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International Conference on Quantum Information

Strong Anisotropy, Unusually Narrow Coincidence Angular Distributions, and Very High Degree of Entanglement of SPDC Biphotons

Mikhail Vladimirovich Fedorov, P. A. Volkov, Maxim A. Efremov, Ekaterina V. Moreva, Stanislav S. Straupe, S. P. Kulik

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Wave packet structure of biphoton states arising in the process of spontaneous parametric down-conversion (SPDC) is studied theoretically and experimentally, and its relation with entanglement is discussed. In theory, a new expression is found for the biphoton wave function, in which anisotropy of the crystal refractive index is properly taken into account. Under the conditions of the experiment we report, the anisotropy effects are shown to be very strong. A scheme, optimal for observing extremely narrow coincidence angular photon distributions is found to be that in which the plane containing both the laser axis and the optical axis of a crystal coincides with the observation plane. The opposite, commonly investigated, case is that when these two planes are orthogonal to each other. We show that in the optimal geometry the coincidence angular distribution can be almost 20 times narrower than in the traditional scheme of measurements, and about 10 times narrower than the pump. Narrowing of coincidence distributions in the optimal geometry is accompanied by broadening the single-particle distributions, and this broadening is stronger pronounced in the optimal than in the commonly used geometry. The ratio R of widths of the single-particle and coincidence distributions in the optimal geometry appears to be as large as about 100, and we interpret this as an appropriate evaluation of the degree of entanglement accumulated in biphoton states. The results described are obtained theoretically and perfectly confirmed experimentally.

DOI
10.1364/icqi.2007.ifc2

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Wave packet structure of biphoton states arising in the process of spontaneous parametric down-conversion (SPDC) is studied theoretically and experimentally, and its relation with entanglement is discussed. In theory, a new expression is found for the biphoton wave function, in which anisotropy of the crystal refractive index is properly taken into account. Under the conditions of the experiment we report, the anisotropy effects are shown to be very strong. A scheme, optimal for observing extremely narrow coincidence angular photon distributions is found to be that in which the plane containing both the laser axis and the optical axis of a crystal coincides with the observation plane. The opposite, commonly investigated, case is that when these two planes are orthogonal to each other. We show that in the optimal geometry the coincidence angular distribution can be almost 20 times narrower than in the traditional scheme of measurements, and about 10 times narrower than the pump. Narrowing of coincidence distributions in the optimal geometry is accompanied by broadening the single-particle distributions, and this broadening is stronger pronounced in the optimal than in the commonly used geometry. The ratio R of widths of the single-particle and coincidence distributions in the optimal geometry appears to be as large as about 100, and we interpret this as an appropriate evaluation of the degree of entanglement accumulated in biphoton states. The results described are obtained theoretically and perfectly confirmed experimentally.
We show that the wave packet of a biphoton generated via spontaneous parametric down-conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison with measurements performed in two different schemes: When the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected results, such as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.
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We report on experimental measurements of coincidence and single particle spectral shapes of biphoton signals when frequency entangled states are generated by SPDC crystals pumped by short pulses.It is shown evidence for biphoton coincidence spectrum narrower and single-particle one wider than the pump spectrum, with a large contrast between coincidence and singles distributions.The investigation of biphoton correlations has been performed by fixing one monochromator at the maximal transmission wavelength on down-converted signal gate and scanning the one placed in the idler branch in order to observe the spectral distribution of single counts and coincidences.The degree of entanglement is evaluated by the ratio of the FWHM of single particle and coincidence distributions: the greater the ratio, the greater is the entanglement.The degree of entanglement in frequency variables can be very high: it increases linearly with the length of the crystal, and decreases with the growing pump pulse.
Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of spontaneous parametric down-conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high in agreement with the earlier performed analysis in the formalism of spherical angles characterizing photon's wave vectors [Phys. Rev. A 93, 033830 (2016)]. In Cartesian variables, very broad curves of single-particle distributions are found to have a rather unusual and peculiar shape. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental schemes this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.
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We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter RRR defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\ensuremath{\tau}$. The function $R(\ensuremath{\tau})$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high (Rmin=73)({R}_{\mathrm{min}}=73)(Rmin​=73). The Schmidt number KKK is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of RRR and KKK are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter Rt{R}_{t}Rt​ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number KKK.