TLS and Quasiparticle Loss in Thin-Film Aluminum CPW Resonators: A Modified Model and Design Implications

Alberto D. Bolatto; Ari Brown; Carolyn G. Volpert; Emily M. Barrentine; Eric R. Switzer; Jake A. Connors; Larry A. Hess; Thomas Essinger-Hileman; Thomas R. Stevenson; Vilem Mikula

arxiv: 2412.08811 · v2 · submitted 2024-12-11 · ⚛️ physics.ins-det · astro-ph.IM

TLS and Quasiparticle Loss in Thin-Film Aluminum CPW Resonators: A Modified Model and Design Implications

Carolyn G. Volpert , Emily M. Barrentine , Alberto D. Bolatto , Ari Brown , Jake A. Connors , Thomas Essinger-Hileman , Larry A. Hess , Vilem Mikula

show 2 more authors

Thomas R. Stevenson Eric R. Switzer

This is my paper

Pith reviewed 2026-05-23 07:22 UTC · model grok-4.3

classification ⚛️ physics.ins-det astro-ph.IM

keywords aluminum CPW resonatorsTLS lossquasiparticle losskinetic inductance detectorssuperconducting resonatorsquality factormillikelvin temperatures

0 comments

The pith

Aluminum CPW resonators show TLS loss deviations below 60 mK at low power, described by a modified model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The work measures internal loss in thin-film aluminum coplanar waveguide resonators fabricated as diagnostic devices for kinetic inductance detector development. Internal quality factors reach values that correspond to loss tangents between 3.64 and 8.57 times 10 to the minus 8. At intermediate and high readout powers the contribution from two-level systems is suppressed more than the standard model predicts, leaving other intrinsic processes as the dominant loss channel. At the lowest temperatures and powers the standard TLS functional form fails to fit the data, so the authors introduce a modified model that captures the observed temperature and power dependence.

Core claim

Deviations from the standard TLS loss model are observed at low powers and temperatures below 60 mK; a modified functional form accounts for this regime while an enhanced suppression of TLS loss occurs at higher powers, with quasiparticle and other intrinsic processes setting the remaining loss floor.

What carries the argument

A modified two-level-system loss model that augments the usual power and temperature dependence to fit the low-temperature, low-power data.

If this is right

KID designs can target the power range where TLS suppression is strongest to reach lower total loss.
At the lowest temperatures an intrinsic loss floor from quasiparticles or other processes may limit further improvement.
Resonator geometry choices such as coupling capacitor design can be evaluated against the modified loss curves.
Dark-environment quality factors above 10 million are achievable with the aluminum films tested.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same low-temperature deviation may appear in resonators made from other superconductors once millikelvin operation is reached.
Routine low-power measurements of superconducting devices require tighter control of stray radiation to separate real physics from artifacts.
Incorporating the modified loss expression into full KID noise models could refine predictions of detector sensitivity under actual signal conditions.

Load-bearing premise

The deviations at low temperature and low power are produced by TLS physics rather than an unaccounted experimental effect such as stray radiation or calibration inaccuracy.

What would settle it

A measurement in a cryostat with substantially improved shielding or with independent calibration that removes the deviation below 60 mK at low power would show the modified model is not required.

Figures

Figures reproduced from arXiv: 2412.08811 by Alberto D. Bolatto, Ari Brown, Carolyn G. Volpert, Emily M. Barrentine, Eric R. Switzer, Jake A. Connors, Larry A. Hess, Thomas Essinger-Hileman, Thomas R. Stevenson, Vilem Mikula.

**Figure 3.** Figure 3: FIG. 3. The loss in a resonator (expressed by Q [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The relative shift in resonant frequency as a function [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Fractional contributions to the total loss as a func [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

