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Polarization-Angle SPDC Spectrum and its Effect on Generated Photon States

A. Agapov, P. P. Gostev, S. Magnitskya, Vladimir V. Firsov, Dmitry N. Frolovtsev

Published Jan 1, 2015• 2 citations
Publisher

Abstract

Analytical formulas for vector components of the polarization vector of spontaneous parametric down-conversion (SPDC) radiation in the degenerated regime and its dependencies on the angle between the principal sections for the pump and SPDC rays are derived. The entanglement losses in the double-crystal SPDC scheme caused by the Migdal effect are analyzed. The analytical expressions are illustrated numerically for the case of BBO crystal.

DOI
10.1051/epjconf/201510303004

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Analytical formulas for vector components of the polarization vector of spontaneous parametric down-conversion (SPDC) radiation in the degenerated regime and its dependencies on the angle between the principal sections for the pump and SPDC rays are derived. The entanglement losses in the double-crystal SPDC scheme caused by the Migdal effect are analyzed. The analytical expressions are illustrated numerically for the case of BBO crystal.
Photonic sources based on spontaneous parametric downconversion (SPDC) are now pervasively employed in optical quantum information processing protocols. The recent focus on engineering efficient photonic sources requires a thorough understanding of several of the subtler characteristics of SPDC, which had previously been negligible. Here, we experimentally investigate one such phenomenon – the dependence of the downconversion polarization on emission angle. Additionally, we discuss the significance of this effect from the perspective of better engineering SPDC sources. We also propose techniques, specifically in the context of a two-crystal scheme for generating polarization-entangled photons, to exploit the effect and drastically improve source quality in certain limiting cases.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
A consistent analysis of the quantum state of polarization of SPDC radiation is presented and the peculiarities of the quantum state of polarization of SPDC in biaxial nonlinear optical crystals are considered. It is shown that the SPDC polarization deviation angle can exceed 15°, and the angle between the signal and idler wave vectors D can exceed 30°. Estimates of the curvature of the cone formed by SPDC radiation in biaxial crystals are also given. The influence of SPDC polarization deviation in a non-collinear mode on the entanglement of biphoton states generated by a double-crystal scheme is analyzed, it is shown that Tangle of the generated quantum state can deteriorate by 6%, and conditions are identified under which entanglement can be completely restored.
Optimizing the brightness of a spontaneous parametric down-conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wave function, generalizing previous known results, by considering collinear and noncollinear emission. We present analytical expressions for our results in the thin-crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is 1/21/\sqrt{2}1/2​ for collinear degenerate emission and approaches 1/21/21/2 for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\ensuremath{\beta}$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin-crystal regime.