Pinpointing the dissipation mechanisms and evaluating their impacts to the performance of Josephson junction (JJ) are crucial for its application in superconducting circuits. In this work, we demonstrate the junction-embedded resonator (JER) as a platform which enables us to identify and quantify various dissipation mechanisms of JJ. JER is constructed by embedding JJ in the middle of an open-circuit, 1/2 λ transmission-line resonator. When the 1st and 2nd harmonics of JER are excited, JJ experiences different boundary conditions, and is dominated by internal and external dissipations, respectively. We systematically study these 2 dissipation mechanisms of JJ by varying the JJ area and number. Our results unveil the completely different behaviors of these 2 dissipation mechanisms, and quantitatively characterize their contributions, shedding a light on the direction of JJ optimization in various applications.
Pinpointing the dissipation mechanisms and evaluating their impacts to the performance of Josephson junction (JJ) are crucial for its application in superconducting circuits. In this work, we demonstrate the junction-embedded resonator (JER) as a platform which enables us to identify and quantify various dissipation mechanisms of JJ. JER is constructed by embedding JJ in the middle of an open-circuit, 1/2 λ transmission-line resonator. When the 1st and 2nd harmonics of JER are excited, JJ experiences different boundary conditions, and is dominated by internal and external dissipations, respectively. We systematically study these 2 dissipation mechanisms of JJ by varying the JJ area and number. Our results unveil the completely different behaviors of these 2 dissipation mechanisms, and quantitatively characterize their contributions, shedding a light on the direction of JJ optimization in various applications.
As a typical nonlinear device, Josephson junction (JJ) can be either served as a microwave device to scatter the traveling microwave or embedded in a transmission line (TL) resonator to modify the mode structure. However, two mutually exclusive circuit models have been proposed to describe the JJ embedded in a TL: one is the series embed model [see, e.g., Zueco et al., Phys. Rev. B 86, 024503 (2012)] and another is the parallel embedded one [see, e.g., Yamamoto et al., Appl. Phys. Lett. 93, 042510 (2008)]. Here, beginning with the comparison of the theoretical predictions of these two models, we fabricate the JJ-embedded TL device and measure its microwave scattering parameters at 50-mK low temperature. The experimental results support the parallel embedded model, thus rule out the series embedded one. The present work might lay the physical foundation for the designs of various microwave JJ devices, such as the microwave photonic crystals, superconducting qubits, also the Josephson parameter amplifiers, etc., by embedding the JJs into the superconducting TLs.
The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
We have investigated numerically a system consisting of a long Josephson junction embedded into a microstrip resonator. For such a configuration the Josephson vortex dynamics in the junction is driven by the oscillating currents in the resonator. We have calculated the complex impedance of the junction at the resonant frequency. The Q factor of the resonator and the change of the resonant frequency of the whole system can then be easily calculated knowing the parameters of the resonator without Josephson junction. The fluxon dynamics and the complex impedance of the junction are simulated for different values of the junction length, damping, dc bias current, and dc magnetic field. This allows us to explain the behavior of the impedance of the junction and different loss mechanisms. In particular, we predict a nonmonotonic dependence of the both real and imaginary parts of the impedance on the amplitude of the oscillating current in the resonator for some range of parameters. Our results show that such a combination of active and passive superconducting elements forms a rather interesting nonlinear physical system which might be useful for development of tunable/switchable superconducting resonators and suggests an experimental technique for detecting trapped vortices in long junctions.
Josephson junctions (JJ) are a fundamental component of microwave quantum circuits, such as tunable cavities, qubits, and parametric amplifiers. Recently developed encapsulated graphene JJs, with supercurrents extending over micron distance scales, have exciting potential applications as a new building block for quantum circuits. Despite this, the microwave performance of this technology has not been explored. Here, we demonstrate a microwave circuit based on a ballistic graphene JJ embedded in a superconducting cavity. We directly observe a gate-tunable Josephson inductance through the resonance frequency of the device and, using a detailed RF model, we extract this inductance quantitatively. We also observe the microwave losses of the device, and translate this into sub-gap resistances of the junction at μeV energy scales, not accessible in DC measurements. The microwave performance we observe here suggests that graphene Josephson junctions are a feasible platform for implementing coherent quantum circuits.
Based on Josephson junction (JJ), superconducting quantum bit (qubit) is operated at frequencies of several GHz. Dissipation of JJs in this frequency range can cause energy relaxation in qubits, and limit coherence time, therefore it is highly concerned and needs to be determined quantitatively. The dissipation of JJs can be quantified by microwave quality factor. It is usually done at very low temperature (~mK) to determine whether a JJ is suitable for qubit devices by measuring the quality factor. In this paper, a method based on nonlinear frequency response of JJs is proposed to determine the quality factor. This method can be used in thermal activation regime, which may bring great conveniences to experiments. To analyze high frequency properties of JJs, the dynamic equation of a current-biased JJ, which describes high frequency oscillation of the JJ, is introduced. A fourth-order potential approximation is used to obtain the analytical equation of non-linear response. The dependence on quality factor, as well as on amplitude, of difference between JJ’s plasma frequency and resonant frequency, is derived from the equation. The approximate treatment is quantitatively validated by our numerical simulations with practical JJ parameters including different environment influences. Thus, based on nonlinear frequency response of JJs, a reliable and simple method to determine quality factor of JJ is proposed, which is desirable for exploring JJ based microwave devices such as parametric amplifier, superconducting qubit. Being driven well into the nonlinear microwave response regime, due to frequency-amplitude interaction, the resonant frequency of a current bias JJ deviates from the JJ’s plasma frequency. The deviation is directly related to the microwave quality factor. Hence, the quality factor can be deducted from the experimental measurement of the resonant frequency deviation, with different microwave power values applied. In comparison with linear resonance experiment, the nonlinear resonance used by the proposed method produces stronger signal. Therefore it is more robust against external noise. When being conducted at high temperature, the proposed method is more reliable. The accuracy of the measured quality factor primarily depends on those of the JJ’s parameters such as critical current and capacitance, while those parameters can be experimentally determined with high precision.