Enhancing Purity of Single Photons in Parametric Down-Conversion through Simultaneous Pump Beam and Crystal Domain Engineering

Spontaneous parametric down-conversion (SPDC) has shown great promise in the generation of pure and indistinguishable single photons. Photon pairs produced in bulk crystals are highly correlated in terms of transverse space and frequency. These correlations limit the indistinguishability of photons and result in inefficient photon sources. Domain-engineered crystals with a Gaussian nonlinear response have been explored to minimize spectral correlations. Here, we study the impact of such domain engineering on spatial correlations of generated photons. We show that crystals with a Gaussian nonlinear response reduce the spatial correlations between photons. However, the Gaussian nonlinear response is not sufficient to fully eliminate the spatial correlations. Therefore, the development of a comprehensive method to minimize these correlations remains an open challenge. Our solution to this problem involves simultaneous engineering of the pump beam and crystal. We achieve purity of single-photon state up to 99 \% without any spatial filtering. Our findings provide valuable insights into the spatial waveform generated in structured SPDC crystals, with implications for applications such as Boson Sampling

Spatial and temporal characteristics of spontaneous parametric down-conversion with varying focal planes of interacting beams

Spontaneous parametric down-conversion (SPDC) is a widely used process to prepare entangled photon pairs. In SPDC, a second-order nonlinear crystal is pumped by a coherent laser beam to generate photon pairs. The photon pairs are usually detected by single-mode fibers (SMF), where only photons in a Gaussian mode can be collected. The collection modes possess typical Gaussian parameters, namely a beam waist and a focal plane position. The collection efficiency of photons highly depends on the choice of both parameters. The exact focal plane position of the pump beam relative to those of the detection modes is difficult to determine in a real experiment. Usually, theoretical and experimental studies assume that the focal plane positions of the pump and the generated beams are positioned in the center of the crystal. The displacement of beam focal planes can lead to deviations from expected results and the coupling efficiency into SMF can increase or decrease. In this work, we consider variable positions of focal planes and investigate how shifts of these focal planes influence the spatial and temporal properties of photon pairs. We present SPDC arrangements, in which the knowledge of the exact position of the focal planes is essential, as well as scenarios, where focal plane displacements do not contribute significantly to experimental outcomes. These findings are of particular interest for achieving higher efficiency in SPDC experiments.Comment: 10 pages, 5 figure

Generalized description of the spatio-temporal biphoton State in spontaneous parametric down-conversion

Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the non-separability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing

Spatio-spectral engineering of entangled and single photons in parametric down-conversion

Photon pairs generated through SPDC inherently exhibit spatio-spectral coupling, which implies that photons with different spatial DOFs possess varying spectra. While quantum optics applications often focus on either spatial or spectral DOFs independently, the correlation between them poses a fundamental challenge in protocols involving entangled photon sources or single-mode photon states. Theoretical studies on SPDC, that address both space and spectrum together, are mostly limited to approximate wave functions of photon pairs or involve numerical computations. Such theoretical studies usually consider either monochromatic signal and idler photons (the narrowband approximation), loosely focused pump and collection beams (the plane wave approximation), or infinitesimally thin crystals (the thin crystal approximation). This dissertation aims to bridge the gap between the fundamental theory of SPDC and its practical applications. In particular, we have developed a comprehensive theory that does not rely on a specific pump beam or nonlinear crystal and goes beyond the common narrowband, plane wave, and thin crystal approximations. The developed approach accurately describes the inseparability of spatial and spectral DOF and applies to a wide range of experimental setups. Furthermore, we show that the origin of the spatio-spectral coupling is closely related to the Gouy phase of the interacting beams. We utilize the developed theory, taking into account the spatio-spectral coupling insights, to control the entanglement of photon pairs from SPDC. As an application, we shape the spatial distribution of the pump beam to design an efficient source of high-dimensional entangled states in the spatial DOF. In our second application, we tailor simultaneously the effective nonlinearity of the crystal and spatial distribution of the pump, to engineer single-mode photons