Two-photon states generated through degenerate spontaneous parametric down-conversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit an enhanced contrast due to the probe two-photon nature. Our findings offer applications for non-interferometric, quantum-enhanced phase imaging.
Two-photon states generated through degenerate spontaneous parametric down-conversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit an enhanced contrast due to the probe two-photon nature. Our findings offer applications for non-interferometric, quantum-enhanced phase imaging.
Two-photon states generated through degenerate spontaneous parametric downconversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit a factor of two contrast enhancement due to the probe’s two-photon nature. Our findings offer a proof of principle application for quantitative phase imaging, particularly in regimes where low light conditions are required to prevent photo-damage and, at the same time, is desirable to preserve high resolution, contrast, and low noise.
The complete measurement of the quantum state of two correlated photons requires reconstructing the amplitude and phase of the biphoton wavefunction. We show how, by means of spatially resolved single photon detection, one can infer the spatial structure of biphotons generated by spontaneous parametric down conversion. In particular, a spatially resolved analysis of the second-order correlations allows us to isolate the moduli of the pump and phase-matching contributions to the two-photon states. When carrying this analysis on different propagation planes, the free-space propagation of pump and phase-matching is observed. This result allows us, in principle, to gain enough information to also reconstruct the phase of the pump and the phase-matching and thus the full biphoton wavefunction. We show this in different examples where the pump is shaped as a superposition of orbital angular momentum modes or as a smooth amplitude with a phase structure with no singularities. The corresponding phase structure is retrieved employing maximum likelihood or genetic algorithms. These findings have potential applications in fast, efficient quantum state characterization that does not require phase locking of the unknown source with a reference biphoton.
In experiments with spontaneous parametric down conversion the near-field plane is usually defined as the output facet of the generating crystal. Experimentally, however, the spatial correlations are accessed via an imaging system and observed in a region around the image of the output facet. We show that the imaged two-photon field has a very rich transverse and longitudinal structure, which is determined by the phase-matching conditions. We observe many intriguing three-dimensional structures that demonstrate the presence of spatial antibunching, an extreme localization of twin photons, and spatial correlations that resemble Bessel beams in propagation. We link these observations with previous results in second harmonic generation and predict the presence of fourth-order phase singularities. Both experiments and theory are presented, yielding further insight into the nature of the two-photon field.
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.
Quantum imaging leverages nonclassical correlations to reveal features that may vanish in conventional event integration [ 1, 2]. While single-photon detectors are well-established, quantum imaging demands complex data acquisition across many thousands of detectors, each generating rich metadata including triggering time, duration, and other properties. Consequently, effective data management, data wrangling, and correlation extraction become critical challenges. In this work, we investigate optimal handling of spatial correlations from a quantum-photonic source (spontaneous parametric down-conversion, SPDC) using an emerging single-photon event-based camera, the TPX3CAM (256×256 array, supported by an intensifier). Utilizing a femtosecond photon-pair source, we comprehensively analyse noise characteristics, including temporal dynamics and spatial distribution, to develop advanced spatio-temporal noise suppression strategies tailored to camera performance. Our primary objectives include real-time isolation and preprocessing of correlative data. Our analysis demonstrates the potential of these real-time correlation detection and noise reduction algorithms to expand quantum imaging capabilities across diverse scientific domains. Potential applications include high-resolution spectroscopy in biology, materials science, and advanced electron microscopy, where these techniques could enable identification of cascaded two-photon processes with atomic-scale precision. Figure 1 shows an excellent example of such a detection in real-space. The ring feature corresponds to the location of the correlated photon-pairs produced from the SPDC process. This is also apparent in figure 2, where we see a strong anti-correlation between the coordinates of the detected photons – corresponding to photon-pairs. <!-- named anchor --> Figure 1: Distribution of SPDC photons on TPX3CAM <!-- named anchor --> Figure 2: Spatial anti-correlation of x-coordinates
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.