Abstract The topic of this thesis is superconducting electric circuits. Technical advances have made possible the experimental study of Josephson junction based circuit elements which sustain quantum mechanical properties long enough to be denoted as quantum devices. The quantum state can be controlled with electronic variables and measured using standard electrical setups. The research is motivated by the possibility to examine quantum phenomena in circumstances that can be customized, prospects of new quantum devices, and the development of quantum information processing. This thesis presents theoretical studies on the nonlinear and stochastic driving of a superconducting quantum two-level system (qubit). We first investigate the energy level shifts a single-Cooper-pair transistor under large amplitude driving realized via the inherently nonlinear Josephson energy by using an external magnetic flux. The effective driving field substantially deviates from a circular polarization and linear coupling. The energy level shifts are compared to the cases of a vanishing and a weak driving field, measured as the Stark shift and the generalized Bloch-Siegert shift, respectively. We describe criteria for the natural basis of the analytical and the numerical calculations. In addition to that, we develop a formalism based on the Floquet method for the weak probe measurement of the strongly driven qubit. In the latter part of the thesis research, we study utilization of a stochastic driving field whose time evolution is not regular but follows probabilistic laws. We concentrate on the motional averaging phenomenon and show that it can be measured with an unparalleled accuracy by employing a flux-modulated transmon qubit. As the stochastically modulated qubit is simultaneously measured with a moderate driving field, we develop a theoretical description accounting the possible interference effects between the modulation and the drive. The comparison with experimental results shows good agreement. Motional averaging phenomenon can be applied to estimate the properties of fluctuation processes occurring in qubits, e.g., the quasiparticle tunneling or the photon shot noise. Resting on the motional averaging, we anticipate that the qubit dephasing times can be improved if one can accelerate the dynamics of two-level fluctuators. We apply a semiclassical formalism where the qubit is treated with quantum mechanical concepts whereas the driving fields are classical. In the solution procedure, the numerical results support the main analytical understanding. As the theoretical results are extensively compared to reflection measurements, we construct an explicit connection between the dynamics of the studied quantum devices and the measured reflection coefficient.

Abstract Elementary experiments of atomic physics and quantum optics can be reproduced on a circuit board using elements built of superconducting materials. Such systems can show discrete energy levels similar to those of atoms. With respect to their natural cousins, the enhanced controllability of these ‘artificial atoms’ allows the testing of the laws of physics in a novel range of parameters. Also, the study of such systems is important for their proposed use as the quantum bits (qubits) of the foreseen quantum computer. In this thesis, we have studied an artificial atom coupled with a harmonic oscillator formed by an LC-resonator. At the quantum limit, the interaction between the two can be shown to mimic that of ordinary matter and light. The properties of the system were studied by measuring the reflected signal in a capacitively coupled transmission line. In atomic physics, this has an analogy with the absorption spectrum of electromagnetic radiation. To simulate such measurements, we have derived the corresponding equations of motion using the quantum network theory and the semi-classical approximation. The calculated absorption spectrum shows a good agreement with the experimental data. By extracting the power consumption in different parts of the circuit, we have calculated the energy flow between the atom and the oscillator. It shows that, in a certain parameter range, the absorption spectrum obeys the Franck-Condon principle, and can be interpreted in terms of vibronic transitions of a diatomic molecule. A coupling with a radiation field shifts the spectral lines of an atom. In our system, the interaction between the atom and the field is nonlinear, and we have shown that a strong monochromatic driving results in energy shifts unforeseen in natural or, even, other artificial atoms. We have used the Floquet method to calculate the quasienergies of the coupled system of atom and field. The oscillator was treated as a small perturbation probing the quasienergies, and the resulting absorption spectrum agrees with the reflection measurement.

