Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

The cavity-coupled Josephson device

Andrew Longacre

Published Oct 1, 1979• 13 citations
Publisher

Abstract

The interaction of a resistance-shunted Josephson junction with a tightly coupled resonant circuit has been examined analytically and in simulation. Parametric dependences are developed and demonstrated for the size of resonance-induced current steps in the device’s V-I curve and the corresponding level of excitation of the resonance.
DOI
10.1063/1.325738

Related papers

Study of Microwave Resonances Induced by Bias Lines of Shunted Josephson Junctions

Uğur Yılmaz, Sasan Razmkhah, Romain Collot +3 more

Bias lines routed over a ground plane naturally form microstrip lines associated with the presence of a capacitance. This can lead to unwanted resonances when coupled to Josephson junctions. This article presents an electrical model of a shunted Josephson junction with its bias lines and pads, fabricated with the 1 kA/cm2rapid single flux quantum niobium process of the FLUXONICS foundry (J. Kunert, 2013), (J. Kunert, 2017). A T-model is used to simulate the microwave behavior of the bias line, predict resonances and design resonance-free superconducting circuits. The I-V characteristics of three shunted Josephson junctions have been obtained from time-domain simulations done with Josephson SIMulator (JSIM) (E. S. Fang and T. Van Duzer, 1989) and show a good match with the experimentally observed resonance at 230 GHz up to the normal resistance branch, measured at 4.2 K. The influence of the position and value of a series resistor placed on bias lines is studied to damp unwanted resonances at the junction.

arXiv:1912.00503•IEEE Transactions on Applied Superconductivity•Jun 25, 2020•4 citations

Resonances and Phase Locking in Josephson High-Q Circuit

Victor K. Kornev, Nikolay V. Kolotinskiy

We consider Josephson junction coupled to a high-quality tank circuit and present both analytic analyses and numerical simulation results for resonances of both force and parametric types as well as Shapiro steps under microwave irradiation with frequency close to the resonance one. Physical mechanisms of the phenomena are studied and discussed.

IEEE Transactions on Applied Superconductivity•Mar 22, 2018•2 citations

Resonator coupled Josephson junctions; parametric excitations and mutual locking

Hans Dalsgaard Jensen, A. Larsen, J. Mygind

Self-pumped parametric excitations and mutual locking in systems of Josephson tunnel junctions coupled to multimode resonators are reported. For the very large values of the coupling parameter, obtained with small Nb-Al/sub 2/O/sub 3/-Nb junctions integrated in superconducting microstrip resonators, the DC I-V characteristic shows an equidistant series of current steps generated by subharmonic pumping of the fundamental resonator mode. This is confirmed by measurement of frequency and linewidth of the emitted Josephson radiation.

IEEE Transactions on Magnetics•Mar 1, 1991•5 citations

Topics in the physics of underdamped Josephson systems

I. Tornes

We describe a variety of models to characterize the behavior of several types of underdamped Josephson systems.We also present numerical results based on these models.We first discuss a stack of small junctions in a single mode resonant cavity.Such a stack is believed to be appropriate to model some high temperature cuprate superconductors such as Bi 2 Sr 2 CaCu 2 O 8+x .Our results show self-induced-resonant-steps in the current voltage (IV) curve.These steps represent a coherent phase locking between the junctions in the stack and the resonant cavity.Next we generalize these results to treat a single long junction coupled to a single mode resonant cavity.We find a number of features not seen in stacks of small junctions.Our numerical results show that if the electromagnetic fields of the cavity mode are spatially periodic, we again see steps in the IV curve and furthermore, for sufficiently large coupling, the cavity frequency is shifted by coupling to the long junction.We also discuss how a stack of long junctions could be used to model a layered high temperature superconductor.We then turn to some properties of single junctions in the "quantum" regime where the phase/number non-commutation is important.This quantum regime is crucial to all proposals to use such junctions as solid state quantum bits (qubits).We show that such qubits, when subjected to external a.c.perturbations, exhibit not only . . . . . . . . . .

