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International Journal of Optics

Pump Spectral Bandwidth, Birefringence, and Entanglement in Type‐II Parametric Down Conversion

Daniel B. Erenso

Published Jan 1, 2009• 2 citations
Publisher

Abstract

The twin photons produced by a type‐II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.

DOI
10.1155/2009/387580

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The twin photons produced by a type‐II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.
Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.
A model is presented to describe spontaneous type-II parametric down-conversion pumped by a broadband source. This process differs from the familiar cw-pumped down-conversion in that a broader range of pump energies is available for down-conversion. The properties of the nonlinear crystal determine how these energies are distributed into the down-converted photons. Because the two photons are polarized along different crystal axes, they have different spectral characteristics and are no longer exactly anticorrelated. As the pump bandwidth is increased, this effect becomes more pronounced. A fourth-order interference experiment is proposed, illustrating some of the features of broadband pumped down-conversion.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.
Spontaneous parametric down-conversion (SPDC) is the most often used source of entangled photon states in quantum optics. Recently, it has been suggested in theory that the reduction of polarization entanglement between the photon pair generated via the type-II SPDC process pumped by a ultrafast laser is due to the asymmetry in the joint spectrum function, which is the indicative of the frequency entanglement between the two photons. In this paper, we report the measurement of the joint spectrum function (i.e., direct observation of the degree of frequency entanglement) of the two-photon state of type-II SPDC in both cw- and ultrafast-laser pumping conditions. We observed that, in agreement with the theory, the degree of frequency entanglement (the shape of the joint spectrum function) is indeed different for cw- and ultrafast-pumped type-II SPDC. Our results are of importance in "engineering" the two-photon state for specific quantum applications, such as quantum cryptography.