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

New Journal of Physics

A general characterization method for nonlinearities in superconducting circuits

Thomas Weißl, Shan W. Jolin, Riccardo Borgani, Daniel Forchheimer, David B. Haviland

Published Apr 9, 2019• 2 citations
Publisher

Abstract

Abstract Detailed knowledge of nonlinearity in superconducting microwave circuits is required for the optimal control of their quantum state. We present a general method to precisely characterize this nonlinearity to very high order. Our method is based on intermodulation spectroscopy at microwave frequencies and does not require DC-connection or DC-measurement of an on-chip reference structure. We give a theoretical derivation of the method and we validate it by reconstructing a known nonlinearity from simulated data. We experimentally demonstrate the reconstruction of the unknown nonlinear current-phase relation of a microwave resonator with superconducting nanowires.

DOI
10.1088/1367-2630/ab175a

Related papers

Intermodulation spectroscopy and the nonlinear response of two-level systems in superconducting coplanar-waveguide resonators

Janka Biznárová, J. C. Rivera Hernández, Daniel Forchheimer +3 more

Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs. Published by the American Physical Society 2024

arXiv:2402.10775•Physical Review Applied•Jul 24, 2024•2 citations

Imaging of microwave intermodulation fields in a superconducting microstrip resonator

Wensheng Hu, Ashfaq S. Thanawalla, B. Johan Feenstra +2 more

Nonlinearities give rise to intermodulation distortion in superconducting microwave devices and currently limit their use to low power applications. We have developed a cryogenic imaging technique to spatially resolve intermodulation distortion and used it to image an 8.2 GHz high temperature superconducting Tl2Ba2CaCu2O8 microwave resonator. The images reveal that the fundamental and intermodulation electric fields obey a fixed relation throughout the device. We note that further refinements of intermodulation theory in resonant devices may be required to fully describe the data.

Applied Physics Letters•Nov 1, 1999•22 citations

In situ tunable nonlinearity and competing signal paths in coupled superconducting resonators

Michael Fischer, Qiming Chen, Christian Besson +10 more

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc superconducting quantum interference devices. We simulate the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents a basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

arXiv:2009.13492•Physical review. B./Physical review. B•Mar 24, 2021•6 citations

Local Broadband Gigahertz Spectroscopy via SQUID-on-Tip DC Readout

Senne Vervoort, Lukas Nulens, Julia Baumgarten +5 more

Superconducting microwave circuits are shaped by their local electromagnetic environment, yet standard microwave measurements do not resolve the local fields and device features that govern their behavior. Here, we combine microwave spectroscopy, nanoscale magnetic sensing, and topographic imaging in a single tapping-mode SQUID-on-tip microscope. The nonlinear Josephson response converts local GHz excitations into Shapiro steps, enabling quantitative measurements of microwave frequency signals and their excitation strength using only DC readout. Applied to a superconducting coplanar waveguide resonator, local spectroscopy reproduces the power-dependent resonance and nonlinear bifurcation observed in microwave transmission measurements. Spatially resolved measurements map the microwave response while simultaneously recording topography and static magnetic features, including vortices and Meissner screening currents. Electromagnetic simulations reveal how coupling through the superconducting probe leads limits spatial resolution and guides localized detector designs. Together, these capabilities establish a platform for correlating microwave circuit dynamics with the local structural and magnetic environment of superconducting devices.

arXiv:2610.35737•Oct 26, 2026•0 citations

Superconducting Microwave Resonators for Hybrid Quantum Systems in Extreme Conditions

Benedikt Wilde

Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.

•Mar 6, 2026•0 citations

Intermodulation measurements in Nb superconducting microstrip resonators

R. Monaco, A. Andreone, F. Palomba

The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.

Journal of Applied Physics•Sep 1, 2000•23 citations
Abstract Detailed knowledge of nonlinearity in superconducting microwave circuits is required for the optimal control of their quantum state. We present a general method to precisely characterize this nonlinearity to very high order. Our method is based on intermodulation spectroscopy at microwave frequencies and does not require DC-connection or DC-measurement of an on-chip reference structure. We give a theoretical derivation of the method and we validate it by reconstructing a known nonlinearity from simulated data. We experimentally demonstrate the reconstruction of the unknown nonlinear current-phase relation of a microwave resonator with superconducting nanowires.
Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs. Published by the American Physical Society 2024
Nonlinearities give rise to intermodulation distortion in superconducting microwave devices and currently limit their use to low power applications. We have developed a cryogenic imaging technique to spatially resolve intermodulation distortion and used it to image an 8.2 GHz high temperature superconducting Tl2Ba2CaCu2O8 microwave resonator. The images reveal that the fundamental and intermodulation electric fields obey a fixed relation throughout the device. We note that further refinements of intermodulation theory in resonant devices may be required to fully describe the data.
We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc superconducting quantum interference devices. We simulate the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents a basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.
Superconducting microwave circuits are shaped by their local electromagnetic environment, yet standard microwave measurements do not resolve the local fields and device features that govern their behavior. Here, we combine microwave spectroscopy, nanoscale magnetic sensing, and topographic imaging in a single tapping-mode SQUID-on-tip microscope. The nonlinear Josephson response converts local GHz excitations into Shapiro steps, enabling quantitative measurements of microwave frequency signals and their excitation strength using only DC readout. Applied to a superconducting coplanar waveguide resonator, local spectroscopy reproduces the power-dependent resonance and nonlinear bifurcation observed in microwave transmission measurements. Spatially resolved measurements map the microwave response while simultaneously recording topography and static magnetic features, including vortices and Meissner screening currents. Electromagnetic simulations reveal how coupling through the superconducting probe leads limits spatial resolution and guides localized detector designs. Together, these capabilities establish a platform for correlating microwave circuit dynamics with the local structural and magnetic environment of superconducting devices.
Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.
The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.