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The single-channel Jost function is calculatedwith the computational R-matrix on a Lagrange-Jacobi mesh,in order to study its behaviour at complex wavenumbers.Three potentials derived from supersymmetric transforma-tions, two of which never previously studied, are used to testthe accuracy of the method. Each of these potentials, withs-wave or p-wave bound, resonance or virtual states, has asimple analytical expression for the Jost function, which iscompared with the calculated Jost function. Siegert statesand Siegert pseudostates are determined by finding the zerosof the calculated Jost function. Poles of the exact Jost func-tion are not present in the calculated Jost function due to thetruncation of the potential in the R-matrix method. Instead,Siegert pseudostates arise in the vicinity of the missing poles., SCOPUS: ar.j, info:eu-repo/semantics/published

Eye cancer encompasses a group of rare malignant tumors that greatly impact the quality oflife of affected patients. Late detection and management at an advanced stage are the leadingcauses of this impact, as eye cancer cells often silently proliferate for years before exhibitingsymptoms. Ion therapy represents a less aggressive alternative to other treatment methodsfor eye cancer, offering a higher chance of preserving both the affected eye and the patient’svision. One key aspect of ion therapy facilities dedicated to eye cancer treatment is their abilityto deliver the total dose of an individual session in an extremely short time, minimizing thepatient’s gazing time. Nevertheless, in most of these facilities, the beam experiences significantlosses during its production and transport to the treatment room, due to the substantial energydegradation required to achieve clinical ranges appropriate for treating ocular tumors. Forthis reason, satisfying the dose rate constraint while simultaneously fulfilling all the clinicalrequirements imposed on the dose deposition profiles poses a considerable challenge. Thegeneral objective of this thesis is to evaluate numerically and enhance the clinical propertiesachieved when treating ocular tumors using proton therapy facilities. In the first part of thework, we start by developing a numerical model of the passive scattering eye treatment beamlineof the proton therapy company Ion Beam Applications (IBA). Using this model, we conductedsimulations to assess its clinical properties, which were validated against experimental datafrom the Westdeutsches Protonentherapiezentrum Essen (WPE) proton therapy center in Essen.Based on this validation, we proposed modifications to the nozzle design, increasing the doserate by up to a factor of 3. Additionally, we explored the feasibility of reducing the dose outsidethe irradiation field through the use of an additional collimator adequately inserted inside ofthe nozzle. In the second part of, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

La non-classicalité d'un état monomode de la lumière et l'intrication d'états photoniques bipartites sont des phénomènes quantiques centraux composant deux des différences les plus essentielles entre les domaines classique et quantique. Depuis leur découverte, ces propriétés ont suscité un intérêt considérable et constant de la part de la communauté des physiciens, dans le but de développer des protocoles basés sur ces phénomènes et qui n'ont pas d'équivalent classique. Pour prendre un seul exemple, l'intrication de deux photons peut être utilisée comme ressource pour effectuer de la cryptographie quantique, c'est-à-dire pour distribuer une clé secrète de manière sécurisée entre deux parties qui n'ont même pas besoin de faire confiance à leurs dispositifs quantiques. Afin d'exploiter ces propriétés et de développer des sources optiques d'états non-classiques ou intriqués, il est crucial de pouvoir détecter si l'état émis par la source est effectivement non-classique ou intriqué. Dans cette optique, de nombreux témoins (conditions suffisantes) de non-classicalité ou d'intrication ont été conçus au fil des années.Dans cette thèse, nous nous intéressons particulièrement à une hiérarchie de critères qui a été développée par Shchukin, Richter et Vogel au début des années 2000. Le témoin le plus courant de l'intrication est le critère PPT de "positive partial transpose", qui stipule que tout état séparable doit rester physique après avoir subi une transposition partielle. Si cette condition n'est pas remplie, cela signifie que l'état est intriqué. Sur cette base, un ensemble complet de critères a été exprimé par ces auteurs à partir d'une matrice de moments des opérateurs de mode (création et annihilation). De même, un ensemble de critères a été construit sur la base d'une matrice de moments dans l'ordre normal afin d'exprimer la non-négativité de la fonction P de Glauber, donnant lieu à une hiérarchie de témoins de non-classicalité.La principale difficulté dans la détect, The so-called nonclassicality of a single-mode state of light and the entanglement of bipartite photonic states are central quantum phenomena which underlie two of the most essential differences between the classical and the quantum. Since their discovery, these properties have attracted a tremendous, constant interest from the quantum physics community, with the goal of developing protocols that take advantage of them and have no classical counterpart. To take a single example, the entanglement of two photons can be used as a resource to perform quantum cryptography