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Physical Review A

Theory of fourfold interference with photon pairs from spatially separated sources

Hui Rong Zhang, Ruo Peng Wang

Published May 3, 2007• 2 citations
Publisher

Abstract

We present a theory for fourfold quantum interference of photons generated from independent spontaneous parametric down-conversion processes. Closed-form expressions for fourfold quantum interference patterns and visibility are found. The theoretical result for fourfold quantum interference patterns is in good agreement with experimental data reported. Detailed numerical calculations for the dependence of fourfold quantum interference visibility on experimentally controllable parameters are carried out. It is found out that higher visibility can be achieved for small biphoton width, short pump pulse coherence time, and narrow bandwidth of spectral filters. The optimal condition for obtaining at the same time higher fourfold interference visibility and intensity is also discussed.

DOI
10.1103/physreva.75.053804

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We present a theory for fourfold quantum interference of photons generated from independent spontaneous parametric down-conversion processes. Closed-form expressions for fourfold quantum interference patterns and visibility are found. The theoretical result for fourfold quantum interference patterns is in good agreement with experimental data reported. Detailed numerical calculations for the dependence of fourfold quantum interference visibility on experimentally controllable parameters are carried out. It is found out that higher visibility can be achieved for small biphoton width, short pump pulse coherence time, and narrow bandwidth of spectral filters. The optimal condition for obtaining at the same time higher fourfold interference visibility and intensity is also discussed.
Theory and experiment of two-photon lquotlquotlquotdirectrquotrquotrquot interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump
Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young’s double-slit experiment. In this experiment, a short focal length lens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.
Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.
The process of parametric down-conversion pumped by a short coherent pulse is analysed. The coherence properties of the down-converted field are investigated. It is found that the spectrum of the down-conversion is mostly determined by the nonlinear medium and is independent of the width of the short pumping pulse and that it is impossible to realize a transform-limited two-photon state. Fourth-order interference between a weak coherent pulse and the down-converted pulse is considered. It is found that high visibility near 100% is achievable by means of narrow optical filtering. It is shown that by gating the detection on one of the down-converted photons, a transform-limited single-photon pulse is achievable in the other conjugate field, but its pulse width is shorter than that of the down-converted pulse and its peak position is uncertain within the pulse width of the down-converted light. However, with narrow optical filtering on the gating detection process, a transform-limited single-photon state can be obtained in the gated field with its peak position synchronized to the pump pulse. The possibility for the realization of a multi-photon interference experiment is explored for the quantum state measurement of the single-photon state.
We experimentally investigate a double-pass parametric down-conversion scheme for producing pulsed, polarization-entangled photon pairs with high visibility. The amplitudes for creating photon pairs on each pass interfere to compensate for distinguishing characteristics that normally degrade two-photon visibility. The result is a high-flux source of polarization-entangled photon pulses that does not require spectral filtering. We observe quantum interference visibility of over 95% without the use of spectral filters for 200fs200\phantom{\rule{0.3em}{0ex}}\mathrm{fs}200fs pulses, and up to 98.1% with 5nm5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}5nm bandwidth filters.