High quality factor coplanar resonators are critical elements in superconducting quantum circuits. We describe the design, fabrication and measurement of stepped impedance resonators (SIRs), which are more compact in size than commonly used uniform impedance resonators (UIRs). With properly chosen impedance ratio, SIRs can be 27% shorter than UIRs. As a result, the area occupied by SIRs can be reduced. Two kinds of designs containing both SIRs and UIRs are fabricated and measured. The power dependence of the extracted internal quality factors (Qi) for all the resonators showed that SIRs and UIRs have comparable performance with Qi around half-million under single-photon level excitation. These results indicate that SIRs could be used in superconducting quantum circuits. The reduced size of SIRs may also lead to reduced overall circuit area and increased integration level.
In this experiment, we couple a superconducting Transmon qubit to a high-impedance $645\ Ω$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate $g$, measured through a large vacuum Rabi splitting of $2g\simeq 910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $ω$, placing our system close to the ultra-strong coupling regime ($\bar{g}=g/ω=0.071$ on resonance). Combining this setup with a vacuum-gap Transmon architecture shows the potential of reaching deep into the ultra-strong coupling $\bar{g} \sim 0.45$ with Transmon q…
The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quan…
By driving a dispersively coupled qubit-resonator system, we realize an "impedance-matched" $Λ$ system that has two identical radiative decay rates from the top level and interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect ($99.7\%$) extinction of the reflection and highly efficient ($74\%$) frequency down-conversion. These proof-of-principle results lead to…
The interaction between superconducting qubits and one-dimensional microwave transmission lines has been studied experimentally and theoretically in the past two decades. In this work, we investigate the spontaneous emission of an initially excited artificial atom which is capacitively coupled to a semi-infinite transmission line, shorted at one end. This configuration can be viewed as an atom in front of a mirror. The distance between the atom and the mirror introduces a time-delay in the system, which we take into account fully. When the delay time equals an integer number of atom oscillatio…
Transmission-line waveguides can mediate long-range fluctuation-induced forces between neutral objects. We present two approaches for the description of these forces between electric components embedded in transmission-line circuits. The first, following ordinary quantum electrodynamics (QED), consists of the quantization and scattering theory of voltage and current waves inside transmission lines. The second approach relies on a simple circuit analysis with additional noisy current sources due to resistors in the circuit, as per the fluctuation-dissipation theorem (FDT). We apply the latter a…
Superconducting metamaterials, which are designed and fabricated with structured fundamental circuit elements, have motivated recent developments of exploring unconventional quantum phenomena in circuit quantum electrodynamics (circuit-QED). We propose a method to engineer 1D Josephson metamaterial as a chiral waveguide by considering a programmed spatiotemporal modulation on its effective impedance. The modulation currents are in the form of traveling waves which phase velocities are much slower than the propagation speed of microwave photons. Due to the Brillouin-scattering process, non-triv…
Hamiltonians of the superconducting qubits of Transmon type involve non-zero ZZ-interaction terms due to their finite and small anharmonicities. These terms might lead to the unwanted accumulation of spurious phases during the execution of the two-qubit gates. Exact calculation of the ZZ-interaction rates requires the full diagonalization of the circuit Hamiltonians which very quickly becomes computationally demanding as the number of the modes in the coupler circuit increases. Here we propose a direct analytical method for the accurate estimation of the ZZ-interaction rates between low-anharm…
We consider the single photon transistor in coupled cavity system of resonators interacting with multilevel superconducting artificial atom simultaneously. Effective single mode transformation is used for the diagonalization of the the hamiltonian and impedance matching in terms of the normal modes. Storage and transmission of the incident field are described by the interactions between the cavities controlling the atomic transitions of lowest lying states. Rabi splitting of vacuum induced multiphoton transitions is considered in input/output relations by the quadrature operators in the absenc…
We demonstrate a new approach to dissipation engineering in microwave quantum optics. For a single mode, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here, we are able to tune the minimal number of lost photons per jump to be two (or more) with a simple dc voltage. As a consequence, different quantum states experience different dissipation. Causality implies that the states must also experience different energy shifts. Our measurements of these Lamb shifts are in good agreement with the predictions of the Kramers-Kronig relations for single quantum state…
We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave induced consecutive passages under a double resonance condition, we observe novel Landau-Zener-Stückelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system, and are consistent with the simulations based on our theoretical model. This study provides an excellent platform f…
Understanding large-scale interacting quantum matter requires dealing with the huge number of quanta that are produced by scattering even a few particles against a complex quantum object. Prominent examples are found from high energy cosmic ray showers to the optical or electrical driving of degenerate Fermi gases. We tackle this challenge in the context of many-body quantum optics, as motivated by the recent developments of circuit quantum electrodynamics at ultrastrong coupling. The issue of particle production is addressed quantitatively with a simple yet powerful concept rooted in the quan…
We study the properties of superconducting electrical circuits, realizing cavity QED. In particular we explore the limit of strong coupling, low dissipation, and elevated temperatures relevant for current and future experiments. We concentrate on the cavity susceptibility as it can be directly experimentally addressed, i.e., as the impedance or the reflection coefficient of the cavity. To this end we investigate the dissipative Jaynes-Cummings model in the strong coupling regime at high temperatures. The dynamics is investigated within the Bloch-Redfield formalism. At low temperatures, when on…
We investigate quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the emitted photonic states, in the framework of the spin-boson model Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we…
Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we stud…
Immittance formulas for exact blackbox quantization and divergence-free effective models in circuit QED
Technical University of Munich（慕尼黑工业大学）；TUM School of Natural Sciences（TUM自然科学学院）；Physics Department（物理系）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
In circuit quantum electrodynamics (circuit QED), an artificial "circuit atom" can couple to a quantized microwave radiation much stronger than its real atomic counterpart. The celebrated quantum Rabi model describes the simplest interaction of a two-level system with a single-mode boson field. When the coupling is large enough, the bare multilevel structure of a realistic circuit atom cannot be ignored even if the circuit is strongly anharmonic. We explored this situation theoretically for flux (fluxonium) and charge (Cooper pair box) type multi-level circuits tuned to their respective flux/c…
In this PhD thesis, we will present the theoretical and experimental work that led to the realization of a radio-frequency circuit quantum electrodynamics system (RFcQED). In chapter 2, we provide a detailed derivation of the Hamiltonian of circuit QED formulated in the context of the Rabi model, and extract expressions for the cross-Kerr interaction. The resulting requirements for the coupling rate in RFcQED are discussed, one of them being the need to dramatically increase the coupling rate compared to typical circuit QED device. In chapter 3 we cover two experimental approaches to increasin…