in a device-independent manner, that is, to distribute a secret key in a secure way between two parties who do not even need to trust their quantum devices. In order to exploit these properties and develop optical sources of nonclassical or entangled states, it is crucial to be able to detect whether the state emitted by the source is effectively nonclassical or entangled. Along this way, numerous witnesses (sufficient conditions) for nonclassicality or entanglement have been conceived over the years.In this thesis, we are especially interested in a hierarchy of criteria that has been developed by Shchukin, Richter, and Vogel in the early 2000s. The most common witness of entanglement is the PPT criterion for "positive partial transpose'', which states that any separable state must remain physical after undergoing a partial transpose. If this condition is not met, it means that the state is entangled. Based on this, a complete set of criteria was expressed by these authors based on a matrix of moments of the mode (creation and annihilation) operators. Similarly, a set of criteria was built based on a matrix of normally-ordered moments in order to express the non-negativity of the Glauber-Sudarshan P-function, giving rise to a hierarchy of nonclassicality witnesses.The main difficulty in the practical detection of nonclassicality or entanglement is the measurement of the quantities that are needed to app, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

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The main purpose of this thesis is to investigate the physics of particle detectors from first principles combining quantum mechanics and statistical physics. In particular, this work aims at studying the Mott problem, that is the issue of the appearance, within the framework of quantum mechanics, of linear tracks in Wilson cloud chambers due to the passage of ionizing particles. Although the Mott problem is closely related to the quantum measurement problem, this thesis focuses on the phenomenological questions regarding the propagation of a quantum particle in a detector rather than the question of the interpretation of quantum mechanics. To this end, models of a quantum particle evolving in a gaseous environment are developed. In the first considered model, called the random Lorentz gas, the constituents of the medium are assumed to be point-like and fixed at random positions. The Schrödinger equation can thus be solved systematically using the Foldy-Lax method. This model is first studied with the tools of scattering theory, namely the cross section and the complex resonance spectrum. An efficient numerical method is devised to compute the density of resonances in the complex plane of the wavenumber, without having to find them one by one. This method leads to hitherto unknown structures in the resonance spectrum. These structures are then explained by resorting to wave transport theory, which includes an effective Schrödinger equation at large wavelength, and an integral transport equation at small wavelength. The phase averaging effect is especially highlighted in the latter case. This effect is the cancellation of most of the off-diagonal elements of the density matrix after the average over the random configurations of the scatterers. The second considered model is more comprehensive, as it accounts for the quantum nature of the gaseous environment. The density matrix of the full system is governed by the quantum Liouville equation. Since the gas is in a the, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point scatterers is derived in detail and expressed in terms of the scattering length. The fundamental properties of the model, such as the cross section and the scattering matrix, are calculated. In addition, the model is shown to verify the optical theorem and thus probability conservation. Finally, the differential and total cross sections are numerically computed in two situations whether the Lorentz gas is smaller or larger than the mean free path. A distinct Airy diffraction peak is obtained for a large enough number of scatterers. This observation is related to the extinction paradox., SCOPUS: ar.j, info:eu-repo/semantics/published

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wave number without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a nonresonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case., SCOPUS: ar.j, info:eu-repo/semantics/published

In the mid-eighties, the development of radioactive-ion beams enabled the exploration ofregions of the nuclear landscape away from the valley of stability. Close to the neutrondripline, in the light neutron-rich region, halo nuclei were observed. These nuclei exhibit asurprisingly large matter radius and a strongly clusterized structure. These two featurescan be explained by the weak binding of one or two neutrons which allows them to tunnelfar from the rest of the nucleons, surrounding the nucleus by a diffuse halo. These nuclearstructures have challenged the usual description of the nucleus, described as a compactmany-body object with nucleons piling up into well defined orbitals. Because they areshort-lived, these nuclei are often studied through reaction processes, such as elasticscattering, breakup and knockout. To infer precise information from the experimentaldata, an accurate reaction model coupled with a realistic description of the nucleus isneeded.Compared to other state-of-the-art methods, the eikonal approximation is very cheapfrom a