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

Power dissipation in an asymmetric superconducting resonator

Albert K. Wandui, B. Steinbach, James J. Bock, Lorenzo Minutolo, Roger C. O'Brient

Published Dec 17, 2025• 0 citations
Publisher

Abstract

Abstract Resonator asymmetry is a common feature in superconducting resonators, often arising from parasitic effects or non-ideal bias conditions in the microwave system. While the effects of asymmetric line shapes on extracting resonator quality factors have been well investigated, the impact of asymmetry on the power dissipation as well as the resonator response to perturbation of resonator properties remains poorly understood. In this paper, we derive the full scattering matrix of an arbitrarily complex reciprocal passive network with a single embedded shunt resonator. We identify a minimal set of approximations that accurately extract the resonator behavior while preserving the relationship between the continuum and resonator modes of the network. The full scattering matrix can be decomposed into the unperturbed continuum, a perturbation to the continuum and the resonant response. The continuum is unperturbed when the resonator is symmetric. Our analysis therefore reveals that resonator asymmetry can significantly affect continuum transmission through the network—an effect that becomes particularly relevant in large resonator arrays. Additionally, using the generalized relationship between S 11 , S 21 , and S 22 , we demonstrate that power dissipation in the resonator is independent of the asymmetry angle. However, the power dissipation is sensitive to the symmetry (even or odd) of the coupling between the resonator and the continuum modes. This approach also provides a framework for modeling dynamic changes in resonator coupling, baseline, and asymmetry in response to variations induced by temperature changes, magnetic fields, applied bias currents and/or optical loading.

DOI
10.1088/1367-2630/ae2e30

Related papers

Nonlinear effects in superconducting thin film microwave resonators

C N Thomas, S Withington, Z Sun +2 more

Abstract We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.

arXiv:2001.02540•New Journal of Physics•May 29, 2020•21 citations

An analysis method for asymmetric resonator transmission applied to superconducting devices

M. S. Khalil, M. J. A. Stoutimore, F. C. Wellstood +1 more

We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that, for certain non-ideal conditions, the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor (Qi), the diameter correction method (DCM), and compare it to the conventional method used for millikelvin resonator measurements, the φ rotation method (φRM). We analytically find that the φRM deterministically overestimates Qi when the asymmetry of the resonance line shape is high, and that this error is eliminated with the DCM. A consistent discrepancy between the two methods is observed when they are used to analyze both simulations from a numerical linear solver and data from asymmetric coplanar superconducting thin-film resonators.

arXiv:1108.3117•Journal of Applied Physics•Mar 1, 2012•281 citations

Nonlinear effects in superconducting thin film microwave resonators

Christopher N. Thomas, S. Withington, Zhixiang Sun +2 more

We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.

•Jun 1, 2020•15 citations

Network modeling of non-ideal superconducting resonator circuits

H. Guan, M Dai, Qing He +5 more

Abstract We originally develop a network analysis method to study the non-ideal superconducting resonator circuits. We model the resonator device by a 3-block serial network, consisting of input feedline, resonator-coupler and output feedline. We show that the resonance curve will be modified if non-negligible discontinuity (reflection) exists at input or output side of the resonator. The extracted resonance parameters (such as coupling quality factor Q c ) from only fitting the transmission deviate from their true values as originally defined in matched impedance conditions, and the deviation depends on a single parameter which includes all the non-ideal effects from the circuits. We prove that the internal quality factor Q i can be accurately extracted from the modified transmission curve by using a very simple graphical method. Our methods and results are quantitatively verified by both simulations and experiments on superconducting microstrip resonators. Comparing to the usual circuit analysis, our network analysis method is more intuitive and easier to understand. It can serve as a general tool to study the non-ideal superconducting resonator circuits.

Superconductor Science and Technology•Apr 16, 2020•12 citations

Suppressing Dissipative Paths in Superconducting Coplanar Waveguide Resonators

J. M. Hornibrook, E.E. Mitchell, D. J. Reilly

The electromagnetic environment can have a significant effect on the resonant line-shape and loadedQ-factor of superconducting coplanar waveguides in the low temperature (<; 100 mK) and low microwave power regime. Here, electromagnetic simulations are used to visualize the electric field strength throughout the resonator environment, highlighting situations in which parasitic modes lead to increased dissipation. Methods used to suppress parasitic coupling include increasing the density of wire bonds and vias, reducing the width of the transmission line (whilst maintaining the characteristic impedance at 50 Ω) and establishing strong grounding to the sample enclosure. The effect of reducing the parasitic coupling on the microwave transmission spectrum is reported.

