such properties as long coherence time, long coherence length, high spectral brightness, and high conversion efficiency. Although there exist two methodologies describing the physical process, we concentrate on the theoretical aspect of the entangled two-photon state produced from the four-wave mixing in a multilevel atomic ensemble using perturbation theory. We show that both linear and nonlinear optical responses to the generated fields play an important role in determining the biphoton waveform and, consequently, on the two-photon temporal correlation. There are two characteristic regimes determined by whether the linear or nonlinear coherence time is dominant. In addition, our model provides a clear physical picture that brings insight into understanding biphoton optics with this new source. We apply our model to recent work on generating narrowband (and even subnatural linewidth) paired photons using the technique of electromagnetically induced transparency and slow-light effect in cold atoms and find good agreement with experimental results.

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