computational viewpoint. This model assumes that the projectile-target relativemotion does not differ much from the initial plane wave. It also makes the adiabaticapproximation, which sees the internal coordinates of the projectile as frozen during thecollision. These two assumptions hold for reactions occurring at high energy, i.e. above60 MeV/nucleon, in which the deflection of the projectile by the target is small and thecollision time is brief.In this thesis, I focus on improvements of the eikonal approximation. First, I studythe extension of the validity of the eikonal model down to 10 MeV/nucleon, in the energyrange of the facilities HIE-ISOLDE at CERN and ReA12 at the upcoming FRIB. To thisend, I analyse different corrections to the eikonal approximation, which account for thedeflection of the projectile by the target. I assess their accuracy for the elastic-scatteringand breakup observables of one-neutron halo nucle, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

One-nucleon halo nuclei are exotic nuclei which can be seen as a core around which orbits a loosely-bound valence nucleon. They are usually studied through reactions such as elastic scattering and breakup. The ratio method has been developed as a tool to study one-neutron halo nuclei at high energies. It consists of the ratio of angular cross sections, breakup and elastic scattering, which removes most of the sensitivity to the reaction mechanism and to the reaction model. In the simple recoil excitation and breakup (REB) model, the ratio simplifies to a form factor dependent solely on the wave function of the projectile. By measuring this observable and comparing it to the REB form factor, i.e. in the ratio method, more detailed information on the structure of the halo could be obtained. For neutron-halo nuclei at high energy, the ratio observable obtained from accurate CDCC and DEA theoretical calculations follows its REB prediction. I study the extension of this method to lower energies of the reaction which could make the measurement appropriate to facilities such as SPIRAL2 (GANIL, Caen, France) and ReA12 at FRIB (Michigan State University) and to proton halos. This is done by comparing the REB form factor to dynamical calculations of the ratio. The reactions investigated are the reaction of 11Be, the archetypical one-neutron halo nucleus, on 12C, 40Ca and 208Pb targets at 20 MeV/nucleon and of 8B, the archetypical one-proton halo nucleus, on 12C, 58Ni and 208Pb targets at44 MeV/nucleon.For these reactions, the adiabatic assumption is no longer valid due to the effect of the Coulomb interaction. This effect is mainly visible at forward angle for 11Be and is aggravated for 8B by the fact that the halo is charged. The ratio works less well than for neutron-halos at intermediate and high energies. Nevertheless, the ratio is shown to be very sensitive to the orbital angular momentum l0 in which the halo is bound and its binding energy E0, i.e. the single-particle s, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The interaction of a quantum particle with a gaseous detector is studied in the quantum-mechanical state space of the particle-detector system by means of a simple stationary scattering 3D model. The particle is assumed to interact with N two-level point-like scatterers depicting the atoms of the detector. Due to the contact interaction, the particle scatters off the atoms in isotropic spherical waves. Remarkably, the Lippmann–Schwinger equation of this multiple scattering problem can be exactly solved in a nonperturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors. It is shown that the differential cross-section of excitation must be large enough in the forward direction to get the formation of tracks. In addition, the relatively small influence of atomic positions is highlighted. These results are explained through a perturbative calculation., SCOPUS: ar.j, info:eu-repo/semantics/published

In modern nuclear physics, a special group of nuclei located close to the drip line named halo nuclei has received tremendous attention due to their unique cluster structure. These nuclei exhibit large matter radii and are qualitatively described as a compact core surrounded by a diffuse halo which is formed by the loosely-bound valence nucleon(s). Their existence breaks down the consistent predictions by the classical shell model and challenges nuclear-structure calculations. To understand this exotic feature from first principles, lots of efforts have been undertaken by nuclear physicists during the past decades. One of the most successful probes to look into these questions is the (d,p) transfer which has been proved to be a very powerful tool to extract single-particle properties of nuclei and hence is ideal to study one-neutron halo nuclei., The main topic of this work is to improve the reliability of the nuclear-structure observables extracted from transfer reactions. In one of our works [Phys. Rev. C 98, 054602 (2018)], the experiment done by Schmitt et al. on the $^{10}$Be(d,p)$^{11}$Be transfer reaction at four beam energies [Phys. Rev. Lett. 108, 192701 (2012)] is reanalyzed. In order to probe only the halo of the nucleus which is represented by the asymptotic normalization coefficient (ANC), the beam energy and angular ranges at which such reaction is strictly peripheral have to be determined. These peripheral conditions are systematically identified by coupling a Halo effective field theory (EFT) description of the $^{11}$Be nucleus at leading order (LO) with the adiabatic distorted wave approximation (ADWA) to model the transfer. The results suggest that focussing on the transfer data collected with low beam energies and at forward scattering angles ensures the peripherality of the reaction and hence is the best way to reliably extract the ANC. The resulting values of ANC are (0.785 ± 0.030) fm$^{-1/2}$ for the ground state and (0.135 ± 0.005) fm$^{-1/2}$ for the first excited state. These values are in excellent agreement with the values predicted by ab initio calculations (0.786 fm$^{-1/2}$ for the ground state and 0.129 fm$^{-1/2}$ for the excited state) [Phys. Rev. Lett. 117, 242501 (2016)]. An alternative way to explore the sensitivity of transfer calculations to the short-range physics of the $^{10}$Be-n wave function using Halo EFT is offered by the supersymmetry (SuSy) method. With this method, the SuSy partner of the original wave function can be generated which shares the same asymptotic behavior but exhibits a very different internal part. Feeding those wave functions into the transfer calculations, the results confirm the above findings with respect to the peripherality of the $^{10}$Be(d,p) transfer., This method has then been extended to study another one-neutron halo nucleus: $^{15}$C which is important in nuclear astrophysics. Its ANC is extracted from the cross sections of the $^{14}$C(d,p) transfer measured by Mukhamedzhanov et al. [Phys. Rev. C, 84, 024616 (2011)]. The values obtained are (1.26 ± 0.02) fm$^{-1/2}$ and (0.056 ± 0.001) fm$^{-1/2}$ for the ground state and first excited state of $^{15}$C, respectively. Especially for the ground state case, again, a perfect agreement is reached between our result and the one predicted by Navrátil et al. (C$_{1/2+}$ = 1.282 fm$^{-1/2}$) in an ab initio calculation. Relying on the inferred ANC value, it enables us to fit an effective $^{14}$C-n interaction at NLO in Halo EFT, which has been used later in other reaction calculations, such as Coulomb breakup and radiative capture [Phys. Rev. C 100, 044615 (2019)]. We have also looked at the extension of this idea to resonant states. After an analogous analysis using a bin description, it is figured out that the resonant width plays a key role in determining the magnitude of the cross sections for such transfers. Its effect on resonance can be comparable to that of the ANC on bound states. But the associated uncertainty is larger than that in the case of bound state., In collaboration with Prof. Obertelli, we have studied the potential use of sub-Coulomb (d,p) transfer to investigate the possible presence of a halo structure in the excitation spectrum of medium to heavy nuclei. Based on the hypothetical case of $^{95}$Sr, the dependencies of the transfer calculation on several crucial parameters including Q-value, nuclear spin and beam energy have been tested to understand better how the halo feature could be revealed by measuring transfer cross sections. The feasibility of this idea requires an accurate theoretical prediction and sensitive detection systems., On the experimental side, efforts have been made to progress in the data analysis of the IS561A experiment on $^{9}$Li(d,p) transfer performed at HIE-ISOLDE, CERN. Thanks to the preprocessing of the acquired data done by Jesper Halkjær Jensen (Aarhus), the necessary information on the elastic scattering channel ($^{9}$Li + d) has been successfully collected and matches well with our theoretical calculation. Due to some practical problems happening during the measurement which would propagate to the analysis and result in a low statistics, the extraction of the (d,p) channel will require further detailed analyses. To make up for this, the available data measured by Jeppesen et al. [Phys. Lett. B, 642(5): 449 – 454, 2006] and Cavallaro et al. [Phys. Rev. Lett. 118, 012701 (2017)] are taken into account to check in those cases the validity of the chosen model which has already been used to study the resonance of $^{11}$Be. The outcome suggests that the method we use is a fast and efficient option to simulate the resonance during the transfer. For the non-resonant part, choosing the prior form of the transition matrix instead of the post one is better suited., Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The evolution of a quantum particle in a gaseous detector governed by the Schrödinger equation is studied by means of a simplified 3D model. The particle is assumed to interact with N excitable two-level point-like scatterers depicting the atoms. In this model, the energy loss experienced by the particle after atomic excitations is accounted for. Using the Green function method, the full wave function is uniquely determined by N times 2 to the power N complex numbers. Remarkably, the Lippmann-Schwinger equation of this multi-scattering problem can be exactly solved in a non-perturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors., info:eu-repo/semantics/published

