We introduce a method of designing NMR pulse sequences, with a specific focus toward complete decoupling of carbon-13 spin qubits coupled to a nitrogen-vacancy (NV) center in diamond. Using Average Hamiltonian Theory, we calculate different intermediate Hamiltonians corresponding to different rotations implemented by NMR pulses. Two novel pulse sequences are obtained containing 24 and 12 evolution periods respectively. Assuming ideal and instantaneous pulses, performance for both sequences is better than the WAHUHA + echo sequence for total evolution times of less than 5 ms and comparable for greater evolution times. Analysis of sensitivity points toward non-robustness for angle errors in the applied pulses when the direction of pulses is not taken into account, however this can be corrected for using chirality sums. Suggestions for further research include the study of non-globally applied pulses and application of the design method to non-zero effective Hamiltonians.

This thesis contains a rigorous derivation of the path integral formulation of the Isingmodel with multiple original proofs. Besides that, thesis also contains various resultsof simulations of the 2D square lattice Ising Model with nearest-neighbour interactionsusing the Swendsen-Wang algorithm. Using finite size scaling to find critical exponentγ, we reported a value of γ = 1.748 ± 0.004. After calculating the relaxation times τ forvarious thermodynamic variables, we found the value for the dynamic critical exponentz to be in the range of z = 0.180 ± 0.004 and z = 0.282 ± 0.005.

Terahertz time-domain spectroscopy (THz-TDS) is an extremely useful method to probe material electrodynamics. The THz regime comprises rich physics, enabling to determine compositional, electronic and vibronic degrees of freedom through THz spectroscopy of a material under study. However, to study nanometre size thin films with THz-TDS, we need to overcome a large mismatch in length scales, since the THz wavelength is on the order of millimeters. A solution lies in the THz probing of metasurfaces, artificial materials made of conductive structures with length scales much smaller than the probing wavelength. Such a metamaterial induces enhanced electromagnetic field strengths near the surface, enabling nonlinear spectroscopy without the need for strong-field terahertz sources. Additionally, they provide sensitivity to the local (micron-scale) electrodynamic environment. In the ideal case, one can infer significant information about the thin film electrodynamics via the resonance frequency and dissipation in the metasurface. This thesis project comprises the optimization of terahertz (THz) resonant electric split ring resonator (eSRR) metasurfaces for enhanced-light matter coupling, suitable for material characterization. Experimental characterization is combined with finite element simulations, to obtain the transmission spectra and near-field electric, magnetic fields and current densities. In simulation, the eSRR design is optimized to obtain an up to four times stronger response at resonance than the designs described in literature. The optimized design is studied on different substrates, revealing the ability to extract a resonance even close to a substrate Reststrahlen band. This thesis concludes with characterization of the metal-insulator transition of transition metal oxide NdNiO3. From the resonance frequency and quality factor it is possible to track this phase transition from time-domain terahertz spectroscopy, thereby revealing the ability to probe extremely thin films, with an outlook on out of equilibrium studies.

In this project, we have done a calibrated measurement on a previously designed and fabricated current pumped Josephson Parametric amplifier. We have installed a microwave switch into our crygenic fridge tobe able to get a calibrated response measurement using Short-Open-Load calibration, which we used withmeasurements of the gain and flux tunability of the device. This showed that our previous measurements onthe gain deviated significantly, with about 10dB. We also did a thermal calibration on the amplifier by heatingthe plate it was attached to, and found that the input noise approximates the limit of a half quantum of noise.

In this report we present a model to simulate the performance and robustness of the Charge-Resonance Check (CR-Check) in the Nitrogen-Vacancy (NV) center. The CR-Check is a routine which verifies that the charge state of the NV center is NV$^-$ and that the lasers, addressing the NV center, are on resonance with the optical lines. This is done by shining a red (λ=637 nm) laser on the NV center and measuring the amount of fluorescence photons, since they are dependent on the resonance frequency being near the frequency of the laser. If these counts do not pass the threshold for success, then either a new measurement of the photons is done or the system is repumped with a green (λ=532 nm) high intensity laser if they are below the repump threshold. The most important parameters are the duration of the red laser (dt) and the spectral diffusion of the NV center (sigma), which is an intrinsic property of the NV center. The model was implemented in Python, where also Numba, a high-performance Python compiler was used. An algorithm for finding the optimal values is included, so that different implementations can be compared. Then parameter sweeps were performed to get insight on the effects of the parameters. The distribution of frequency spectrum was investigated, it follows the shape of the Generalized Normal distribution with a disturbance due to the memory parameter. We observed that the mean time till success goes up linearly with the sigma after it is higher than 80 MHz for dt. This effect can be explained by taking into account the Normal distribution which was used to determine the resonance frequency. It became clear that the N_thr_repump and N_thr_success often come as pairs, which have been shown to be linearly dependent on the rate. Also it has been observed that after a certain sigma amount the N_thr_repump and N_thr_success do not change anymore. We noticed that for fixed sigma there is a optimal value of dt. This optimal value of dt is dependent on sigma. Average number of photon counts was nearly independent of sigma and only linearly dependent on dt. This is a sign that the CR-Check can always bring the NV center sufficiently on resonance. It has been observed that when the NV center's spectral diffusion is below 40 MHz, it is significantly faster to use the CR-strategy with dt = 25 μs compared to the standard dt of 50 μs. Lastly new implementations, where p-values are used rather than the measured counts, were shown to be capable of performing a CR-Check procedure. These implementations have used either the cumulative density function (cdf) of the Poisson distribution or the t-test or the Wilcoxon signed-rank test. The test using the cdf performed very similar to the current implementation. The other two test were slower with regards to the mean time till success, as they seem to require a lower spectral diffusion than was mandated.

In this study, ultrathin films of the itinerant 4d ferromagnet SrRuO3 were epitaxially deposited on SrTiO3 and capped with a thin LaAlO3 layer. Top gates and a dielectric layer were patterned onto contacted films and magnetotransport properties were characterized at low temperatures as a function of top gate voltage. A particular focus was placed on the anomalous Hall resistivity. The magnitude of the Hall signal and the sheet resistance were shown to vary with top gate voltage. In particular, the anomalous Hall loops were compared to numerical tight-binding models. The model is proposed as an alternate explanation to the skyrmion picture and as a complement to the two-channel phenomenological model put forth to explain the unusual low-temperature anomalous signal of ultrathin SrRuO3 . Model predictions were found to be valid at
low temperatures in semiconducting Ru-deficient SrRuO3 films.

This thesis investigates intrinsic frustrated magnetic systems on an insulating square lattice. The frustrated systems were successfully engineered from magnetic iron atoms on top of an insulating square c(2x2) reconstruction of nitrogen on Cu3Au(100) (copper-gold) surface. Vertical atom manipulation was used to position the magnetic atoms atomically precise on the surface and methods were found to increase the success rate of this. For the investigation of frustration, a numerical simulator was made in Python for modelling frustrated spin structures based on already existing spin models and the following experimental measurements were taken: topography, spectroscopy and current-time traces. The simulations of a frustrated spin system show low energy excited states and the measurements show switching of the system between states.