Chapter 2 - Spontaneous Parametric Down-Conversion in Nonlinear Layered Structures

Presented during my PhD defense at ICFO - The institute of Photonic Sciences. Barcelona (Spain), March 12 (2010) This talk shows that * The two-photon mode function, for photons generated in SPDC, can be written in a matrix form which is not as computational demanding as other ways to describe the downconverted state. * The internal correlations in the two-photon state can be suppress or enhance by tailoring the SPDC parameters. * The OAM content of the pump is completely transferred to the signal and idler photons, emitted all over a cone. It is only possible to introduce a selection rule that always holds if all possible emission directions are considered.<br>* The SPDC parameters and the detection system determine the portion of the cone that is detected in a noncollinear configuration, and therefore the amount of OAM that can be detected.

In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.

Single-photon source is an essential element in quantum information processing, and extensively used in the proof-in-principle demonstration in quantum physics, quantum imaging, quantum cryptography, etc. Considering the operating temperature and system complexity, it is a favorable option to choose spontaneous parametric down-conversion (SPDC) combined with the enhancement effect of a cavity. When generating significant single-photon source via the cavity-enhanced type-II spontaneous parametric down-conversion method, there appears inevitable birefringence effect which obviously influences the resonance condition. In order to compensate for birefringence effect, different approaches have been used such as introducing compensating crystal, placing a half-wave plate, tuning the temperature of the nonlinear crystal, customized conjoined double-cavity structure, and cluster effect. In this work, two quarter-wave plates, with an angle of 45° between the optical axis and the crystal axis, are placed in the cavity to ensure the double resonance of signal photon and idler photon. In the process, the signal photon and idler photon generated simultaneously have different polarizations perpendicular to each other through the type-II nonlinear crystal. Considering horizontally polarized photon, its polarization is changed into left circular polarization by the first quarter-wave plate and then returns as vertical polarization. After traversing a long optical path, it shifts to right circular polarization through the second quarter-wave plate. When the photon passes through the same quarter-wave plate again, the polarization state is originally converted into horizontal polarization state. Then the photon completes a round-trip. The other photon with vertical polarization experiences the same process. As a result, the signal photon and idler photon travel identical optical path. The general explanation is described by the Jones matrices, with the emphasis on the transformation of the polarizations of photons. This method can effectively compensate for birefringence effect, achieving double resonance by using a relatively simple device under the condition of smaller intra-cavity loss and more flexible for adjustment. The signal (idler) photon has a sub-natural linewidth of &lt;inline-formula&gt;&lt;tex-math id="Z-20230611154134"&gt;\begin{document}$1.01( 1.08 )\;{\rm{MHz}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230422_Z-20230611154134.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230422_Z-20230611154134.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, demonstrating the feasibility of the proposed technique. This introduced compensating method paves the way to the realization of single-photon quantum source applied to the research of single-photon-single-atom quantum information processing, quantum interface and quantum network node with a single cesium atom confined in the strongly coupled cavity quantum electrodynamics system.

In order to fulfill the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of ${\ensuremath{\chi}}^{(2)}$ nonlinearity, additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of nonlinear layered structures shows.

Spontaneous parametric down conversion (SPDC)-based sources of photonic entangled states are usually generated using coherent pump fields. For temporal, spatial, and polarization degree of freedom, the down-converted light entanglement is limited by the coherence of the pump in the same degree of freedom. However, the effect of pump coherence on the entanglement in a different degree of freedom remains largely unexplored. Here we experimentally demonstrate the generation of polarization entanglement from SPDC pumped by a light emitting diode (LED), a spatiotemporally incoherent pump. The two-photon state is found to have a concurrence of 0.562 and purity of 0.647.

In this paper, we demonstrate the generation of high-performance entangled photon-pairs in different degrees of freedom from a single piece of fiber pigtailed periodically poled LiNbO3 (PPLN) waveguide. We utilize cascaded second-order nonlinear optical processes, i.e., second-harmonic generation (SHG) and spontaneous parametric downconversion (SPDC), to generate photon-pairs. Previously, the performance of the photon-pairs is contaminated by Raman noise photons. Here by fiber-integrating the PPLN waveguide with noise-rejecting filters, we obtain a coincidence-to-accidental ratio (CAR) higher than 52,600 with photon-pair generation and detection rate of 52.36 kHz and 3.51 kHz, respectively. Energy-time, frequency-bin, and time-bin entanglement is prepared by coherently superposing correlated two-photon states in these degrees of freedom, respectively. The energy-time entangled two-photon states achieve the maximum value of CHSH-Bell inequality of S = 2.71 ± 0.02 with two-photon interference visibility of 95.74 ± 0.86%. The frequency-bin entangled two-photon states achieve fidelity of 97.56 ± 1.79% with a spatial quantum beating visibility of 96.85 ± 2.46%. The time-bin entangled two-photon states achieve the maximum value of CHSH-Bell inequality of S = 2.60 ± 0.04 and quantum tomographic fidelity of 89.07 ± 4.35%. Our results provide a potential candidate for the quantum light source in quantum photonics.

