One-dimensional Transmission Line Research Articles

Dynamics and resonance fluorescence from a superconducting artificial atom doubly driven by quantized and classical fields

We report an experimental demonstration of resonance fluorescence in a two-level superconducting artificial atom under two driving fields coupled to a detuned cavity. One of the fields is classical and the other is varied from quantum (vacuum fluctuations) to classical by controlling the photon number inside the cavity. The device consists of a transmon qubit strongly coupled to a one-dimensional transmission line and a coplanar waveguide resonator. We observe a sideband anticrossing and asymmetry in the emission spectra of the system through a one-dimensional transmission line, which is fundamentally different from the weak-coupling case. By changing the photon number inside the cavity, the emission spectrum of our doubly driven system approaches the case when the atom is driven by two classical bichromatic fields. We also measure the dynamical evolution of the system through the transmission line and study the properties of the first-order correlation function, Rabi oscillations, and energy relaxation in the system. The study of resonance fluorescence from an atom driven by two fields promotes understanding decoherence in superconducting quantum circuits and may find applications in superconducting quantum computing and quantum networks. Published by the American Physical Society 2024

Error-insensitive preparation of entangled states between a Josephson qubit and microwave photons via invariant-based shortcuts

Optimal preparation of quantum entanglement is of significance to information processing and state engineering. In this paper, an efficient scheme is proposed to implement error-insensitive generation of entangled states between a Josephson qubit and microwave photons by the technique of invariant-based shortcuts to adiabaticity. A superconducting qubit is dispersively coupled to a quantized cavity field of one-dimensional transmission line resonator. Within a considered subspace spanned by three composite states, we deal with an effective interaction of the composite system with two classical drivings. A maximally entangled qubit-photon state can be deterministically induced using a splitting-like quantum state transfer. To nullify the deviation errors of Rabi coupling and frequency detuning, we optimize the driving parameters and then make the entanglement creation insusceptible to these control imperfections. Thanks to the mitigation of deviation effects, robustness against the residual noisy environment could be obtained numerically. The proposed strategy could provide a promising avenue towards fast and robust information processing with superconducting circuit quantum electrodynamics.

Design of PGM-Free Cathode Catalyst Layers for PEMFC Applications: The Impact of Electronic Conductivity

The impact of the electronic resistance of platinum-group-metal-free cathode catalyst layers (PGM-free CCLs) for proton-exchange-membrane fuel cells (PEMFCs) was systematically investigated. Here we selected two different PGM-free catalysts (having high and low electronic conductivity) and integrated them into CCLs without and with conductive carbon fiber additives. To investigate the impact of the electronic resistivity () of PGM-free catalysts and CCLs, their through-plane values were quantified by an in situ electrochemical impedance spectroscopy (EIS) approach based on a one-dimensional transmission line model. The results indicate that the electronic conductivity of PGM-free CCLs can be increased by adding carbon additive, resulting in a significant improvement of the fuel cell performance (by ∼60 mV at 1 A cm−2 in H2/O2 configuration). Ex situ four-point probe measurements of the in-plane values of some of the CCLs were found to differ vastly from the through-plane values. This difference is attributed to the anisotropic morphology of the CCLs, caused by preferential fiber orientation and/or cracks in the CCLs. In the end, we suggest guidelines for the design and evaluation of PGM-free CCLs and for assessing and improving their electronic resistance.

Modulation instability and modulated wave patterns in a nonlinear electrical transmission line with the next-nearest-neighbor coupling

In this paper, we investigate modulation instability and solitary waves in a one-dimensional nonlinear electrical transmission line with second-neighbor interactions. Through the quasi-discrete multiple scale method, we derive coupled nonlinear Schrödinger equations. To investigate the modulation instability in the structure, we use the linear stability analysis, and an expression for the modulation instability spectrum is derived. From the analytical investigation, we show that the second neighbor coupling affects both the modulation instability growth rate and modulation instability bands. Furthermore, we show via single and coupled mode excitation that bright and dark solitary waves can propagate at the lower and upper cutoff frequencies. To evaluate the robustness of the analytical investigation, we use a direct numerical simulation of the continuous wave. We conclude that the second-neighbor couplings generate rogue waves in the structure during the long-time evolution of the plane wave. We also demonstrate that with a variation of the excitation wave number, the nonlinear electrical transmission line can support new objects as wave molecules for high values of the wave number. This feature is not yet observed in nonlinear electrical transmission lines and will be useful in many fields of physics.

Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line.

A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equationsof motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.

Superconducting transmon qubit-resonator quantum battery

Quantum battery (QB) is the miniature energy storage and release device and plays a crucial role in future quantum technology. Here an implementation scheme of a QB is proposed on a superconducting circuit, which is composed by $N$ coupled transmon qubits and a one-dimensional transmission line resonator. We derive the Hamiltonian of the QB system and investigate its charging performance by considering three decay channels. We find that the presence of the decay channels suppresses the high oscillation of the energy storage process, thereby realizing a stable and powerful QB. In particular, compared with the resonator decay and the qubit relaxation, the qubit dephasing shows a counterintuitive advantage in our QB. We show that the nearest-neighbor interaction always has a positive impact on the stable energy and the coupling only significantly influences the maximum charging power in the fully nondegenerate ground-state region. We also demonstrate the feasibility of our approach by evaluating the QB performance under experimental parameters.

On the Computation of Hierarchical Control results for One-Dimensional Transmission Line

In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in a one-dimensional wave equation in domains with a moving boundary. Some controls act in part of the boundary and define a strategy of equilibrium between them, considering a leader control and a follower. Thus, we introduced the concept of hierarchical control to solve the problem and mapped the Stackelberg Strategy between these controls. A total discretization of the problem is presented for a numerical evaluation in spaces of finite dimension, an algorithm for evaluation of the problem is presented as the combination of finite element method (FEM) and finite difference method (FDM). The algorithm efficiency and computational results are illustrated for some experiments using the softwares Freefem++ and MatLab.

Impedance tube method for characterization of one-dimensional electro-momentum coupled materials

Electro-momentum coupling is a macroscopically observable material response resulting from heterogeneous piezoelectric media with microscale asymmetries that produce unique cross-coupling between the bulk momentum of the material and the generated electric field. Recently, Pernas-Salomon et al. used a one-dimensional transmission line model to demonstrate that the electro-momentum coupling effect must be considered in order to retrieve physically meaningful effective properties of heterogeneous media with subwavelength asymmetries [Wave Motion 106, 102797, (2021)]. This work presents the specialization of their transmission line model to the classical impedance tube measurement technique in which the scattering coefficients and the spatial averages of the mechanical and electrical fields of a one-dimensional material can be measured in order to obtain estimates of the frequency-dependent effective properties of an electro-momentum coupled sample. We investigate an idealized analytical approximation and then a finite element model of the realistic impedance tube configurations in order to link the analytical model to realistic experimental conditions and geometry. We then provide preliminary test results extracted from an electro-momentum coupled unit cell in a water-filled impedance tube. [Research sponsored by the Defense Advance Research Project Agency and the Army Research Office and was accomplished under Grant No. W911NF-20-1-0349.]

Advanced impedance modeling for micropatterned polymer electrolyte membrane fuel cells

Cathode patterning is an effective means of improving the oxygen reduction reaction in polymer electrolyte membrane fuel cells. Because the conventional one-dimensional transmission line model cannot be applied to micropatterned electrodes, impedance modeling for micropatterned electrodes is conducted using a two-dimensional transmission line matrix model. In this study, the charge transfer resistance is considered a function of proton potential in the equivalent circuit based on the Butler–Volmer equation. Micropatterned membrane electrode assemblies (MEAs) with three different pattern depths are fabricated, and electrochemical measurements are performed on them. The measured and simulated impedances are evaluated using the distribution of relaxation times analysis results. This study validates the proposed model by comparing the simulated and measured impedances of the MEAs. The experimental and matrix model simulation results confirm that cathode patterning reduces both the charge transfer and proton conduction resistances. For each MEA, the charge transfer resistances obtained by fitting the matrix model to the measured impedances are plotted on a straight line; thus, the Tafel slope is obtained. The matrix model demonstrated in this study leads to the design of patterned electrodes through the impedance analysis of various patterned electrodes.

Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

Quantum versus classical regime in circuit quantum acoustodynamics

We experimentally study a circuit quantum acoustodynamics system with a superconducting artificial atom coupled to both a two-dimensional surface acoustic wave resonator and a one-dimensional microwave transmission line. The strong coupling between the artificial atom and the acoustic wave resonator is confirmed by the observation of the vacuum Rabi splitting at the base temperature of dilution refrigerator. We show that the propagation of microwave photons in the microwave transmission line can be controlled by a few phonons in the acoustic wave resonator. Furthermore, we demonstrate the temperature effect on the measurements of the Rabi splitting and temperature induced transitions from high excited dressed states. We find that the spectrum structure of two-peak for the Rabi splitting could become into those of several peaks under some special experimental conditions, and gradually disappears with the increase of the environmental temperature T. The continuous quantum-to-classical crossover is observed around the crossover temperature T c, which is determined via the thermal fluctuation energy k B T and the characteristic energy level spacing of the coupled system. Experimental results agree well with the theoretical simulations via the master equation of the coupled system at different effective temperatures.

A novel framework for approximating resistance–temperature characteristics of a superconducting film based on artificial neural networks

Resistance versus temperature characteristics of superconducting films have been studied for decades, and are still considered an important subject of condensed matter physics. They have recently received increased attention, primarily motivated by electromagnetic metamaterial strategy, which has been used in the implementation of one-dimensional microwave transmission lines with high-temperature superconducting films. In some of the recent works, it has been argued that the physical measurement of these curves is a strenuous and costly process, which becomes tedious when incessantly performed for a wide range of parameters. Contemplating on their significance, in this work, we propose a resistance–temperature curves approximation framework using three different artificial neural networks architectures, and carry out a detailed comparison between the variants in terms of the accuracy they achieve. We demonstrate that the mean-squared error, between the approximated and the physically measured curves, is negligible, which justifies extrapolation of these curves over a wide range of parameters using the proposed framework.

Semiclassical analysis of dark-state transient dynamics in waveguide circuit QED

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 oscillation periods, the atom converges into a dark state after an initial decay period. The dark state is an effect of destructive interference between the reflected part of the field and the part directly emitted by the atom. Based on circuit quantization, we derive linearized equations of motion for the system and use these for a semiclassical analysis of the transient dynamics. We also make a rigorous connection to the quantum optics system-reservoir approach and compare these two methods to describe the dynamics. We find that both approaches are equivalent for transmission lines with a low characteristic impedance, while they differ when this impedance is higher than the typical impedance of the superconducting artificial atom.

Generation of quantum entangled states of multiple groups of qubits distributed in multiple cavities

Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of $N$-group qubits distributed in $N$ cavities can be created via a three-step operation. The GHZ states of the $N$-group qubits are generated by using $N$-group qutrits placed in the $N$ cavities. Here, ``qutrit'' refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for coupling the cavities. The operation time is independent of the number of qubits. The GHZ states are prepared deterministically because no measurement on the states of qutrits or cavities is needed. In addition, the third energy level of the qutrits during the entire operation is virtually excited and thus decoherence from higher energy levels is greatly suppressed. This proposal is quite general and can in principle be applied to create GHZ states of many qubits using different types of physical qutrits (e.g., atoms, quantum dots, NV centers, various superconducting qutrits, etc.) distributed in multiple cavities. As a specific example, we further discuss the experimental feasibility of preparing a GHZ state of four-group transmon qubits (each group consisting of three qubits) distributed in four one-dimensional transmission line resonators arranged in an array.

The study of entropy in a transmission line resonator interacting with a capacitively coupled Cooper pair box

In the present work, we theoretically study the entropy of a Cooper pair box coupled to a one-dimensional transmission line resonator. The proposed scheme uses the Jaynes-Cummings model in presence of losses to study the time avolution of the system entropy. The coupling of these two subsystems provides an important indication of the influence of Cooper pair box on the evolution of system entropy. Decaying CPB allows us to control variation of entropy at certain times.

PT-symmetric direct electrical transmission lines: Localization behavior.

