Circuit quantum electrodynamics (cQED) models describe cavity-qubit interactions through a set of coupling parameters that are typically assumed to be known.However, these parameters depend strongly on the resonator geometry and local electromagnetic field distribution.This study presents a geometry-aware full-wave electromagnetic workflow for extracting electromagnetic quantities required for cQED charge-photon coupling estimation from realistic superconducting coplanar waveguide (CPW) resonator structures.The proposed method combines full-wave microwave simulations with stored-energy normalization to determine the zero-point electric field required for charge-photon coupling strength.A representative dipole-resonator configuration is used as a proof-of-concept example, showing how realistic microwave geometries can be translated into the parameters required for cQED analysis.Rather than introducing a new quantum-mechanical model, the framework provides an electromagnetic front-end that complements existing cQED Hamiltonians.
Circuit quantum electrodynamics (cQED) models describe cavity-qubit interactions through a set of coupling parameters that are typically assumed to be known.However, these parameters depend strongly on the resonator geometry and local electromagnetic field distribution.This study presents a geometry-aware full-wave electromagnetic workflow for extracting electromagnetic quantities required for cQED charge-photon coupling estimation from realistic superconducting coplanar waveguide (CPW) resonator structures.The proposed method combines full-wave microwave simulations with stored-energy normalization to determine the zero-point electric field required for charge-photon coupling strength.A representative dipole-resonator configuration is used as a proof-of-concept example, showing how realistic microwave geometries can be translated into the parameters required for cQED analysis.Rather than introducing a new quantum-mechanical model, the framework provides an electromagnetic front-end that complements existing cQED Hamiltonians.
Quantum information processing technologies are gaining interest due to their potential for performance exceeding what is possible with the best classical computers. One of the most promising platforms is the circuit quantum electrodynamics (cQED) architecture that controls superconducting circuit qubits by coupling them to electromagnetic fields in microwave resonators or waveguides. As these devices become increasingly complex, existing analysis and design approaches that often rely on lumped element circuit approximations can become inadequate due to their lack of accuracy and flexibility. This is leading to a growing interest in developing quantum full-wave numerical modeling methods for the high-fidelity analysis of cQED devices. In this work, we focus on a quantum full-wave modeling approach that uses a projector-based quantization approach that allows a problem to be decomposed into distinct subdomains whose fields can be quantized more easily. This leads to a framework that can naturally incorporate microwave ports, which is not straightforward with other formulations. Here, we consider an explicit problem of a coaxial-fed rectangular waveguide cavity to validate parts of our projector-based formalism. Toward this end, we apply this approach to a classical Hamiltonian analysis of this system that can be used to more easily validate the relevant full-wave aspects of the corresponding quantum formulation. In addition to presenting the formulation of the full-wave classical Hamiltonian of the system, we derive equations of motion and discuss an analytical solution procedure with an input-output theory approach. We validate our formulation by comparing the input-output theory results to standard finite element method (FEM) scattering parameter simulations.
Spin-photon interactions are commonly described using quantum-mechanical Hamiltonian models, whereas the influence of local EM-field overlap on the coupling response is less explored.This study presents a dipole-based fullwave EM analogue for investigating resonator perturbations inspired by spin-qubit systems.An effective oscillating electric dipole is introduced as an EM analogue of qubit-induced polarization within a superconducting coplanar waveguide (CPW) resonator.The effects of dipole resonance frequency, orientation, and spatial position on the transmission response are systematically investigated.The results show that the magnitude of the resonator perturbation is governed by the local dipole-field overlap and decreases as the dipole is displaced from the high-field region or rotated away from the dominant electric-field direction.A coupled-resonator configuration is furthermore used as a consistency test and exhibits hybridized resonant modes and avoided-crossing behaviour in agreement with classical coupled-mode theory.The proposed framework is an electromagnetic analogue rather than a quantum-state model, and is intended to provide physical and geometryaware insight for future integration with quantitative cQED parameter-extraction methods.
