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Chinese Physics B

Quantum analysis on the four-photon interference

Wang Ruo-Peng, Zhang Hui-Rong

Published Jan 1, 2008• 4 citations
Publisher

Abstract

We present a theory for quantum interference of four photons generated by spontaneous parametric down-conversion. Detailed investigation of the dependence of fourfold coincidence count rate on time delay between the incident and the reflective pump laser pulses is carried out. Gaussian type dependence is found, and good agreement between our theoretical results and experimental data reported in the literature is achieved.

DOI
10.1088/1674-1056/17/1/034

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We present a theory for quantum interference of four photons generated by spontaneous parametric down-conversion. Detailed investigation of the dependence of fourfold coincidence count rate on time delay between the incident and the reflective pump laser pulses is carried out. Gaussian type dependence is found, and good agreement between our theoretical results and experimental data reported in the literature is achieved.
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.
We have experimentally demonstrated two-photon interference between biphoton amplitudes arising from two well-separated pump pulses. It is important to note the following. 1) The pump pulse intensity was low enough so that single counting rates of the detectors were kept much smaller than pulse repetition rates: the probability of having one spontaneous parametric down conversion (SPDC) photon pair per pulse in our experiment is negligible. Hence the interference cannot be explained as two SPDC photons from two pump pulses (one SPDC photon pair from each pulse) interfering at the detectors. The two pump pulses simply provide two biphoton amplitudes which could result in coincidence counts, and interference occurs between these two biphoton amplitudes only when they are indistinguishable. 2) The BBO crystal in our experiment was only 100 /spl mu/m thick, so the two-pulse did not exist in BBO at the same time at any moment. 3) Due to the delays in the interferometer (/spl tau/ /spl tau//sub 1/), the signal-idler never met at the beamsplitter. Therefore, the existence of two-photon interference cannot be viewed as the interference between the signal and idler photons. These three points again emphasize the fact that it is the indistinguishability of the two-photon Feynman alternatives for the biphoton amplitudes which is responsible for the two-photon quantum interference effects.
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.
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
It was shown by Riedmatten et al. [J. Mod. Opt. 51 1637 (2004)] that two different four-photon states could be generated according to the relation between the duration time of the pump laser T and the coherence time t of the single photon from spontaneous parametric down-conversion (SPDC). In this paper, using four photons generated by the SPDC in a Periodically Poled Potassium Titanyl Phosphate (PPKTP), we experimentally observe the four-photon interference in a Michelson interferometer. All experimental results can be explained by the product of two independent two-photon interferences. Our experimental condition corresponds to the case of T ≫ t. This experiment clearly confirms the theory given by Riedmatten et al.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.