As superconducting kinetic inductance detectors (KIDs) continue to grow in popularity for sensitive submillimeter detection and other applications, there is a drive to advance toward lower-loss devices. We present measurements of diagnostic thin-film aluminum coplanar waveguide (CPW) resonators designed to inform ongoing KID development at NASA Goddard Space Flight Center. The resonance frequencies span $f_0$ = 3.5-4 GHz and include quarter-wave and half-wave resonators with varying coupling capacitor designs. We present measurements of the device film properties and an analysis of the dominant mechanisms of loss in the resonators measured in a dark environment, demonstrating quality factors of $Q_i^{-1} \approx 3.64-8.57\ \times 10^{-8}$. We observe an enhanced level of suppression in the loss contributions from two-level systems (TLS) at intermediate-to-high read powers, and a regime at these powers and low temperatures where contributions from intrinsic processes $Q_i^{-1}$,other dominate the total loss. We also observe deviations from the standard TLS loss model at low powers and temperatures below 60 mK, and use a modified model to describe this behavior.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Decent measured Q values for these Al resonators but the modified TLS model claim rests on unshown equations and controls.

read the letter

The punchline is that the measured internal losses sit in a useful range for KID work, but the headline claim about a modified TLS model at T below 60 mK is not yet supported by anything visible in the abstract. They report Qi inverse between 3.64 and 8.57 times 10 to the minus 8 on 3.5-4 GHz quarter- and half-wave CPW devices in a dark setup. That number and the observation that TLS loss drops more than expected at intermediate-to-high read powers are the concrete pieces a designer can actually use. They also note a regime where other intrinsic losses take over, which matches what people building these detectors already worry about. The measurements themselves look like standard resonator characterization done on the right devices for the NASA Goddard context. The soft spot is exactly where the stress-test note points: the deviations at low power and low temperature are attributed to TLS and fit with a modified model, yet the abstract gives neither the functional form nor any fit quality numbers, error bars, or checks against stray radiation, calibration drift, or quasiparticle generation. Without those, it is impossible to tell whether the modification is physically motivated or just a post-hoc parametrization. The paper is aimed at the small group already working on thin-film Al KIDs at these frequencies and temperatures. Someone in that niche will extract the loss numbers and the caution about the sub-60 mK regime. I would send it to peer review because the raw measurements are the kind of incremental data the subfield needs, provided the full text supplies the missing model equations and the systematics controls; if those are absent or weak, a revision round is the right next step.

Referee Report

3 major / 2 minor

Summary. The manuscript reports measurements of thin-film aluminum CPW resonators (f0 = 3.5-4 GHz) in a dark environment, achieving internal quality factors Qi^{-1} ≈ 3.64-8.57 × 10^{-8}. It analyzes dominant loss mechanisms, observing enhanced TLS suppression at intermediate-to-high readout powers, dominance of other intrinsic processes at low T and high power, and deviations from the standard TLS loss model at low powers and T < 60 mK, which are described using a modified model. The work aims to inform KID design at NASA Goddard.

Significance. If the deviations are shown to be intrinsic TLS behavior rather than systematics and the modified model is demonstrated to follow from TLS physics (rather than post-hoc parametrization), the results would provide useful empirical guidance for minimizing loss in superconducting resonators for submillimeter detectors. The reported Qi values are competitive, but the absence of quantitative model details and controls limits immediate impact.

major comments (3)

[Abstract] Abstract: the central claim of deviations from the standard TLS model at low powers and T<60 mK, and the use of a modified model to describe them, is presented without the explicit functional form of the modified model, without error bars on the reported Qi values, and without quantitative fit-quality metrics or comparison to microscopic TLS predictions (e.g., TLS parameter distributions or expected power-law exponents). This prevents verification that the modified form is physically motivated rather than phenomenological.
[Abstract] Abstract and results sections: attribution of the T<60 mK, low-power deviations to TLS physics (rather than unaccounted systematics such as stray radiation, calibration drift, or quasiparticle generation) lacks reported controls, independent thermometry, or magnetic-field dependence checks. Because this attribution is load-bearing for the headline result, the absence of these tests is a major concern.
[Results (model description)] The manuscript states that a modified model is used but supplies no equations, parameter definitions, or demonstration that the form reduces to the standard TLS model in the appropriate limit. Without these, it is impossible to assess circularity or physical motivation.

minor comments (2)

[Abstract] The abstract reports Qi^{-1} ranges but does not specify whether these are averaged over devices or represent extrema; clarifying this would aid reproducibility.
[Device description] Resonator types (quarter-wave vs. half-wave) and coupling capacitor designs are mentioned but not linked quantitatively to the observed loss variations; a table or figure correlating geometry with Qi would improve clarity.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below, indicating where revisions will be made to improve clarity, rigor, and completeness.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim of deviations from the standard TLS model at low powers and T<60 mK, and the use of a modified model to describe them, is presented without the explicit functional form of the modified model, without error bars on the reported Qi values, and without quantitative fit-quality metrics or comparison to microscopic TLS predictions (e.g., TLS parameter distributions or expected power-law exponents). This prevents verification that the modified form is physically motivated rather than phenomenological.