Robust modeling using non-elliptically contoured multivariate [formula omitted] distributions

A two-photon coincidence experiment of the kind recently proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] has been carried out with signal and idelr photons produced in the process of parametric down-conversion. The coincidence rate registered by the two detectors is found to exhibit a cosine variation with the optical path difference, with periodicity equal to the wavelength.

Aims and

Frequency-angular characteristics of signal and idler photons generated under spontaneous parametric down-conversion are studied in a strongly frequency nondegenerate regime, without paraxial approximation, accounting for possible inherent absorption of idler waves in a nonlinear crystal, classical thermal field fluctuations, and the multimode character of parametric interaction induced by transverse spatial limitation of the pump beam. Spatial limitation is shown to lead to a huge increase in angular divergence of the idler photons generated at terahertz frequencies. General expressions are obtained for the frequency-angular sensitivity function of the nonlinear-optical terahertz wave detector and for power densities of the signal and idler photon fluxes. The absorption-induced difference in the parametric conversion coefficients for the noise and externally incident radiation of the idler frequency is shown to be described by approximately the same loss factor for all active spatial idler modes. Two different parametric contributions of the internal thermal noise to the number of output idler photons were revealed with different dependence on the idler-wave absorption. Expressions for the loss factors, which describe absorption-induced effects in signal and idler channels, are obtained and shown to be turning into one another by changing the sign of the absorption coefficient. Relative contribution of thermal and quantum field fluctuations into the intrinsic radiation of a nonlinear crystal at signal and idler frequencies is analyzed accounting for the crystal absorption properties.

In spontaneous parametric downconversion (SPDC), a pump photon spontaneously splits into signal and idler photons in media with quadratic nonlinearity. This phenomenon is the most widely utilized source of entangled photons with multiple applications in quantum information technology. SPDC on a chip is usually treated as a local process, meaning that signal and idler photons are created in the same position at which the pump photon is destroyed. We reveal that this locality condition can be violated in an array of coupled waveguides. By utilizing higher-order modes of individual waveguides, it is possible to destroy a pump photon in one waveguide and to generate signal and idler photons in other waveguides. This phenomenon of nonlocal photon-pair generation opens new opportunities for the engineering of spatial photon entanglement.

A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also, structures efficiently generated photon pairs showing antibunching and anticoalescence can be obtained. Three reasons for splitting the correlated area in photonic-band-gap structures are revealed: zig-zag movement of photons inside the structure, spatial symmetry, and polarization-dependent properties. Also, spectral splitting can be observed in these structures.

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.

Two-photon entangled states generated by the nonlinear optical process of spontaneous parametric downconversion (SPDC) have found extensive use for testing the basic foundations of quantum theory. At the same time, the area of ultrafast femtosecond optics using conventional lasers has blossomed. We have carried out a set of experimental and theoretical studies at the crossroads of these two fields. The pulsed light is generated by a tunable Ti:sapphire femtosecond laser. After conversion to second harmonic, the pulses are directed towards the downconversion nonlinear crystal. A two-photon quantum state is generated by means of type-II SPDC in a collinear configuration. We have experimentally demonstrated that the quantum interference of a twin pair generated in the nonlinear crystal degrades significantly as the duration of the femtosecond pump pulse becomes shorter than the coherence time of the signal and idler photons. In this domain the spectrum of the pump pulse is wider than the spectral widths of the signal and the idler photons, which are defined by the natural phase matching in nonlinear parametric processes. The pulsed pump introduces a knowledge in principle of the creation time of the photon pair. This additional information destroys the quantum interference. We have developed a different (noninvasive in terms of total number of photons) approach to restoring the quantum interference of entangled photons with femtosecond pulses, based on the indistinguishability of quantum amplitudes that lead to a final event. We compare and contrast these approaches. We discuss implications of our results in the areas of multiple-particle quantum interferometry and practical two-photon cryptography.

The article is devoted to the poorly studied problem of the formation of talent in the conditions of different degrees of freedom in activity and the impact on that formation of a person’s conservative and innovative semantic attitudes towards the introduction of new equipment. The main objective of the study is to describe how the conditions of different degrees of freedom in the activity are refracted with internal conditions, which are conservative and innovative semantic attitudes and various talent structures. The study was conducted on a sample of 54 qualified railway drivers using a specialized simulator which allows to simulate three degrees of freedom in the activity. The psychological analysis of the activity revealed seven abilities ensuring the implementation of the activity. Based on empirical data, the article shows that low, medium and high degrees of freedom in activity are manifested in different degrees of productivity. Conservative and innovative semantic attitudes to the introduction of new equipment do not have a significant effect on the productivity of the activity in the conditions of different degrees of freedom. Along with this, depending on the conservative and innovative semantic attitudes, different structures of talent in terms of composition and degree of integration under the conditions of different degrees of freedom in the activity are formed. On the one hand, conservative and innovative semantic attitudes act as internal determinants; on the other hand, low, medium and high degrees of freedom in the activity act as external determinants of the formation of various talent structures.