IEEE Transactions on Applied Superconductivity•Apr 5, 2013•6 citations

An analysis method for transmission measurements of superconducting resonators with applications to quantum-regime dielectric-loss measurements

Chunqing Deng, Martin R. Otto, Adrian Lupaşcu

Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter S21(ω), with ω the excitation frequency, based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of S21(ω). Since the voltage V of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between V and the forward propagating wave voltage Vin+, with the latter being the parameter controlled in experiments. Due to the dependence of the quality factor on voltage, V is not simply proportional to Vin+. We find a self-consistent way to determine the relation between V and Vin+, which employs only the fitting parameters for S21(ω) and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method used for the LC resonator can be generalized to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are closest to the resonance frequency. This Closest Pole and Zero Method is a valuable tool for analyzing physical measurements of high-Q resonators.

arXiv:1304.4533•Journal of Applied Physics•Aug 6, 2013•27 citations
Abstract Resonator asymmetry is a common feature in superconducting resonators, often arising from parasitic effects or non-ideal bias conditions in the microwave system. While the effects of asymmetric line shapes on extracting resonator quality factors have been well investigated, the impact of asymmetry on the power dissipation as well as the resonator response to perturbation of resonator properties remains poorly understood. In this paper, we derive the full scattering matrix of an arbitrarily complex reciprocal passive network with a single embedded shunt resonator. We identify a minimal set of approximations that accurately extract the resonator behavior while preserving the relationship between the continuum and resonator modes of the network. The full scattering matrix can be decomposed into the unperturbed continuum, a perturbation to the continuum and the resonant response. The continuum is unperturbed when the resonator is symmetric. Our analysis therefore reveals that resonator asymmetry can significantly affect continuum transmission through the network—an effect that becomes particularly relevant in large resonator arrays. Additionally, using the generalized relationship between S 11 , S 21 , and S 22 , we demonstrate that power dissipation in the resonator is independent of the asymmetry angle. However, the power dissipation is sensitive to the symmetry (even or odd) of the coupling between the resonator and the continuum modes. This approach also provides a framework for modeling dynamic changes in resonator coupling, baseline, and asymmetry in response to variations induced by temperature changes, magnetic fields, applied bias currents and/or optical loading.
Abstract We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.
We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that, for certain non-ideal conditions, the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor (Qi), the diameter correction method (DCM), and compare it to the conventional method used for millikelvin resonator measurements, the φ rotation method (φRM). We analytically find that the φRM deterministically overestimates Qi when the asymmetry of the resonance line shape is high, and that this error is eliminated with the DCM. A consistent discrepancy between the two methods is observed when they are used to analyze both simulations from a numerical linear solver and data from asymmetric coplanar superconducting thin-film resonators.
We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.
Abstract We originally develop a network analysis method to study the non-ideal superconducting resonator circuits. We model the resonator device by a 3-block serial network, consisting of input feedline, resonator-coupler and output feedline. We show that the resonance curve will be modified if non-negligible discontinuity (reflection) exists at input or output side of the resonator. The extracted resonance parameters (such as coupling quality factor Q c ) from only fitting the transmission deviate from their true values as originally defined in matched impedance conditions, and the deviation depends on a single parameter which includes all the non-ideal effects from the circuits. We prove that the internal quality factor Q i can be accurately extracted from the modified transmission curve by using a very simple graphical method. Our methods and results are quantitatively verified by both simulations and experiments on superconducting microstrip resonators. Comparing to the usual circuit analysis, our network analysis method is more intuitive and easier to understand. It can serve as a general tool to study the non-ideal superconducting resonator circuits.
The electromagnetic environment can have a significant effect on the resonant line-shape and loadedQ-factor of superconducting coplanar waveguides in the low temperature (<; 100 mK) and low microwave power regime. Here, electromagnetic simulations are used to visualize the electric field strength throughout the resonator environment, highlighting situations in which parasitic modes lead to increased dissipation. Methods used to suppress parasitic coupling include increasing the density of wire bonds and vias, reducing the width of the transmission line (whilst maintaining the characteristic impedance at 50 Ω) and establishing strong grounding to the sample enclosure. The effect of reducing the parasitic coupling on the microwave transmission spectrum is reported.
Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter S21(ω), with ω the excitation frequency, based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of S21(ω). Since the voltage V of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between V and the forward propagating wave voltage Vin+, with the latter being the parameter controlled in experiments. Due to the dependence of the quality factor on voltage, V is not simply proportional to Vin+. We find a self-consistent way to determine the relation between V and Vin+, which employs only the fitting parameters for S21(ω) and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method used for the LC resonator can be generalized to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are closest to the resonance frequency. This Closest Pole and Zero Method is a valuable tool for analyzing physical measurements of high-Q resonators.