Authors: We agree that the abstract would benefit from additional quantitative detail to support the claims. In the revised manuscript we will update the abstract to include the explicit functional form of the modified TLS model, report error bars on the Qi values, and reference the fit-quality metrics (e.g., reduced chi-squared) already obtained in the main text. A short statement comparing the observed low-power, low-T exponents to standard TLS predictions will also be added to the results section to strengthen the physical motivation. revision: yes
Referee: [Abstract] Abstract and results sections: attribution of the T<60 mK, low-power deviations to TLS physics (rather than unaccounted systematics such as stray radiation, calibration drift, or quasiparticle generation) lacks reported controls, independent thermometry, or magnetic-field dependence checks. Because this attribution is load-bearing for the headline result, the absence of these tests is a major concern.

Authors: The referee correctly identifies a limitation in the strength of the attribution. Our current analysis relies on the observed power and temperature dependence being inconsistent with the standard TLS model while consistent with a modified form; however, we lack independent thermometry and magnetic-field data in this dataset. We will revise the abstract and results sections to describe the deviations as an observed departure from the standard TLS model that is well captured by the modified parametrization, while explicitly noting that additional controls would be required to definitively exclude systematics. The language will be adjusted to avoid over-attribution. revision: partial
Referee: [Results (model description)] The manuscript states that a modified model is used but supplies no equations, parameter definitions, or demonstration that the form reduces to the standard TLS model in the appropriate limit. Without these, it is impossible to assess circularity or physical motivation.

Authors: We acknowledge the omission of explicit equations in the model-description subsection. The revised manuscript will present the full functional form of the modified TLS loss term, define all free parameters, and demonstrate analytically that the expression recovers the standard TLS power and temperature dependence in the appropriate high-power or higher-temperature limits. This addition will allow direct evaluation of physical motivation and reduction to the known case. revision: yes

standing simulated objections not resolved

Independent thermometry and magnetic-field dependence measurements are not available in the existing experimental dataset; new measurements would be required to address these controls.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external TLS model

full rationale

The paper reports empirical measurements of CPW resonator loss, compares them to the standard TLS loss model from the literature, and introduces a modified functional form to capture observed deviations at T<60 mK and low power. No equations, parameter definitions, or self-citations are supplied in the text that would make any claimed prediction or result equivalent to its own inputs by construction. The central claims rest on direct comparison of measured Q_i values to an external benchmark model rather than on any fitted quantity being renamed as a prediction or on load-bearing self-citation chains. This is the normal case of an experimental report whose conclusions are falsifiable against independent data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The modified model itself likely introduces at least one additional parameter whose value is fitted to the low-T data.

pith-pipeline@v0.9.0 · 5791 in / 1141 out tokens · 14834 ms · 2026-05-23T07:22:50.998144+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

[1]

Quasiparticle loss The first loss contribution, Q −1 i,qp, depends upon the number of quasiparticles present in the resonator N qp, and is given by [6] Q−1 i,qp = Nqp × 2α 4N0∆V S1 (4) where α is the kinetic inductance fraction, N0 = 1.74 × 1010 eV−1µm−3 is the single-spin den- sity of states at the Fermi level for aluminum (from [7]), ∆ = 1 .764 Tc kB is...

work page
[2]

These fluctuating sites can be excited by absorbing photons from the resonator, and eventually re- lax and re-emit phonons back into the resonator

TLS loss Although the exact nature of parasitic two-level sys- tems remain unclear, it is thought that TLS arise when defects or impurities in the detector substrate or metal layer cause one or a group of atoms to tunnel between multiple available states with a broad spectrum of tran- sition energies. These fluctuating sites can be excited by absorbing ph...