Abstract In this thesis we study the interaction between radiation and matter using superconducting circuits that behave analogously with the conventional photon-atom interaction in quantum optics. The research is done with a system consisting of a waveguide resonator (radiation) strongly coupled to a transmon device (matter). We focus on the phenomena caused by strong coupling between the radiation and matter, and by driving the resonator to higher excited states with a strong monochromatic radiation. These have been studied little in the traditional radiation-matter systems. Increasing the strength of the monochromatic radiation drive, the dynamics of the system experiences a transition from the quantum to the classical regime. Also, the free-particle states of the transmon start being populated. In the weak driving limit, the transmon can be regarded as a two-state system. As a consequence, the resonator-transmon system is conventionally discussed in terms of the linear Jaynes–Cummings model. However, for strong coupling the Bloch–Siegert shift, caused by the terms neglected in the Jaynes–Cummings model, is strong and the Jaynes–Cummings model is insufficient for describing the dynamics of the system. We study the effects caused by strong coupling and the excitation of the higher transmon states instigated by the driving of the resonator. With reflection spectroscopy, we measure the absorption spectrum of the system and compare this with the spectrum calculated numerically using the Floquet–Born–Markov approach. We find that, in the region of the quantum-to-classical transition, the two-state approximation for the transmon is insufficient and the higher transmon states are necessary for accurate simulations. By calculating the average resonator occupation, we compare different numerical models: the Lindblad master equation, the Floquet–Born–Markov, and the semiclassical model. Coupling a transmon to a resonator shifts the energy levels of the resonator. This shift in the energy levels prevents the higher resonator states from being populated if the system is weakly driven with a frequency that is near the resonance frequency of the resonator. We simulate this photon blockade numerically and show that the blockade is substantially different for the two-state and multistate transmon approximations. / Original papers Original papers are not included in the electronic version of the dissertation. Pietikäinen, I., Danilin, S., Kumar, K. S., Vepsäläinen, A., Golubev, D. S., Tuorila, J., & Paraoanu, G. S. (2017). Observation of the Bloch-Siegert shift in a driven quantum-to-classical transition. Physical Review B, 96(2). https://doi.org/10.1103/PhysRevB.96.020501 http://jultika.oulu.fi/Record/nbnfi-fe201803073899 Pietikäinen, I., Danilin, S., Kumar, K. S., Tuorila, J., & Paraoanu, G. S. (2018). Multilevel Effects in a Driven Generalized Rabi Model. Journal of Low Temperature Physics, 191(5–6), 354–364. https://doi.org/10.1007/s10909-018-1857-8 http://jultika.oulu.fi/Record/nbnfi-fe2018061325770 Pietikäinen, I., Tuorila, J., Golubev, D. S., & Paraoanu, G. S. (2019) Quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator, Manuscript. https://arxiv.org/abs/1901.05655

Microscopic approaches enable one to study nuclear bound states as well as nuclear collisions in a unified framework.<p>At non-relativistic energies, all physical quantities are determined by the solutions of the many-body Schrödinger equation based on an interaction potential between nucleons.<p>The difficulty of solving this equation for collisions and taking the antisymmetrization principle into account restricts these approaches to light nuclei and requires the development of nuclear models based on some simplifying assumptions.<p>One of these assumptions, which is done in this work, is to consider that the nucleons are aggregated in clusters in the nuclear systems. <p><p>Another major problem of the microscopic description is the difficulty of determining a reliable interaction potential between nucleons.<p>In spite of many years of efforts to establish such potentials, none has yet been proved to accurately describe both the spectroscopic properties of nuclei and the reactions between light nuclei.<p>For this reason, many effective NN interactions, adapted to the model space and to the studied collision, have been built and used in microscopic models.<p>In parallel, for a few years, some efforts have been done to use in the microscopic models more realistic NN interactions, adjusted to reproduce the two-nucleon properties.<p>However, this requires solving much more accurately the Schrödinger equation by relaxing, for instance, the cluster assumption.<p>These approaches therefore need large computational times, which limits the size of the systems that can be studied.<p><p>In this work, a two-body realistic interaction has been adapted to the simple microscopic cluster model by using the Unitary Correlation Operator Method. This new realistic effective interaction has been adjusted so that the α+α elastic phase shifts obtained with the microscopic cluster model agree rather well with the experimental data.<p>This interaction has been used to study α+N and α+3He scattering.<p>The calculated phase shifts give a rather good agreement with experimental data without additional adjustment, without three-body interactions and with simple basis functions. <p><p>Besides this study of elastic scattering between light nuclei, this work deals with the nucleus-nucleus bremsstrahlung.