Nataliya Maleeva

Electrodynamics of a ring-shaped spiral resonator

We present analytical, numerical, and experimental investigations of electromagnetic resonant modes of a compact monofilar Archimedean spiral resonator shaped in a ring, with no central part. Planar spiral resonators are interesting as components of metamaterials for their compact deep-subwavelength size. Such resonators couple primarily to the magnetic field component of the incident electromagnetic wave, offering properties suitable for magnetic meta-atoms. Surprisingly, the relative frequencies of the resonant modes follow the sequence of the odd numbers as f1:f2:f3:f4… = 1:3:5:7…, despite the nearly identical boundary conditions for electromagnetic fields at the extremities of the resonator. In order to explain the observed spectrum of resonant modes, we show that the current distribution inside the spiral satisfies a particular Carleman type singular integral equation. By solving this equation, we obtain a set of resonant frequencies. The analytically calculated resonance frequencies and the current ...

Inductively shunted transmon qubit with tunable transverse and longitudinal coupling

This thesis is set in the framework of superconducting transmon-type qubit architectures with special focus on two important types of coupling between qubits and harmonic resonators: transverse and longitudinal coupling. We will see that longitudinal coupling offers some remarkable advantages with respect to scalability and readout. This thesis will focus on a design, which combines both these coupling types in a single circuit and provides the possibility to choose between pure transverse and pure longitudinal or have both at the same time. We will start with an introduction to circuit quantization, where we will explain how to describe and analyze superconducting electrical circuits in a systematic way and discuss which characteristic circuit elements make up qubits and resonators. We will then introduce the two types of coupling between qubit and resonator which are provided in our design. Translating this discussion from the Hamiltonian level to the language of circuit quantization, we will show how to design circuits with specifically tailored couplings. We will focus on our circuit design that consists of an inductively shunted transmon qubit with tunable coupling to an embedded harmonic mode. The distinctive feature of the tunable design is that the transverse coupling disappears when the longitudinal is maximal and vice versa. Subsequently, we will turn to the implementation of our circuit design, discuss how to choose the parameters, and present an adapted alternative circuit, where coupling strength and anharmonicity scale better than in the original circuit. In addition, we present a proposal for an experimental device that will serve as a prototype for a first experiment. We will conclude the thesis discussing different possibilities to do readout with our circuit design, including a short discussion of the influence of dissipation.

An argon ion beam milling process for native AlOx layers enabling coherent superconducting contacts

We present an argon ion beam milling process to remove the native oxide layer forming on aluminum thin films due to their exposure to atmosphere in between lithographic steps. Our cleaning process is readily integrable with conventional fabrication of Josephson junction quantum circuits. From measurements of the internal quality factors of superconducting microwave resonators with and without contacts, we place an upper bound on the residual resistance of an ion beam milled contact of 50 mΩ μm2 at a frequency of 4.5 GHz. Resonators for which only 6% of the total foot-print was exposed to the ion beam milling, in areas of low electric and high magnetic fields, showed quality factors above 106 in the single photon regime, and no degradation compared to single layer samples. We believe these results will enable the development of increasingly complex superconducting circuits for quantum information processing.

Circuit quantum electrodynamics of granular aluminum resonators

Granular aluminum (grAl) is a promising high kinetic inductance material for detectors, amplifiers, and qubits. Here we model the grAl structure, consisting of pure aluminum grains separated by thin aluminum oxide barriers, as a network of Josephson junctions, and we calculate the dispersion relation and nonlinearity (self-Kerr and cross-Kerr coefficients). To experimentally study the electrodynamics of grAl thin films, we measure microwave resonators with open-boundary conditions and test the theoretical predictions in two limits. For low frequencies, we use standard microwave reflection measurements in a low-loss environment. The measured low-frequency modes are in agreement with our dispersion relation model, and we observe self-Kerr coefficients within an order of magnitude from our calculation starting from the grAl microstructure. Using a high-frequency setup, we measure the plasma frequency of the film around 70 GHz, in agreement with the analytical prediction.The electrodynamics of superconducting devices make them suitable for applications as detectors, amplifiers, and qubits. Here the authors show that resonators made from granular aluminum, which naturally realizes a network of Josephson junctions, have practically useful impedances and nonlinearities.