High-dimensional spatial entanglement of photons is versatile yet difficult to harness. We demonstrate an efficient direct measurement of the OAM spectrum of an SPDC source using the stimulated parametric down-conversion in the low-gain regime.
Recent progress in the study of the non-classical macroscopic state of light sheds light on the characterization of high-gain spontaneous parametric down-conversion (SPDC). However, the theory of high-dimensional entangled photon pairs with SPDC in this high-gain regime is far from being complete. Here, we present a numerical study of the effect of the phase-matching function on the OAM entanglement in high-gain SPDC. We use a recently developed classical model of high-gain SPDC to compute the OAM spectrum of the entangled photon pair and examine how the OAM entanglement depends on various physical parameters determining the phase-matching function. Our study offers guidelines for quantum state engineering with bright sources of photon pairs entangled in high-dimensional OAM spaces.
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
High-dimensional spatially entangled two-photon state generated by spontaneous parametric down-conversion process (SPDC) has become a promising resource for several quantum information science applications. For harnessing high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is because for radial coordinates, there is neither a Schmidt-decomposed form for the SPDC photons nor is there a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that the azimuthal averaging of SPDC two-photon state yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of radial Schmidt spectrum of upto 50 radial Schmidt modes with about 98\% fidelity.
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.