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

Photon-Assisted Cooper-Pair Tunneling and Microwave Power Renormalization in Small Josephson Junction Arrays

Godwill Mbiti Kanyolo, Kouichi Takeda, Yoshinao Mizugaki, Takeo Kato, Hiroshi Shimada

Published Nov 3, 2019• 0 citations
OpenAlex

Abstract

The influence of radio frequency microwaves on the Coulomb blockade characteristics in small Josephson junctions was studied using a one-dimensional array of ten small Al tunnel junctions in the frequency range from 1 MHz to 1000 MHz. Coulomb blockade voltage ($V_{\rm th}$) is diminished with increasing microwave power ($V_{\rm ac}$), where the $V_{\rm th}$-$V_{\rm ac}$ plots for varied frequencies fall on a single curve. We observed and theoretically analyzed a magnetic field $dependent$ renormalization of the applied microwave power, in addition to a magnetic-field $independent$ renormalization effect explained using an effective circuit approach of the array. Due to its high sensitivity to microwave power, the array is well-suited for on-chip detection applications in low temperature environments.

Related papers

Renormalization of Electromagnetic Quantities in Small Josephson Junctions

Godwill Mbiti Kanyolo

This doctorate thesis focuses on the effects of the electromagnetic environment on applied electromagnetic fields in single small junctions as well as arrays. We apply radio-frequency (RF) microwaves in the sub-gigahertz frequency range on a one-dimensional array of small Josephson junctions exhibiting distinct Coulomb blockade characteristics. We observed a gradual lifting of Coulomb blockade with increase in the microwave power which we interpret is due to photon-assisted tunneling of Cooper pairs in the classical (multi-photon absorption) regime. We observe that, due to its high sensitivity to microwave power, the array is well-suited for in situ microwave detection applications in low temperature environments. A detailed analysis of the characteristics in the classical (multi-photon absorption) limit reveals that the microwave amplitude is rescaled (renormalized), which we attribute to the difference in dc and ac voltage response of the array. We proceed to rigorously consider the origin of the aforementioned renormalization effect by considering the effect of the electromagnetic environment of the Josephson junction on applied oscillating voltages. We theoretically demonstrate that its effect is simply to renormalize the amplitude of oscillation in a predictable manner traced to the physics of wave function renormalization (Lehmann weights) consistent with circuit-QED. We also introduce Einstein's A and B coefficients for small Josephson junctions, in a bid to relate the renormalization effect to the modification of photon absorption and emission amplitudes. Such renormalization implies that the sensitivity of the single junction and the array to oscillating electromagnetic fields (e.g. microwaves) is modulated and depends on the environmental impedance. The renormalization effect can be exploited to configure `opaque', `translucent' or `transparent' quantum circuits to microwaves.

arXiv:2109.02440•Sep 1, 2021•7 citations

Quantum effects in small-capacitance single Josephson junctions

道生 渡部, David B. Haviland

We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures $(T=0.02--0.6\mathrm{K}),$ where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.

arXiv:cond-mat/0301467•Physical review. B, Condensed matter•Mar 17, 2003•32 citations

Coulomb Blockade and Coherent Single-Cooper-Pair Tunneling in Single Josephson Junctions

道生 渡部, David B. Haviland

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.

arXiv:cond-mat/0103502•Physical Review Letters•May 28, 2001•60 citations

Fabrication and measurement of one-dimensional arrays of small capacitance Josephson junctions

David B. Haviland, S. H. M. Persson, Per Delsing +1 more

We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.

Journal of Vacuum Science & Technology A Vacuum Surfaces and Films•May 1, 1996•13 citations

Wireless Josephson Junction Arrays as Tunable Metamaterials: Inducing Discrete Frequency Steps with Microwave Radiation

Laura Adams

We report low temperature, microwave transmission measurements on a new switchable and tunable class of nonlinear metamaterials. A wireless two dimensional array of Josephson junctions (JJ) is probed as a metamaterial where each plaquette in the array is considered as a meta-atom. In the presence of microwaves, this compact metamaterial of 30,000 connected meta-atoms synchronizes the flow of Cooper pairs to yield a single robust resonant signal with a quality factor of 2800 at the lowest temperature for our measurements. The transmission signal is switched on and off and its amplitude and frequency are tuned with either temperature, incident rf power or dc magnetic field. Surprisingly, increasing the incident rf power above a threshold causes the resonance to split into multiple discrete resonances that extend over a range of 240 MHz for a wide temperature window. We posit that this effect is a new incarnation of the inverse ac Josephson effect where the Josephson plasma frequency locks to the rf drive frequency generating quantized frequency steps, instead of voltage steps, in the absence of a dc bias.