Proton therapy facilities, as other industrial applications using ionizing radiations, are confronted to radioprotection problems and seek to mitigate the undesirable effects. The aim of this thesis is to study the IBA compact proton therapy center, the Proteus®One in this radioprotection context. The compactness of this system implies important radioprotection issues, mainly the concrete shielding activation where a model allowing to predict and characterize the impact of secondary radiations on the system is required. Numerical simulations using Monte Carlo methods are used and in particular, a benchmark between different existing software has been carried out to validate the use of the Geant4 software in this work. The first part of this thesis focuses on the design of the structural shielding taking into account neutron sources in the model. In particular, the concept of neutron-equivalent source is introduced. In this framework, the quantity and the localization of the generated nuclear waste in concrete are determined. The second part of the work investigates the beam properties and its interactions with matter along the transport beamline. After the analysis of the existing system, a new degrader, which is one of the critical elements for the emission of secondary radiations and for the performances of the device, is proposed. Comparisons between existing (aluminium, graphite, beryllium) and novel (boron carbide and diamond) degrader materials are provided and evaluated against semi-analytical models of multiple Coulomb scattering. The use of diamond with a geometry adaptation allows beam emittance reduction and beam transmission increase. The third part of this thesis considers a complete 3D model of the Proteus®One system. It contributes to acquire a detailed knowledge of the beam properties inside the beamline. This model is validated with experimental data and the assumption of neutron-equivalent source is verified. Finally, maps of proton and neutron int, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The symplectic formalism applied to the phase-space representation of bosonic quantum systems provides us with a powerful mathematical tool for the characterisation of Gaussian states and transformations. As a consequence, quantum information protocols involving the latter are very well understood from a theoretical point of view. Nevertheless, it has become clear in recent years that the use of non-Gaussian resources is necessary in order to perform various crucial information-processing tasks. An illustration of this fact can for instance be found in situations where a Gaussian no-go theorem precludes the use of Gaussian transformations in order to achieve a task involving Gaussian states, such as quantum entanglement distillation, quantum error correction, or universal quantum computation. In the first part of this thesis, we develop a new method based on the generating function of a sequence, which gives rise to an elegant description of intrinsically non-Gaussian objects. Building on the generating function of the matrix elements of Gaussian unitaries in Fock basis, our approach gives access to the multi-photon transition probabilities via unexpectedly simple recurrence equations. The method is developed for Gaussian unitaries effecting both passive and active linear coupling between two bosonic modes. It predicts an interferometric suppression term which generalises the Hong-Ou-Mandel effect for more than two indistinguishable photons impinging on a balanced beam splitter. Furthermore, it exhibits an unsuspected 2-photon suppression effect in optical parametric amplification of gain 2, which originates from the indistinguishability between the input and output photon pairs. Finally, we extend our method to Bogoliubov transformations acting on an arbitrary number of modes. In the second part of this thesis, we introduce a class of Gaussian-dilatable bosonic quantum channels (characterised by a Gaussian unitary in their Stinespring dilation) called passive-envir, Le formalisme symplectique appliqué à la représentation des systèmes bosoniques dans l'espace des phases donne accès à un outil mathématique puissant pour la caractérisation des états gau-ssiens et transformations gaussiennes. Les protocoles d'information quantique impliquant ces derniers sont d'ailleurs très bien compris d'un point de vue théorique. Toutefois, il s'est avéré clair durant ces dernières années que l'utilisation de ressources non-gaussiennes est nécessaire afin d'effectuer des tâches cruciales de traitement de l'information. En effet, certaines tâches — telles que la distillation d’intrication quantique, le codage quantique ou encore le calcul quantique — impliquant des états gaussiens ne peuvent être effectuées avec des transformations gaussiennes. Dans la première partie de cette thèse, nous développons une nouvelle méthode basée sur la fonction génératrice d'une suite qui donne lieu à une description élégante d'objets intrinsèquement non-gaussiens. Se basant sur la fonction génératrice des éléments de matrice d'unitaires gaussiens dans la base de Fock, notre approche donne accès aux probabilités de transition multi-photon via des équations de récurrence étonnamment simples. La méthode est développée pour des unitaires gaussiens produisant des couplages linéaires passifs et actifs entres deux modes bosoniques. Elle prédit un terme d'interférence destructive qui généralise l'effet Hong-Ou-Mandel pour plus de deux photons indistinguables pénétrant dans un diviseur de faisceau équilibré. De plus, elle met en évidence un effet inattendu de suppression de deux photons dans un amplificateur paramétrique optique de gain 2. Cette suppression résulte de l’indistinguabilité entre les paires de photons d’entrée et de sortie. Finalement, nous étendons notre méthode à des transformations de Bogoliubov agissant sur un nombre de modes arbitraire. Dans la seconde partie de cette thèse, nous introduisons une classe de canaux quantiques bosoniques gaussiens-dilatable, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished