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arXiv:0904.3009 · Europhysics Letters (EPL)

Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime

G. Brida, Valentina Caricato, Mikhail Vladimirovich Fedorov, Marco Genovese, Marco Gramegna, S. P. Kulik

Published Sep 1, 2009• 60 citations
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Abstract

We verified the operational approach based on the direct measurement of the entanglement degree for bipartite systems. In particular spectral distributions of single counts and coincidence for pure biphoton states generated by a train of short pump pulses have been measured and the entanglement quantifier has been calculated. The approach gives an upper bound of entanglement stored in total biphoton states, which can reach extremely high values up to 10 4 –10 5 .

DOI
10.1209/0295-5075/87/64003

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arXiv:quant-ph/0608009•Physical Review A•Apr 26, 2007•47 citations
We verified the operational approach based on the direct measurement of the entanglement degree for bipartite systems. In particular spectral distributions of single counts and coincidence for pure biphoton states generated by a train of short pump pulses have been measured and the entanglement quantifier has been calculated. The approach gives an upper bound of entanglement stored in total biphoton states, which can reach extremely high values up to 10 4 –10 5 .
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.
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.
The frequency entangled biphoton source generated via spontaneous parametric down-conversion (SPDC) process has found important applications in the fields of quantum clock synchronization, quantum communication, quantum information processing, etc. As quantum technologies evolve, quantitative characterization of the frequency entanglement becomes necessary and has been implemented by measuring the spectral properties of the biphoton state. However, due to the high dark rate and low quantum efficiency of the InGaAs single-photon detectors, direct measurement of the spectral properties of the biphoton state at optical communication wavelength is hard to implement. In this paper, we report the measurement of the spectral properties of a biphoton state at optical communication wavelength which is generated from periodically poled potassium titanyl phosphate (PPKTP) pumped by an ultra-short pulsed optical source at 787 nm. Based on the coincidence measurement setup together with two infrared spectrometers, the spectra of the signal and idler photons are obtained with their center wavelengths being 1574.4 nm and 1574.9 nm, while their 3-dB bandwidths being 35.3 nm and 37.6 nm respectively. The joint spectrum of the photon pair is observed as well and shows a coincident-frequency entanglement and a joint spectrum bandwidth of 3 nm. According to the ratio of the single-photon spectral bandwidth to the joint spectral bandwidth of the photon pairs, the degree of frequency entanglement is quantified to be 12, denoting a relatively high quality of the entanglement.
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R 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. This function is shown to have a minimum and even in the minimum, at rather natural conditions, the parameter R is found to be very high (R=73>>1). The Schmidt number K is found for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of R and K are found to be identical and numerical difference between them is shown to be not exceeding 20%. Two-time temporal wave function of a biphoton state is investigated in details, 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 R is defined as the ratio of durations of the single-particle and coincidence signals, and the defined in such a way parameter R is shown to be very close to the Schmidt number K.
Abstract Frequency entangled biphoton sources have played an important role in quantum information. There are two key characteristics which determine the extent of their applications: the spectral indistinguishability and the degree of frequency entanglement. Previously, the spectral indistinguishability of the biphoton state is measured by the Hong–Ou–Mandel (HOM) interference visibility, whereas the degree of frequency entanglement is normally characterized with independent spectral measurements. However, these two quantum features have not been successfully measured with a single experimental setup. In this paper, we deduce the temporal distribution of a short-pulse pumped type-II spontaneous parametric down converted (SPDC) biphoton source and its relevant temporal entanglement parameter R t for operationally quantifying the degree of frequency entanglement. Furthermore, we theoretically and experimentally demonstrate, due to the inherent group delay, the difference between the signal and idler photons at the exit of the type-II nonlinear crystal, resulting in a HOM-shape dip at both sides of the center fringed envelope of the MZ interferometric coincidence diagram. By measuring the HOM-shape dip depth, the separation between the two sideband dips as well as the MZ fringed envelope width, both the spectral indistinguishability and the temporal entanglement parameter can thus be simultaneously quantified. This implementation provides us a unified and convenient method to characterize the frequency entanglement of the short-pulse pumped biphotons.
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.