In this paper, we study a finite direct electrical transmission line when we distribute resistors R_{n} according to a parity-time (PT) distribution composed of a gain (-R) and loss (+R) sequence. Considering zero boundary conditions, we find analytical results for the frequency spectrum ω(R,k_{d}) as a function of resistance R and the wave number k_{d}. A frequency spectrum analysis shows a phase transition from real to complex eigenvalues as a function R for fixed k_{d=N}, where 2N is the size of the transmission line. Numerically, we study localization properties through the normalized localization length Λ(R,k_{d}). This measure shows good agreement with the analytical results and gives an account of the PT-phase transition. Our results pave a solid way toward studying the interplay between parity-time symmetry concepts and one-dimensional electrical transmission lines, aiming to find another generation of electronic devices capable of controlling the flow of energy.

Shortcuts to adiabatic for implementing controlled phase gate with Cooper-pair box qubits in circuit quantum electrodynamics system

We theoretically present a protocol to realize the controlled phase gate with Cooper-pair box (CPB) qubits in circuit quantum electrodynamics (circuit QED) system. In this protocol, the one-dimensional transmission line resonator in circuit QED system acting as quantum data bus generates a common cavity mode and interacts with each CPB qubit. The Rabi frequencies of driven pluses can be designed with simple Gaussian or trigonometric functions by utilizing the universal SU(2) transformation. Moreover, the level configurations of CPB qubits have been reported by previous protocol (Feng and Zhang in Phys C 470:240–243, 2010). Thus, the protocol can be realized easily in experiment. In addition, the influence of various decoherence processes such as spontaneous emissions, dephasings of the CPB qubits and the decay of the cavity mode on the fidelity is discussed by numerical simulations. The results show that the protocol is robust against the decoherence and parameter variations. Therefore, the protocol may be useful for the fields of quantum computations.

Phase and amplitude control of microwave pulse in a linear array of superconducting artificial atoms

Based on phase controlled electromagnetically induced transparency, we propose a scheme for coherent control and storage of a microwave pulse in a linear array of artificial atoms. In particular, we consider the effects of the amplitude and phase of the fields driving the superconducting artificial atoms attached to a one-dimensional transmission line on the storage of a microwave pulse. We show that controlling the relative-phase of the microwave fields coupling the artificial atoms in a three-level Δ-configuration can yield tunable transparency window, which allows the propagation of a microwave pulse. The amplitude-control of the lower-levels coupling field adds a gain signature to the transparency window. Our results show that the absorption of the probe microwave pulse is suppressed and it gets amplified while propagating through an array of artificial atoms. The group velocity of the probe pulse is considerably reduced as a result atoms in a linear array act as coherent microwave memories.

Modulation of energy spectrum and control of coherent microwave transmission at single-photon level by longitudinal field in a superconducting quantum circuit**Project supported by the Ministry of Science and Technology of China (Grant Nos. 2014CB921401, 2017YFA0304300, 2014CB921202, and 2016YFA0300601), the National Natural Science Foundation of China (Grant No. 11674376), and the Strategic Priority Research Program of the Chinese Academy of Sciences

We study the effect of longitudinally applied field modulation on a two-level system using superconducting quantum circuits. The presence of the modulation results in additional transitions and changes the magnitude of the resonance peak in the energy spectrum of the qubit. In particular, when the amplitude λz and the frequency ωl of the modulation field meet certain conditions, the resonance peak of the qubit disappears. Using this effect, we further demonstrate that the longitudinal field modulation of the Xmon qubit coupled to a one-dimensional transmission line could be used to dynamically control the transmission of single-photon level coherent resonance microwave.

WIDEBAND UHF LOADS BASED ON STEPPED-HETEROGENEOUS LINES WITH LOSSES

The relevance of wideband load devices application in the modern UHF equipment is described in this paper. The basic structure and principle of operation of microstrip load are described. Design methods of high power wideband UHF loads in a series connection of line segments with increasing value of dissipative losses are considered in this paper. The stepped-heterogeneous loads frequency properties analysis based on one-dimensional transmission lines theory and numeric electrodynamic modelling is carried out. It was shown, that considered loads based on large length transmit lines with dissipative losses have good matching quality on high frequencies, which worsen with frequency reduction. Frequency characteristics, calculated via numeric electrodynamic modelling method of one-step and two-step centimeter wavelength microstrip loads are represented. A convergence of modelling and theoretic characteristics is shown.