arXiv:1501.05796•Jan 23, 2015•0 citations

Control of the electromagnetic environment for single Josephson junctions using arrays of dc SQUIDs

道生 渡部, David B. Haviland, Richard L. Kautz

We have measured the current–voltage characteristics of small-capacitance single Josephson junctions at low temperatures T ≤ 0.04 K, where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. When the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e 2 ≈ 26 kΩ, a transition to a clear Coulomb blockade of Cooper-pair tunnelling is induced in the single junction. The measured blockade voltage agrees with the theoretical prediction.

Superconductor Science and Technology•Sep 25, 2001•6 citations
The influence of radio frequency microwaves on the Coulomb blockade characteristics in small Josephson junctions was studied using a one-dimensional array of ten small Al tunnel junctions in the frequency range from 1 MHz to 1000 MHz. Coulomb blockade voltage (VthV_{\rm th}Vth​) is diminished with increasing microwave power (VacV_{\rm ac}Vac​), where the VthV_{\rm th}Vth​-VacV_{\rm ac}Vac​ plots for varied frequencies fall on a single curve. We observed and theoretically analyzed a magnetic field dependentdependentdependent renormalization of the applied microwave power, in addition to a magnetic-field independentindependentindependent renormalization effect explained using an effective circuit approach of the array. Due to its high sensitivity to microwave power, the array is well-suited for on-chip detection applications in low temperature environments.
This doctorate thesis focuses on the effects of the electromagnetic environment on applied electromagnetic fields in single small junctions as well as arrays. We apply radio-frequency (RF) microwaves in the sub-gigahertz frequency range on a one-dimensional array of small Josephson junctions exhibiting distinct Coulomb blockade characteristics. We observed a gradual lifting of Coulomb blockade with increase in the microwave power which we interpret is due to photon-assisted tunneling of Cooper pairs in the classical (multi-photon absorption) regime. We observe that, due to its high sensitivity to microwave power, the array is well-suited for in situ microwave detection applications in low temperature environments. A detailed analysis of the characteristics in the classical (multi-photon absorption) limit reveals that the microwave amplitude is rescaled (renormalized), which we attribute to the difference in dc and ac voltage response of the array. We proceed to rigorously consider the origin of the aforementioned renormalization effect by considering the effect of the electromagnetic environment of the Josephson junction on applied oscillating voltages. We theoretically demonstrate that its effect is simply to renormalize the amplitude of oscillation in a predictable manner traced to the physics of wave function renormalization (Lehmann weights) consistent with circuit-QED. We also introduce Einstein's A and B coefficients for small Josephson junctions, in a bid to relate the renormalization effect to the modification of photon absorption and emission amplitudes. Such renormalization implies that the sensitivity of the single junction and the array to oscillating electromagnetic fields (e.g. microwaves) is modulated and depends on the environmental impedance. The renormalization effect can be exploited to configure `opaque', `translucent' or `transparent' quantum circuits to microwaves.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.
We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.
We report low temperature, microwave transmission measurements on a new switchable and tunable class of nonlinear metamaterials. A wireless two dimensional array of Josephson junctions (JJ) is probed as a metamaterial where each plaquette in the array is considered as a meta-atom. In the presence of microwaves, this compact metamaterial of 30,000 connected meta-atoms synchronizes the flow of Cooper pairs to yield a single robust resonant signal with a quality factor of 2800 at the lowest temperature for our measurements. The transmission signal is switched on and off and its amplitude and frequency are tuned with either temperature, incident rf power or dc magnetic field. Surprisingly, increasing the incident rf power above a threshold causes the resonance to split into multiple discrete resonances that extend over a range of 240 MHz for a wide temperature window. We posit that this effect is a new incarnation of the inverse ac Josephson effect where the Josephson plasma frequency locks to the rf drive frequency generating quantized frequency steps, instead of voltage steps, in the absence of a dc bias.
We have measured the current–voltage characteristics of small-capacitance single Josephson junctions at low temperatures T ≤ 0.04 K, where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. When the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e 2 ≈ 26 kΩ, a transition to a clear Coulomb blockade of Cooper-pair tunnelling is induced in the single junction. The measured blockade voltage agrees with the theoretical prediction.