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Dynamics of a LC Shunted

Floriana Lombardi, Thilo Bauch, G. Rotoli, T. Lindström, Jesper Johansson, Karin Cedergren, Francesco Tafuri, T. Claeson

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

We have measured the energy level separation from the ground state to the first excited state in a high critical tem- perature superconductor d-wave Josephson junction. We observe that the bias current dependence of the energy level separation is strongly affected by the large shunt capacitance and inductance of the junction electrodes. In order to describe the effect of a shunt capacitance and shunt inductance on the junction dynamics we de- rive the equation of motion of the total system. In general such a circuit displays two resonance frequencies corresponding to two different energy scales. We discuss various limits for the values of the shunt inductor and capacitor. Index Terms—High-temperature superconductors, Josephson junctions, resonance, superconducting devices.

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We have measured the energy level separation from the ground state to the first excited state in a high critical tem- perature superconductor d-wave Josephson junction. We observe that the bias current dependence of the energy level separation is strongly affected by the large shunt capacitance and inductance of the junction electrodes. In order to describe the effect of a shunt capacitance and shunt inductance on the junction dynamics we de- rive the equation of motion of the total system. In general such a circuit displays two resonance frequencies corresponding to two different energy scales. We discuss various limits for the values of the shunt inductor and capacitor. Index Terms—High-temperature superconductors, Josephson junctions, resonance, superconducting devices.
Dynamics of a LC Shunted YBa2Cu3O7-δ{\rm YBa}_{2}{\rm Cu}_{3}{\rm O}_{7{\hbox {-}}\delta}YBa2​Cu3​O7-δ​ Josephson Junction
We have measured the energy level separation from the ground state to the first excited state in a high critical temperature superconductor d-wave Josephson junction. We observe that the bias current dependence of the energy level separation is strongly affected by the large shunt capacitance and inductance of the junction electrodes. In order to describe the effect of a shunt capacitance and shunt inductance on the junction dynamics we derive the equation of motion of the total system. In general such a circuit displays two resonance frequencies corresponding to two different energy scales. We discuss various limits for the values of the shunt inductor and capacitor.
We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases, can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using the Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show excellent agreement with theory taking into account the shunt inductance and capacitance in the resistively and capacitively shunted junction model. The results clearly show that the dynamics of the system are two-dimensional, resulting in two resonant modes of the system. These findings have important implications for the design and operation of Josephson junction based quantum bits.
We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω J becomes equal to the natural frequency ωrc of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.
Double-barrier Josephson junctions, with outer electrodes of superconducting Nb and a central thin layer of non-superconducting Al, are being developed as self-shunted junctions for high-frequency superconducting integrated circuits. This paper presents a simplified phenomenological model of the behaviour of such junctions (often called SINIS, for superconductor-insulator-normal-insulator-superconductor) based on the resistively shunted junction model, using Josephson coupling between the layers and the time-dependent Ginzburg-Landau equation to describe the dynamics of the weak induced energy gap in the Al layer. This analysis shows how non-hysteretic I - V characteristics can be obtained but suggests some limitations in their high-frequency performance. Predictions for critical current generally agree with prior experiments. The technological implications of this model are discussed.
The choice of impedance used to shunt a Josephson junction determines if the charge transferred through the circuit is quantized: a capacitive shunt renders the charge discrete, whereas an inductive shunt gives continuous charge. This discrepancy leads to a paradox in the limit of large inductances L. We show that while the energy spectra of the capacitively and inductively shunted junction are vastly different, their high-frequency responses become identical for large L. Inductive shunting thus opens the possibility to observe charging effects unimpeded by charge noise.
Relaxation oscillations at subharmonics of the Josephson frequency may occur in a resistively shunted superconducting tunnel junction, where the shunt loop has a large inductance. We have studied the variation in the relaxation period with the shunt inductance and resistance, the Josephson critical current, and the bias current. Steps in the current-voltage curve were noted at bias points where the subharmonic number changed. Radiation powers of the order of a nW were coupled out of small, single, tunnel junctions at 10 GHz. Linewidths scaled with the frequency square as compared with those of the Josephson mode oscillations. Wide signals centered around harmonics of the relaxation frequency were due to amplified noise. Injection locking to a fraction of the frequency of a relatively strong signal occurred, while weaker signals were amplified. Gains up to 15 dB were achieved within a fairly large bandwidth, but the noise temperature was high. The importance of parametrically up-converted noise from low idler frequencies is emphasized.