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Optica

Characterizing an entangled-photon source with classical detectors and measurements

Lee A. Rozema, Chao Wang, Dylan H. Mahler, Alex Hayat, Aephraim M. Steinberg, John E. Sipe, Marco Liscidini

Published Apr 27, 2015• 49 citations
Publisher

Abstract

Entangled-photon pairs are essential for many applications in quantum computation and communication, and quantum state tomography (QST) is the universal tool to characterize such entangled-photon sources. In QST, very low-power signals must be measured with single-photon detectors and coincidence logic. Here, we experimentally implement a new protocol, “stimulated-emission tomography” (SET), allowing us to obtain the information provided by QST when the photon pairs are generated by parametric fluorescence. This approach exploits a stimulated process that results in a signal several orders of magnitude larger than in QST. In particular, we characterize the polarization state of photons that would be generated in spontaneous parametric downconversion using SET. We find that SET accurately predicts the purity and concurrence of the spontaneously generated photons in agreement with the results of QST. We expect that SET will be extremely useful to characterize entanglement sources based on parametric fluorescence, providing a fast and efficient technique to potentially replace or supplement QST.

DOI
10.1364/optica.2.000430

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Entangled-photon pairs are essential for many applications in quantum computation and communication, and quantum state tomography (QST) is the universal tool to characterize such entangled-photon sources. In QST, very low-power signals must be measured with single-photon detectors and coincidence logic. Here, we experimentally implement a new protocol, “stimulated-emission tomography” (SET), allowing us to obtain the information provided by QST when the photon pairs are generated by parametric fluorescence. This approach exploits a stimulated process that results in a signal several orders of magnitude larger than in QST. In particular, we characterize the polarization state of photons that would be generated in spontaneous parametric downconversion using SET. We find that SET accurately predicts the purity and concurrence of the spontaneously generated photons in agreement with the results of QST. We expect that SET will be extremely useful to characterize entanglement sources based on parametric fluorescence, providing a fast and efficient technique to potentially replace or supplement QST.
Entangled-photon pairs are essential for many applications in quantum computation and communication, and quantum state tomography (QST) is the universal tool to characterize such entangled-photon sources. In QST, very low-power signals must be measured with single-photon detectors and coincidence logic. Here, we experimentally implement a new protocol, “stimulated-emission tomography” (SET), allowing us to obtain the information provided by QST when the photon pairs are generated by parametric fluorescence. This approach exploits a stimulated process that results in a signal several orders of magnitude larger than in QST. In particular, we characterize the polarization state of photons that would be generated in spontaneous parametric downconversion using SET. We find that SET accurately predicts the purity and concurrence of the spontaneously generated photons in agreement with the results of QST. We expect that SET will be extremely useful to characterize entanglement sources based on parametric fluorescence, providing a fast and efficient technique to potentially replace or supplement QST.
We identify a relation between the number of photon pairs generated by parametric fluorescence, through either spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, and the number generated by the corresponding stimulated process, respectively, either difference-frequency generation or stimulated four-wave mixing. On the basis of this very general result, we show that the characterization of SPDC sources of two-photon states in a given system can be performed solely by studying stimulated emission. We call this technique stimulated emission tomography (SET). We show that the number of photons detected in SET can be 9 orders of magnitude larger than the average number of coincidence counts in two-photon quantum state tomography. These results open the way to the study of sources of quantum-correlated photon pairs with unprecedented precision and unparalleled resolution.
We perform a multidimensional characterization of a polarization-entangled photon-pair source using stimulated emission tomography (SET). We measure the frequency-resolved polarization density matrix, which is composed of thousands of individual polarization density matrices, each corresponding to a different frequency pair. The measurement exhibits detailed information about correlations that would be difficult to observe using traditional quantum state tomography. This demonstration exhibits the power of SET to characterize a source of quantum states with multi-dimensional correlations and hyper-entanglement. The SET technique can be applied to a variety of photon-pair-based sources for the optimization and engineering of quantum states.
In this work, we demonstrate the use of stimulated emission tomography to characterize a hyperentangled state generated by spontaneous parametric downconversion in a cw-pumped source. In particular, we consider the generation of hyperentangled states consisting of photon pairs entangled in polarization and path. These results extend the capability of stimulated emission tomography beyond the polarization degree of freedom and demonstrate the use of this technique to study states in higher dimension Hilbert spaces.
Frequency nondegenerate entangled photon pairs have been employed in quantum communication, imaging, and sensing. To characterize quantum entangled states with long-wavelength [infrared (IR) or even terahertz (THz)] photons, one needs to either develop the single-photon detectors at the corresponding wavelengths or use a novel tomography technique that does not rely on single-photon detections, such as stimulated emission tomography (SET). We use standard quantum state tomography and SET to measure the density matrix of entangled photon pairs, with one photon at 1550 nm and the other one at 810 nm, and obtain highly consistent results, showing the reliability of SET. Our work paves the way for efficient measurement of entangled photons with highly dissimilar frequencies, even to the frequencies where single-photon detections are not available.
Stimulated-emission tomography (SET) is an excellent tool for characterizing the process of spontaneous parametric down conversion (SPDC), which is commonly used to create pairs of entangled photons for use in quantum information protocols. The use of stimulated emission increases the average number of detected photons by several orders of magnitude compared to the spontaneous process. In a SET measurement, the parametric down conversion is seeded by an intense signal field prepared with specified mode properties rather than by broadband multimodal vacuum fluctuations, as is the case for the spontaneous process. The SET process generates an intense idler field in a mode that is the complex conjugate to the signal mode. In this work we use SET to estimate the joint spatial mode distribution (JSMD) in the Laguerre-Gaussian (LG) basis of the two photons of an entangled photon pair. The pair is produced by parametric down conversion in a beta barium borate (BBO) crystal with type-II phase matching pumped at a wavelength of 405 nm along with a 780 nm seed signal beam prepared in a variety of LG modes to generate an 842 nm idler beam of which the spatial mode distribution is measured. We observe strong idler production and good agreement with the theoretical prediction of its spatial mode distribution. Our experimental procedure should enable the efficient determination of the photon-pair wavefunctions produced by low-brightness SPDC sources and the characterization of high-dimensional entangled-photon pairs. Published by the American Physical Society 2024