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.
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.
Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of electric field quadratures are squeezed below the shot-noise level. The high-gain PDC could be used not only in the same applications as SPDC, it also can provide new ones. Apart from that the high-gain PDC has many remarkable spectral and statistical properties, which are in the focus of this work. The description starts from the PDC generation in normal and anomalous group velocity dispersion ranges. The spectrum and mode content of high-gain PDC is considered as well as their change with the parametric gain are demonstrated. Then, there are the interference effects emerging from the PDC correlations presented, namely the macroscopic analogue of the Hong-Ou-Mandel interference. In addition, it is shown how spatial and temporal walk-off matching could be used for the generation of giant narrowband twin beams. Finally, the statistical properties of high-gain PDC are reviewed as well as their use for multiphoton effects is demonstrated. Photon-number fluctuations of PDC are studied via normalized correlation functions and probability distributions. These fluctuations enhance the generation efficiency for multiphoton effects by orders of magnitude and lead to tremendously fluctuating light described by heavy-tailed photon-number probability distributions.
The generation of entangled photon pairs through spontaneous parametric down conversion (SPDC) is widely used and considered one of the key entanglement generation techniques in quantum optics. The quality of the entanglement produced depends significantly on the physical properties of the nonlinear crystal employed in the SPDC process. In this study, we investigate the influence of the crystal parameters such as phase matching configurations on the degree of entanglement. Our results demonstrate the importance of crystal selection for achieving highly entangled photon sources, which are essential for applications in quantum communication and quantum information.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
Summary form only given. Spontaneous parametric down-conversion (SPDC), one of the most important nonlinear processes, is of paramount interest especially in the field of quantum optics due to its intrinsic capability in generating entangled photon pairs in different degree of freedoms (DoFs). The spatial distribution of the paired photons generated through SPDC process are highly influenced by different crystal parameters including birefringence and length, and the spatial structure of the pump beam [1]. Recent studies have shown the transfer of pump properties such as phase profile and doughnut intensity distribution [2] into the transverse amplitude of heralded single photon. Here we report, first time to best of our knowledge, the direct transfer of the non-separable state in OAM and polarization DoFs of classical pump beam to generate two photons state with hybrid entanglement in both OAM and polarization. Using same scheme one can produce macroscopic entanglement with very high quanta of OAM.
Spontaneous parametric down-conversion (SPDC) is one of the most important sources of entangled photons in quantum optics and underpins a wide range of applications in quantum communication, quantum imaging, quantum sensing, and photonic quantum information processing. In this nonlinear optical process, a pump photon is converted into a pair of lower-energy photons that exhibit strong correlations in multiple degrees of freedom. While the generation of photon pairs is governed by energy and momentum conservation, the resulting biphoton state possesses a rich spatial structure whose properties are determined by the interplay among the pump field, the nonlinear medium, and subsequent propagation. This thesis investigates the spatial properties of entangled photon pairs generated through SPDC, focusing on the evolution of their correlations in the near field and on the behavior of orbital-angular-momentum (OAM) entangled states under tight focusing conditions. A common theme throughout this work is the examination of physical effects that emerge when the full biphoton wavefunction is retained rather than reduced through the simplifying approximations often employed in theoretical treatments. The principal contribution of this thesis concerns the near-field propagation of SPDC photon pairs. The spatial correlations of SPDC-generated photons are commonly analyzed within the thin-crystal approximation, where the biphoton wavefunction is assumed to factorize into independent functions of the sum and difference coordinates. We demonstrate that birefringence-induced transverse walk-off breaks this factorization and introduces an intrinsic coupling between these coordinates. More importantly, this coupling survives free-space propagation and remains observable even for crystals that nominally satisfy the thin-crystal condition. As a result, the joint spatial correlations develop a characteristic tapering near the crystal image plane that cannot be captured by conventional factorized models. Numerical simulations and experimental measurements are found to be in excellent agreement, revealing a previously overlooked feature of SPDC and providing a more complete description of photon-pair generation and propagation in birefringent nonlinear media. The second part of the thesis explores the propagation of OAM-entangled photon pairs beyond the paraxial regime. While OAM correlations are typically studied under weak-focusing conditions, many emerging quantum technologies require structured quantum states to be manipulated in highly confined optical systems. We show that tight focusing modifies the OAM correlation spectrum, leading to a broadening of the accessible mode distribution. This broadening exhibits distinct transverse and longitudinal characteristics and arises from the emergence of nonparaxial field components absent in conventional scalar descriptions. These results provide new insight into the behavior of structured quantum light in strongly focused optical fields and establish a framework for understanding OAM entanglement beyond the paraxial approximation. Together, the results presented in this thesis reveal previously unexplored aspects of the structure and propagation of entangled photon pairs. By moving beyond widely used approximations, this work uncovers physical effects that influence the generation, evolution, and measurement of spatially entangled states, with implications for quantum imaging, high-dimensional quantum communication, and the broader development of structured-light-based quantum technologies.
Orbital angular momentum (OAM)-entangled states produced by spontaneous parametric down-conversion (SPDC) are considered ideal for realizing high-dimensional entangled states, which have several advantages for quantum technologies. However, the limited sensitivity of current two-photon OAM detectors is a major roadblock not only for realizing such technologies but also for resolving foundational questions, such as OAM conservation in SPDC. The current theoretical understanding is that OAM is not conserved in Type-II SPDC but is conserved in Type-I. Experimentally, although non-conservation in TypeII has not been demonstrated, conservation in Type-I has been reported frequently and has become an underlying assumption for techniques generating high-dimensional OAM entangled states. In this work, we experimentally demonstrate a high-sensitivity two-photon OAM detector, using which, contrary to the current understanding, we report non-conservation of OAM in Type-I SPDC. We attribute this to a spatial walk-off effect and prove it using a framework free of standard phase-matching approximations.