•Jan 1, 2006•0 citations

Dynamics of a Josephson array in a resonant cavity

Eivind Almaas, D. Stroud

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B 63, 144522 (2001); 64, 179902(E) (2001)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman et al [Phys. Rev. Lett. 79, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions; that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's); that when ${N}_{a}$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in ${N}_{a};$ and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.

arXiv:cond-mat/0111028•Physical review. B, Condensed matter•Mar 19, 2002•40 citations

Perturbation treatment of mixing in Josephson junctions

Mogens T. Levinsen, B. T. Ulrich

We consider a current biased, resistively shunted josephson junction irradiated at two frequencies. The perturbation technique introduced by Aslamasov and Larkin is used in the calculations. Both signals are treated as perturbations. The second order calculation yields the size of the mixing steps atV_{\pm}=h(\omega_{1}\pm\omega_{2})/2e. As in the case of a single frequency we show that subharmonic mixing steps are absent. The amplitude of the voltage oscillation at the difference and sum frequencies is shown to be non-zero at all voltages. We calculate the microwave resistance for one frequency ω2to third order in the perturbation. There are negative resistance regions nearV\pm(as well as nearV_{2}= h\omega_{2}/2e). Near V, the negative resistance region appears for bias voltage V just aboveV_{-}, while near V the region appears for V just belowV_{+}. This means that when an incident frequency mixes with a cavity mode the mixing step atV_{-}will be inverted compared to the cavity step itself.

IEEE Transactions on Magnetics•Mar 1, 1975•4 citations
Bias lines routed over a ground plane naturally form microstrip lines associated with the presence of a capacitance. This can lead to unwanted resonances when coupled to Josephson junctions. This article presents an electrical model of a shunted Josephson junction with its bias lines and pads, fabricated with the 1 kA/cm2rapid single flux quantum niobium process of the FLUXONICS foundry (J. Kunert, 2013), (J. Kunert, 2017). A T-model is used to simulate the microwave behavior of the bias line, predict resonances and design resonance-free superconducting circuits. The I-V characteristics of three shunted Josephson junctions have been obtained from time-domain simulations done with Josephson SIMulator (JSIM) (E. S. Fang and T. Van Duzer, 1989) and show a good match with the experimentally observed resonance at 230 GHz up to the normal resistance branch, measured at 4.2 K. The influence of the position and value of a series resistor placed on bias lines is studied to damp unwanted resonances at the junction.
Self-pumped parametric excitations and mutual locking in systems of Josephson tunnel junctions coupled to multimode resonators are reported. For the very large values of the coupling parameter, obtained with small Nb-Al/sub 2/O/sub 3/-Nb junctions integrated in superconducting microstrip resonators, the DC I-V characteristic shows an equidistant series of current steps generated by subharmonic pumping of the fundamental resonator mode. This is confirmed by measurement of frequency and linewidth of the emitted Josephson radiation.
We describe a variety of models to characterize the behavior of several types of underdamped Josephson systems.We also present numerical results based on these models.We first discuss a stack of small junctions in a single mode resonant cavity.Such a stack is believed to be appropriate to model some high temperature cuprate superconductors such as Bi 2 Sr 2 CaCu 2 O 8+x .Our results show self-induced-resonant-steps in the current voltage (IV) curve.These steps represent a coherent phase locking between the junctions in the stack and the resonant cavity.Next we generalize these results to treat a single long junction coupled to a single mode resonant cavity.We find a number of features not seen in stacks of small junctions.Our numerical results show that if the electromagnetic fields of the cavity mode are spatially periodic, we again see steps in the IV curve and furthermore, for sufficiently large coupling, the cavity frequency is shifted by coupling to the long junction.We also discuss how a stack of long junctions could be used to model a layered high temperature superconductor.We then turn to some properties of single junctions in the "quantum" regime where the phase/number non-commutation is important.This quantum regime is crucial to all proposals to use such junctions as solid state quantum bits (qubits).We show that such qubits, when subjected to external a.c.perturbations, exhibit not only . . . . . . . . . .
We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B 63, 144522 (2001); 64, 179902(E) (2001)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman et al [Phys. Rev. Lett. 79, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions; that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's); that when Na{N}_{a}Na​ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in Na;{N}_{a};Na​; and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.
We consider a current biased, resistively shunted josephson junction irradiated at two frequencies. The perturbation technique introduced by Aslamasov and Larkin is used in the calculations. Both signals are treated as perturbations. The second order calculation yields the size of the mixing steps atV_{\pm}=h(\omega_{1}\pm\omega_{2})/2e. As in the case of a single frequency we show that subharmonic mixing steps are absent. The amplitude of the voltage oscillation at the difference and sum frequencies is shown to be non-zero at all voltages. We calculate the microwave resistance for one frequency ω2to third order in the perturbation. There are negative resistance regions nearV\pm(as well as nearV_{2}= h\omega_{2}/2e). Near V, the negative resistance region appears for bias voltage V just aboveV_{-}, while near V the region appears for V just belowV_{+}. This means that when an incident frequency mixes with a cavity mode the mixing step atV_{-}will be inverted compared to the cavity step itself.