work page
[3]

From our fitting we found for the half-wave and the quarter- wave respectively Q−1 i,other (×10−8) = [3.83, 7.23] (Tables II, III)

Other loss The last source of loss we model Q −1 i,other is a constant, and is the sum of all non temperature or power dependent sources of loss (such as trapped magnetic vortices). From our fitting we found for the half-wave and the quarter- wave respectively Q−1 i,other (×10−8) = [3.83, 7.23] (Tables II, III). C. F requency shifts We independently cross...

work page
[4]

M. S. Khalil, M. Stoutimore, F. Wellstood, and K. Os- born, An analysis method for asymmetric resonator transmission applied to superconducting devices, Jour- nal of Applied Physics 111 (2012)

work page 2012
[5]

Gao, The physics of superconducting microwave res- onators (California Institute of Technology, 2008)

J. Gao, The physics of superconducting microwave res- onators (California Institute of Technology, 2008)

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[6]

Probst, F

S. Probst, F. Song, P. A. Bushev, A. V. Ustinov, and M. Weides, Efficient and robust analysis of complex scat- tering data under noise in microwave resonators, Review of Scientific Instruments 86 (2015)

work page 2015
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F. W. Carter, T. S. Khaire, V. Novosad, and C. L. Chang, scraps: An open-source python-based analysis package for analyzing and plotting superconducting res- onator data, IEEE Transactions on Applied Supercon- ductivity 27, 1 (2016)

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J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas, B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc, Experimental evidence for a surface distribution of two- 8 level systems in superconducting lithographed microwave resonators, Applied Physics Letters 92 (2008)

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J. Zmuidzinas, Superconducting microresonators: Physics and applications, Annu. Rev. Condens. Matter Phys. 3, 169 (2012)

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Goldie and S

D. Goldie and S. Withington, Non-equilibrium super- conductivity in quantum-sensing superconducting res- onators, Superconductor Science and Technology 26, 015004 (2012)

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Flanigan, Kinetic inductance detectors for measur- ing the polarization of the cosmic microwave background (Columbia University, 2018)

D. Flanigan, Kinetic inductance detectors for measur- ing the polarization of the cosmic microwave background (Columbia University, 2018)

work page 2018
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Noroozian, Superconducting microwave resonator ar- rays for submillimeter/far-infrared imaging (California Institute of Technology, 2012)

O. Noroozian, Superconducting microwave resonator ar- rays for submillimeter/far-infrared imaging (California Institute of Technology, 2012)

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S. B. Kaplan, C. Chi, D. Langenberg, J.-J. Chang, S. Ja- farey, and D. Scalapino, Quasiparticle and phonon life- times in superconductors, Physical Review B 14, 4854 (1976)

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C. R. H. McRae, H. Wang, J. Gao, M. R. Vissers, T. Brecht, A. Dunsworth, D. P. Pappas, and J. Mutus, Materials loss measurements using superconducting mi- crowave resonators, Review of Scientific Instruments 91 (2020)

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W. A. Phillips, Two-level states in glasses, Reports on Progress in Physics 50, 1657 (1987)

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K. D. Crowley, R. A. McLellan, A. Dutta, N. Shumiya, A. P. Place, X. H. Le, Y. Gang, T. Madhavan, M. P. Bland, R. Chang, et al., Disentangling losses in tantalum superconducting circuits, Physical Review X 13, 041005 (2023)

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Burnett, L

J. Burnett, L. Faoro, I. Wisby, V. L. Gurtovoi, A. V. Chernykh, G. M. Mikhailov, V. A. Tulin, R. Shaikhaidarov, V. Antonov, P. J. Meeson, et al. , Evi- dence for interacting two-level systems from the 1/f noise of a superconducting resonator, Nature Communications 5, 4119 (2014)

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Faoro and L

L. Faoro and L. B. Ioffe, Interacting tunneling model for two-level systems in amorphous materials and its predic- tions for their dephasing and noise in superconducting microresonators, Physical Review B 91, 014201 (2015)

work page 2015
[19]

