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Journal of Modern Optics

Four photons interfering but showing the two-photon interference behaviour

Bao‐Sen Shi, Akihisa Tomita

Published Feb 17, 2006• 3 citations
Publisher

Abstract

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.

DOI
10.1080/09500340500443151

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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.
Periodically poled crystals, such as periodically poled potassium titanyl phosphate (PPKTP) or lithium niobate, recently became more attractive because of their high efficiency for producing a photon pair in both cw and pulse cases. The time uncertainty of photon pair creation in a crystal is crucial for many important applications. In this paper, we experimentally demonstrate that the time uncertainty of the photon pair creation in a PPKTP crystal is much larger than the coherence time of a femtosecond pump laser by using phase-sensitive two-photon interference using a Michelson interferometer, which means the femtosecond laser cannot be considered as a clock that announces the creation of the photon pairs. The experimental results can be well explained by an effective Franson-type interferometer, if the PPKTP is regarded as a narrow band filter at the same time. Our experiment also shows a way by which the Franson-typetwo-photon interference phenomenon can be observed even if the coherence length of the pump laser is less than the path-length difference between the two interfering beams.
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.
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.
The Periodically Poled Potassium Titanyl Phosphate (PPKTP) is a type of non linear crystal that serves as a source of production of entangled pairs of photons. The produced pair of photons, known as the Signal and Idler photons, possess unique characteristics within their entanglement that allow the production of new technologies such as quantum cryptography and quantum teleportation. The creation of the Signal and Idler photons occur through a process named Spontaneous Parametric Down Conversion (SPDC), which occurs when the pump laser beam penetrates a non linear medium. SPDC follows conservation of momentum and energy, thus imposing phase matching conditions on the generated photon pairs. These conditions result in specific space and frequency correlations of the photons. The aim of this project is to characterize the entangled photon pairs in their spatial profile and frequency spectrum, known as the Joint Spectrum.
After a very brief review of the historical Einstein, Podolsky, and Rosen (EPR) experiments, a new two-photon interference type EPR experiment is reported. A two-photon state was generated by optical parametric down conversion. Pairs of light quanta with degenerate frequency but divergent directions of propagation were sent to two independent Michelson interferometers. First and second order interference effectors were studied. Different than other reports, we observed that the second order interference visibility vanished when the optical path difference of the interferometers were much less than the coherence length of the pumping laser beam. However, we also observed that the second order interference behaved differently depending on whether the interferometers were set at equal or different optical path differences.