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

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.