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.
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.
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 spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices with nontrivial band structures have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.
In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission line resonator, quantum optical effects can be studied in these electrical circuits.The possibility of using a frequency tunable transmission line resonators for coupling of superconducting quantum bits is investigated. Tunable superconducting resonators consisting of coplanar waveguide structures, terminated to ground in one end via a superconducting quantum interference device (SQUID), are characterized. By applying a magnetic field to the SQUID loop, the boundary condition of the resonator changes leading to a change in resonance frequency.A change of the resonance frequency by more than 250 linewidths is demonstrated. It is also demonstrated that the resonator can be tune by several hundred MHz on a time scale that is much shorter than the photon lifetime of the resonator.Circuits containing both one and two transmon qubits coupled to the resonator are characterized. Quantum mechanical interactions between the resonator and the qubits, in form of vacuum Rabi splitting, are observed. Coherent control of a single qubit coupled to the resonator is demonstrated by performing Rabi oscillations of the qubit. In the two qubit case, coherent interaction between the qubits is observed in terms of a nonlinear scaling of the coupling strength between the resonator and the collective two qubit system.Measurements on a strongly driven single Cooper-pair box, using a quantum capacitance readout, are also presented. A rich structure in the response is well explained in terms of longitudinal dressed states of the single-Cooper pair box.When measuring the response of a single-electron box, a gate dependent excess dissipation is observed. The dissipation is understood by considering the internal dynamics of the single electron box. The excess dissipation is modeled as an effective resistance named the Sisyphus resistance.
We have fabricated and characterized systems consisting of superconducting quantum bits (qubits) of the transmon type, coupled to a tunable transmission line resonator. The resonator consists of a superconducting quarter wavelength coplanar waveguide (CPW) resonator that is made tunable by terminating the transmission line to ground through a superconducting quantum interference device (SQUID). Here we present measurements on two devices where we observe Rabi oscillations as we drive the qubit, and vacuum Rabi splitting both as we tune the qubits into resonance with the resonator and as we tune the resonator into resonance with the qubits. We also observe coherent interaction between two resonant qubits. In addition, we demonstrate that we can calculate the response very accurately using a multilevel Hamiltonian.
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.
In cavity quantum electrodynamics (QED), the key physical systems include Fabry-Pérot cavity resonators and multilevel cold atoms. Since ultra-strong electromagnetic interaction between photons and quantized cavity modes occurs in cavity QED, many novel quantum optical effects such as optical Rabi oscillation, quantum collapse/revival of atomic-level population and atom-field quantum entanglement can be realized in such quantum microcavities. As is known in quantum optics, these schemes can be generalized to circuit QED, which is a circuit analog of cavity QED. Fundamental devices in circuit QED are superconducting coplanar waveguide microwave resonators and mesoscopic Cooper-pair boxes. Here, the coplanar waveguide resonator with photons stored can be identified as a resonant cavity and the Cooper-pair boxes with large electric dipoles play the role of multilevel cold atoms. Thus, all the quantum optical effects in conventional cavity QED can also be exhibited in the present superconducting circuit QED system. We consider the theoretical working mechanism of superconducting charge qubits based on tunable Josephson junction coupling. It can be found that an analog of optical Rabi oscillation in Cooper-pair boxes can be achieved by tuning an applied external magnetic field. Time evolution of energy levels in a Cooper-pair box, which is manipulated by a time-dependent magnetic flux through its Josephson-junction ring, is studied within the framework of time-dependent quantum mechanics.