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

arXiv:1502.04878 · Physical Review B

Quantum phase-slip junction under microwave irradiation

Angelo Di Marco, F. W. J. Hekking, Gianluca Rastelli

Published May 19, 2015• 25 citations
arXivHTMLPDF

Abstract

We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ${\ensuremath{\omega}}_{\mathrm{mw}}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}$ in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the $I\text{\ensuremath{-}}V$ characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.

DOI
10.1103/physrevb.91.184512

Related papers

NbSi nanowire quantum phase-slip circuits: dc supercurrent blockade, microwave measurements, and thermal analysis

C H Webster, J. C. Fenton, T. T. Hongisto +3 more

We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage ${V}_{\mathrm{c}}$, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.

arXiv:1302.2808•Physical Review B•Apr 18, 2013•54 citations

Simulation of effect of microwave irradiation on I-V characteristics of Josephson junction using RCLSJ model with noise into consideration

Mohammed Shahabuddin

I-V characteristics of Josephson junction (JJ) under microwave irradiation is simulated taking the resistance, capacitance and inductance of the junction (RCLSJ) into account. Since most of the JJ made with high TC material operates at high temperature where the thermal fluctuation is playing significant role. In the present simulation, thermal noise is also taken into consideration and simulated result explains the rounding behaviour of the Shapiro step observed in the experimental I-V curve. The simulated results also confirm the growing of Shapiro steps with increasing microwave power. This model also clearly account for the appearance of broad minima and reduction of the maxima in the power dependence of the step amplitude ΔIn/2Ic as observed in the experimental data of Kautz et al. (1992).

International Journal of Nano and Biomaterials•Jan 1, 2009•0 citations

Dual Shapiro steps and fundamental transconductance in the dc-driven Bloch transistor

A. B. Zorin

We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency $f_J = 2e\overline{V_J}/h$, related to the average transistor voltage $\overline{V_J}$, and Bloch oscillations of frequency $f_B = \overline{I_B}/2e$, related to the average current $\overline{I_B}$ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., $f_J = f_B$. This leads to the formation of a current step on the current-voltage curve at $\overline{I_B} = 2ef_J$, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency $f$ on the current-voltage curve of a small Josephson Junction at current $I=2ef$. Moreover, the Bloch transistor transconductance $\overline{I_B}/\overline{V_J}$ takes the fundamental value of $1/R_Q$, where $R_Q = h/4e^2$ is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.

cond-mat.supr-conCross-listedarXiv:2605.14080•Physical review. B./Physical review. B•May 15, 2026•0 citations

Shapiro Steps Observed in a Superconducting Single Electron Transistor

Saxon Liou, Watson Kuo, Y. W. Suen +3 more

The dc current-voltage (Ⅳ) characteristics of a superconducting single electron transistor irradiated with microwaves up to 18 GHz are experimentally studied. The switching current as a function of gate voltage demonstrates clear phase-charge duality in a Josephson junction. At higher microwave power levels, Shapiro steps in Ⅳ characteristics are observed. The step height in Ⅳ can be analyzed using the model an ac-voltage source applied to a single Josephson junction.

Chinese Journal of Physics•Apr 1, 2007•3 citations

Incoherent microwave-induced resistive states of small Josephson junctions

Yuri Koval, M. V. Fistul, Alexey Vladimirovich Ustinov

We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.

Low Temperature Physics•Oct 1, 2010•2 citations

Demonstration of dual Shapiro steps in small Josephson junctions

Fabian Kaap, Christoph Kissling, Victor Gaydamachenko +2 more

Abstract Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = ± n × 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I ≈ 3 nA. Inspired by today’s voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.

arXiv:2401.06599•Nature Communications•Oct 9, 2024•14 citations
We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency \ensuremathωmw{\ensuremath{\omega}}_{\mathrm{mw}}\ensuremathωmw​. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of e\ensuremathωmw/\ensuremathπe{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}e\ensuremathωmw​/\ensuremathπ in the current-voltage (I\ensuremath-V)(I\text{\ensuremath{-}}V)(I\ensuremath-V) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I\ensuremath-VI\text{\ensuremath{-}}VI\ensuremath-V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.
We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc{V}_{\mathrm{c}}Vc​, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.
I-V characteristics of Josephson junction (JJ) under microwave irradiation is simulated taking the resistance, capacitance and inductance of the junction (RCLSJ) into account. Since most of the JJ made with high TC material operates at high temperature where the thermal fluctuation is playing significant role. In the present simulation, thermal noise is also taken into consideration and simulated result explains the rounding behaviour of the Shapiro step observed in the experimental I-V curve. The simulated results also confirm the growing of Shapiro steps with increasing microwave power. This model also clearly account for the appearance of broad minima and reduction of the maxima in the power dependence of the step amplitude ΔIn/2Ic as observed in the experimental data of Kautz et al. (1992).
We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency fJ=2eVJ‾/hf_J = 2e\overline{V_J}/hfJ​=2eVJ​​/h, related to the average transistor voltage VJ‾\overline{V_J}VJ​​, and Bloch oscillations of frequency fB=IB‾/2ef_B = \overline{I_B}/2efB​=IB​​/2e, related to the average current IB‾\overline{I_B}IB​​ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., fJ=fBf_J = f_BfJ​=fB​. This leads to the formation of a current step on the current-voltage curve at IB‾=2efJ\overline{I_B} = 2ef_JIB​​=2efJ​, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency fff on the current-voltage curve of a small Josephson Junction at current I=2efI=2efI=2ef. Moreover, the Bloch transistor transconductance IB‾/VJ‾\overline{I_B}/\overline{V_J}IB​​/VJ​​ takes the fundamental value of 1/RQ1/R_Q1/RQ​, where RQ=h/4e2R_Q = h/4e^2RQ​=h/4e2 is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.
We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.
Abstract Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = ± n × 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I ≈ 3 nA. Inspired by today’s voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.