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arXiv:2205.09338 · Physical Review A

Reconstructing the full modal structure of photonic states by stimulated-emission tomography in the low-gain regime

Arne Keller, Antonio Zelaquett Khoury, Nicolas Fabre, Maria I. Amanti, F. Baboux, S. Ducci, P. Milman

Published Dec 14, 2022• 2 citations
arXivHTMLPDF

Abstract

Stimulated emission tomography (SET) is a powerful and successful technique to both improve the resolution and experimentally simplify the task of determining the modal properties of biphotons. In the present paper we provide a theoretical description of SET valid for any quadratic coupling regime between a nonlinear medium and pump fields generating photons by pairs in the low-gain regime. We use our results to obtain not only information about the associated modal function modulus but also its phase, for any mode, and we discuss the specific case of time-frequency variables as well as the quantities and limitations involved in the measurement resolution.

DOI
10.1103/physreva.106.063709

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Stimulated emission tomography (SET) is a powerful and successful technique to both improve the resolution and experimentally simplify the task of determining the modal properties of biphotons. In the present paper we provide a theoretical description of SET valid for any quadratic coupling regime between a nonlinear medium and pump fields generating photons by pairs in the low-gain regime. We use our results to obtain not only information about the associated modal function modulus but also its phase, for any mode, and we discuss the specific case of time-frequency variables as well as the quantities and limitations involved in the measurement resolution.
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.
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
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.
Stimulated Emission Tomography (SET) is a technique which maps the Joint Spectral Amplitude (JSA) of photon pairs with extremely high signal to noise ratio and low integration times. While the modulus of the JSA is easy to access, the retrieval of the Joint Spectral Phase (JSP) is far more challenging and requires advanced interferometric techniques. Here we present and validate a scheme to measure the complex JSA by using a reconfigurable silicon chip. In particular, we map the rich structure of the JSP of a silicon microresonator.