Superconducting coplanar-waveguide (CPW) resonators are one of the key devices in circuit quantum electrodynamics (cQED). Their performance can be limited by dielectric losses in the substrate and in the material interfaces. Reliable modeling is required to aid in the design of low-loss CPW structures for cQED. We analyze the geometric dependence of the dielectric losses in CPW structures using finite-element modeling of the participation ratios of the lossy regions. In a practical scenario, uncertainties in the the dielectric constants and loss tangents of these regions introduce uncertainties in the theoretically predicted participation ratios. We present a method for combining loss simulations with measurements of two-level-system-limited quality factors and resonance frequencies of CPW resonators. Namely, we solve an inverse problem to find model parameters producing the measured values. High quality factors are obtainable by properly designing the cross-sectional geometries of the CPW structures, but more accurate modeling and design methods for low-loss CPW resonators are called for major future improvements. Our nonlinear optimization methodology for solving the aforementioned inverse problem is a step in this direction.
High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.
A single photon interacting with a single atom is the most fundamental form of light interacting with matter and has been extensively studied in the field of Cavity Quantum Electrodynamics (cavity QED). Here, a non-linearity like an atom is coupled to a single mode of the electromagnetic field in a cavity. Another field which explores the quantum mechanical nature of photons is Circuit Quantum Electrodynamics (cQED) where photons are the quantized excitations of a superconducting microwave resonator and non-linearity is introduced by the Josephson junction. Like this, setups analog to that of in cavity QED can be copied to cQED, with a number of differences. For example, the photons propagating in a transmission line are more confined and the circuits are made with conventional lithography techniques, allowing for more freedom in engineering the system parameters. In the first part of the thesis, we build a numerical model in order to examine the feasibility of quenching the ground state of a coplanar waveguide (CPW) interrupted by a tunable coupling element. Next, by means of experiments and simulations we considered the feasibility of observing experimentally a synchronization effect in a driven CPW with its central conductor interrupted by equally spaced capacitively shunted Josephson junctions (Josephson crystal) based on a recent proposal. Finally, we made a first step in understanding the synchronization from a classical perspective by modelling a Josephson crystal of two junctions as two degenerate non-linearly coupled Duffng oscillators. Concerning the quenching experiment, we found that the plasma frequency must be tuned faster than 1/f with f the resonance frequency of the CPW, which is in the sub-nanosecond regime and therefore unfeasible with current state the art electronics. We also found that, in contrast to what was claimed in the proposal, the synchronization effect cannot be observed for the parameters common in cQED. One way would be to push the limits of the capacitances to several picofarads. Finally, we found that the non-linear coupling causes the two degenerate non-linearly coupled Duffng oscillator to synchronize, which is a first step in understanding the proposed synchronization effect in a fully classical way.
We present a method for the numerical analysis of superconducting quantum circuits combining lumped elements, either linear or nonlinear (i.e., Josephson junctions), and distributed coplanar waveguide (CPW) structures. CPW transmission lines and multiline couplers are directly modeled without discretizing them into lumped-element equivalents, and the circuit Hamiltonian parameters are extracted by using the energy-participation ratio (EPR) method. This approach enables fast and accurate extraction of mode frequencies, anharmonicities, cross-Kerr interactions, and Purcell decay rates without relying on full electromagnetic simulations, while naturally accounting for higher-order modes of distributed components. We have implemented the proposed method in a Python framework, QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), which we have used to validate the approach against full electromagnetic simulations (Ansys HFSS, pyEPR), existing circuit-analysis tools (QuCAT), and designs reported in the literature. The comparisons show excellent agreement with orders-of-magnitude reductions in computational time relative to full-wave solvers. We demonstrate applications including Purcell-protected readout, multimode ultrastrong coupling, and multiplexed qubit readout, illustrating how the method can support fast and reliable early-stage circuit design.