<p>Previous microscopic models of nucleus-nucleus bremsstrahlung were based on a photon-emission operator fully neglecting the meson-exchange currents. <p>In this work, a microscopic cluster model of bremsstrahlung is developed, which implicitly takes them partially into account by using an extension of the Siegert theorem. <p>Then, the photon-emission operator can be deduced from the charge density rather than from the current density.<p>Although this extension of the Siegert theorem does not fully remove the nuclear-current dependence, the effects of the meson-exchange currents should be largely reduced, especially at low photon energy.<p><p>The microscopic cluster model of nucleus-nucleus bremsstrahlung developed in this work has been applied to the α+ α and α+N systems. This model is based on an effective NN interaction, which enables a good reproduction of the elastic phase shifts for the α+ α and α+N systems.<p>The agreement with experimental bremsstrahlung cross sections is rather good but the comparison between theory and experiment requires more numerous and more accurate data to be conclusive. With an extension to the p shell, the present model could also describe heavier cluster systems such as 12C+p and 16O+p for which experimental data exist at low energies.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Cette thèse présente l'étude théorique de processus cohérents d'excitation et d'ionisation dans les alcalino-terreux. Les paramètres atomiques indispensables pour décrire la dynamique sont calculés en combinant la méthode de matrice R et la théorie du défaut quantique à plusieurs voies (MQDT). Nous analysons les résultats expérimentaux obtenus par l'équipe d'Elliott concernant le contrôle des taux de production de trois états ioniques du baryum obtenus par interférence entre deux chemins d'ionisation quasi-résonnants avec un état intermédiaire dans un processus à deux photons de couleurs différentes. Introduisant un hamiltonien effectif, nous montrons que la dynamique d'évolution suit l'état adiabatique formé par l'excitation cohérente des deux états intermédiaires. Nous utilisons un formalisme MQDT dépendant du temps, valable en champ faible, pour analyser l'expérience de Ramsey optique, réalisée par van Leeuween et al, portant sur le contrôle des énergies et des distributions angulaires de photoélectrons émis par un paquet d'onde autoionisant créé dans le calcium par excitation du c÷ur isolé d'un état de Rydberg. Le flux radial instantané d'électrons créé par une ou deux impulsions pouvant présenter une dérive de fréquence est aussi étudié. Nous présentons un formalisme nouveau adapté à l'étude de la dynamique de paquets d'onde autoionisants créés par des impulsions brèves et intenses excitant des résonances étroites. Les résonances sont introduites explicitement dans les équations d'évolution. Leur énergie complexe (position et largeur), leurs couplages avec les voies ouvertes induits par le potentiel atomique et ceux avec les états discrets dûs aux laser sont déduits des expressions MQDT par le calcul numérique des pôles et des résidus de la matrice de diffusion physique S et de l'opérateur déplacement lumineux. Le lien entre ces pôles et les états de Siegert permet d'associer une fonction d'onde aux résonances et donc de les identifier.

Magnetic Resonance Imaging (MRI) is a non-ionizing form of medical imaging which has practical uses in diagnosing, characterizing, and studying diseases in vivo. Current clinical practice utilizes a highly trained radiologist to view MR images and qualitatively diagnose, characterize, or study a disease. There is no easy way to compare qualitative data. That is why developing quantitative measures in MRI show promise. Quantitative measures of disease can be compared across a population, MRI sites, and over time. Osteoarthritis is one disease where those who have it may benefit from the development of quantitative MRI measures. Those benefits may include earlier diagnosis and treatment of the disease or treatment which may halt or even reverse the damage from the disease.The work presented in this dissertation focuses on analyzing and developing new methods of radiofrequency (B1) field mapping to improve quantitative MRI measures. The dissertation opens with an introduction and a brief primer on MRI physics, followed by an introduction to B1 and flip-angle mapping in MRI (Chapters 1-3). Chapter 4 presents a careful statistical analysis of a recent and popular B1 mapping method, the Bloch-Siegert shift (BSS) method, along with a comparison of the technique to other common B1 mapping methods. The statistical models developed in chapter 4 are verified using both Monte Carlo simulation and actual MRI experiments in phantoms. Chapter 5 analyzes and details the potential errors introduced in B1 mapping when a 3D slab-selective excitation is employed. A method for correcting errors introduced by 3D slab-selective B1 mapping is then introduced in chapter 6, along with metrics to quantify the error involved. The thesis closes with a summary of other scientific contributions made by the author in chapter 7. The chapters comprising the bulk of the presented research (4-7) are briefly summarized below. Chapter 4, the statistical analysis of B1 mapping methods, demonstrates the effectiveness of deriving the B1 estimate from the phase of the MR image. These techniques are shown to perform particularly well in low signal-to-noise ratio (SNR) applications. However, there are benefits and drawbacks of each B1 mapping technique. The BSS method deposits a significant amount of radiofrequency (RF) power into the patient, causing a concern that tissue heating may occur. The Phase-Sensitive (PS) method of B1 mapping outperforms the other techniques in many situations, but suffers from significant sensitivity to off-resonance. The Dual-Angle (DA) method is very simple to implement and the analysis is straightforward, but it can introduce significant mean bias in the estimate. No B1 mapping technique performs well for all situations. Therefore, the best B1 mapping method needs to be determined for each situation. The work in chapter 4 provides guidance for that choice. Many B1 mapping techniques rely on a linear relationship between flip angle and transmit voltage. That assumption breaks down when a 3D slab-selective excitation is used. 3D slab-selective excitation is a common technique used to reduce the field-of-view (FOV) in MRI, which can directly reduce scan time. The problem with slab-selective excitation in conjunction with B1 mapping has been documented, but the potential errors in B1 estimation have never been properly analyzed across different techniques. The analysis in chapter 5 demonstrates that the errors introduced in B1 mapping using a slab-selective excitation in conjunction with the ubiquitous DA B1 mapping method can be significant. It is then shown that another B1 mapping technique, the Actual Flip Angle Imaging (AFI) method, doesn't suffer from the same limitation. The analysis presented in Chapter 6 demonstrates that some errors introduced by 3D slab-selective B1 mapping may be modeled and corrected allowing the use of 3D slab-selective excitation to reduce field-of-view, and potentially reduce scan time. The errors are modeled and corrected with a general numerical method using Bloch simulations. The general method is applied to the DA method as an example, but is general and could easily be extended to other methods as well. Finally, a set of metrics are proposed and briefly explored that can be used to better understand the topology and severity of errors introduced into B1 mapping methods. With a better understanding of the errors introduced, the need for correction can be determined. Chapter 7 details other significant ancillary contributions made by the author including: (1) presentation of a new B1 mapping method, the decoupled RF-pulse phase-sensitive B1 mapping method, which has potential for parallel transmit MRI; (2) demonstration of an ultra-short TE method which has potential for imaging Alzheimers brain lesions in vivo; (3) introduction of a new steady-state diffusion tensor imaging technique; (4) phase-sensitive B1 mapping in sodium is demonstrated, a feat not previously demonstrated; (5) a comparison between a dual-tuned and single-tuned sodium coil; (6) introduction of a water- and fat-separation technique using multiple acquisition SSFP; (7) an inter-site and inter-vendor quantitative MRI study is introduced; (8) a relaxation and contrast optimization for laryngeal imaging at 3T is introduced; and (9) diffusion imaging with insert gradients is introduced.

Nuclear electromagnetic breakup processes at low energy are particularly relevant in the astrophysical context. In this Thesis we analyse the Beryllium-9 photodisintegration reaction, whose inverse process, under certain astrophysical conditions, is related to the Carbon-12 formation. A preliminary study of the Carbon-12 photodisintegration is also carried out. The interaction of these nuclei with a low-energy photon induces a transition to a state consisting of cluster sub-units, the alpha-particles, and possibly a neutron, n. The theoretical study of the cross section in the low-energy regime is conducted by using a three-body ab initio approach. Beryllium-9 exhibits a clear separation of energy scales, since its alpha-alpha-n three-body binding energy is shallow compared to the binding of the alpha-particle. Within this framework a halo/cluster Effective Field Theory (EFT) can be developed. The alpha-alpha and alpha-n effective interactions are defined in momentum space as a series of contact terms, regularized by a momentum-regulator function. The Low Energy Constants are expressed in terms of scattering observables, i.e. scattering length and effective range. A three-body potential is also introduced in the model. Carbon-12 is studied on the same footing. By means of an integral transform approach, the problem of the transition to a state in the continuum can be advantageously reformulated in terms of a bound-state problem: in the calculations we use the Lorentz Integral Transform method, in conjunction with the Non-Symmetrized Hyperspherical Harmonics method. In determining the low-energy photodisintegration cross section, the nuclear current matrix element is evaluated through the electric dipole, or quadrupole, transition operator (Siegert theorem). Since the continuity equation is used explicitly, the contribution of the one-body and the many-body current operators is implicitly included in the calculation. By comparing the results with those obtained by using a one-body convection current, the effect of the many-body terms can be quantified. The dependence of the results on different EFT parameters is discussed, always in connection with the experimental data available in the literature. By following the power counting dictated by the EFT approach for Beryllium-9, the inclusion of different partial waves in the potential model is explored. In addition to a alpha-alpha S-wave, a alpha-n P-wave and a three-body effective interaction, a alpha-n S-wave term is also required to obtain results more consistent with the experimental data. The contribution of the many-body currents to the cross section is found to be non-negligible. Although at an early stage, Carbon-12 results show interesting features. The formalism presented in this Thesis can be extended to study the photodisintegration of Oxygen-16 within a fully four-body ab initio approach.