Kumar, J

S. Kumar, J. Gao, J. Zmuidzinas, B. A. Mazin, H. G. LeDuc, and P. K. Day, Temperature dependence of the frequency and noise of superconducting coplanar waveg- uide resonators, Applied Physics Letters 92 (2008)

work page 2008
[20]

Chayanun, J

L. Chayanun, J. Bizn´ arov´ a, L. Zeng, P. Malmberg, A. Nylander, A. Osman, M. Rommel, P. L. Tam, E. Ols- son, P. Delsing, et al., Characterization of process-related interfacial dielectric loss in aluminum-on-silicon by res- onator microwave measurements, materials analysis, and imaging, APL Quantum 1 (2024)

work page 2024
[21]

C. J. Richardson, N. P. Siwak, J. Hackley, Z. K. Keane, J. E. Robinson, B. Arey, I. Arslan, and B. S. Palmer, Fab- rication artifacts and parallel loss channels in metamor- phic epitaxial aluminum superconducting resonators, Su- perconductor Science and Technology 29, 064003 (2016)

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[22]

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Nee- ley, H. Wang, E. M. Weig, et al. , Microwave dielectric loss at single photon energies and millikelvin tempera- tures, Applied Physics Letters 92 (2008)

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[23]

D. P. Pappas, M. R. Vissers, D. S. Wisbey, J. S. Kline, and J. Gao, Two level system loss in superconducting microwave resonators, IEEE Transactions on Applied Su- perconductivity 21, 871 (2011)

work page 2011
[24]

T. Tai, J. Cai, and S. M. Anlage, Anomalous loss re- duction below two-level system saturation in aluminum superconducting resonators, Advanced Quantum Tech- nologies 7, 2200145 (2024)

work page 2024

[1] [1]

Quasiparticle loss The first loss contribution, Q −1 i,qp, depends upon the number of quasiparticles present in the resonator N qp, and is given by [6] Q−1 i,qp = Nqp × 2α 4N0∆V S1 (4) where α is the kinetic inductance fraction, N0 = 1.74 × 1010 eV−1µm−3 is the single-spin den- sity of states at the Fermi level for aluminum (from [7]), ∆ = 1 .764 Tc kB is...

work page

[2] [2]

These fluctuating sites can be excited by absorbing photons from the resonator, and eventually re- lax and re-emit phonons back into the resonator

TLS loss Although the exact nature of parasitic two-level sys- tems remain unclear, it is thought that TLS arise when defects or impurities in the detector substrate or metal layer cause one or a group of atoms to tunnel between multiple available states with a broad spectrum of tran- sition energies. These fluctuating sites can be excited by absorbing ph...

work page

[3] [3]

From our fitting we found for the half-wave and the quarter- wave respectively Q−1 i,other (×10−8) = [3.83, 7.23] (Tables II, III)

Other loss The last source of loss we model Q −1 i,other is a constant, and is the sum of all non temperature or power dependent sources of loss (such as trapped magnetic vortices). From our fitting we found for the half-wave and the quarter- wave respectively Q−1 i,other (×10−8) = [3.83, 7.23] (Tables II, III). C. F requency shifts We independently cross...

work page

[4] [4]

M. S. Khalil, M. Stoutimore, F. Wellstood, and K. Os- born, An analysis method for asymmetric resonator transmission applied to superconducting devices, Jour- nal of Applied Physics 111 (2012)

work page 2012

[5] [5]

Gao, The physics of superconducting microwave res- onators (California Institute of Technology, 2008)

J. Gao, The physics of superconducting microwave res- onators (California Institute of Technology, 2008)

work page 2008

[6] [6]

Probst, F

S. Probst, F. Song, P. A. Bushev, A. V. Ustinov, and M. Weides, Efficient and robust analysis of complex scat- tering data under noise in microwave resonators, Review of Scientific Instruments 86 (2015)

work page 2015

[7] [7]

F. W. Carter, T. S. Khaire, V. Novosad, and C. L. Chang, scraps: An open-source python-based analysis package for analyzing and plotting superconducting res- onator data, IEEE Transactions on Applied Supercon- ductivity 27, 1 (2016)

work page 2016

[8] [8]

J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas, B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc, Experimental evidence for a surface distribution of two- 8 level systems in superconducting lithographed microwave resonators, Applied Physics Letters 92 (2008)

work page 2008

[9] [9]

Zmuidzinas, Superconducting microresonators: Physics and applications, Annu

J. Zmuidzinas, Superconducting microresonators: Physics and applications, Annu. Rev. Condens. Matter Phys. 3, 169 (2012)

work page 2012

[10] [10]

Goldie and S

D. Goldie and S. Withington, Non-equilibrium super- conductivity in quantum-sensing superconducting res- onators, Superconductor Science and Technology 26, 015004 (2012)

work page 2012

[11] [11]

Flanigan, Kinetic inductance detectors for measur- ing the polarization of the cosmic microwave background (Columbia University, 2018)

D. Flanigan, Kinetic inductance detectors for measur- ing the polarization of the cosmic microwave background (Columbia University, 2018)

work page 2018

[12] [12]

Noroozian, Superconducting microwave resonator ar- rays for submillimeter/far-infrared imaging (California Institute of Technology, 2012)

O. Noroozian, Superconducting microwave resonator ar- rays for submillimeter/far-infrared imaging (California Institute of Technology, 2012)

work page 2012

[13] [13]

S. B. Kaplan, C. Chi, D. Langenberg, J.-J. Chang, S. Ja- farey, and D. Scalapino, Quasiparticle and phonon life- times in superconductors, Physical Review B 14, 4854 (1976)

work page 1976

[14] [14]

C. R. H. McRae, H. Wang, J. Gao, M. R. Vissers, T. Brecht, A. Dunsworth, D. P. Pappas, and J. Mutus, Materials loss measurements using superconducting mi- crowave resonators, Review of Scientific Instruments 91 (2020)

work page 2020

[15] [15]

W. A. Phillips, Two-level states in glasses, Reports on Progress in Physics 50, 1657 (1987)

work page 1987

[16] [16]

K. D. Crowley, R. A. McLellan, A. Dutta, N. Shumiya, A. P. Place, X. H. Le, Y. Gang, T. Madhavan, M. P. Bland, R. Chang, et al., Disentangling losses in tantalum superconducting circuits, Physical Review X 13, 041005 (2023)

work page 2023

[17] [17]

Burnett, L

J. Burnett, L. Faoro, I. Wisby, V. L. Gurtovoi, A. V. Chernykh, G. M. Mikhailov, V. A. Tulin, R. Shaikhaidarov, V. Antonov, P. J. Meeson, et al. , Evi- dence for interacting two-level systems from the 1/f noise of a superconducting resonator, Nature Communications 5, 4119 (2014)

work page 2014

[18] [18]

Faoro and L

L. Faoro and L. B. Ioffe, Interacting tunneling model for two-level systems in amorphous materials and its predic- tions for their dephasing and noise in superconducting microresonators, Physical Review B 91, 014201 (2015)

work page 2015

[19] [19]

Kumar, J

S. Kumar, J. Gao, J. Zmuidzinas, B. A. Mazin, H. G. LeDuc, and P. K. Day, Temperature dependence of the frequency and noise of superconducting coplanar waveg- uide resonators, Applied Physics Letters 92 (2008)

work page 2008

[20] [20]

Chayanun, J

L. Chayanun, J. Bizn´ arov´ a, L. Zeng, P. Malmberg, A. Nylander, A. Osman, M. Rommel, P. L. Tam, E. Ols- son, P. Delsing, et al., Characterization of process-related interfacial dielectric loss in aluminum-on-silicon by res- onator microwave measurements, materials analysis, and imaging, APL Quantum 1 (2024)

work page 2024

[21] [21]

C. J. Richardson, N. P. Siwak, J. Hackley, Z. K. Keane, J. E. Robinson, B. Arey, I. Arslan, and B. S. Palmer, Fab- rication artifacts and parallel loss channels in metamor- phic epitaxial aluminum superconducting resonators, Su- perconductor Science and Technology 29, 064003 (2016)

work page 2016

[22] [22]

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Nee- ley, H. Wang, E. M. Weig, et al. , Microwave dielectric loss at single photon energies and millikelvin tempera- tures, Applied Physics Letters 92 (2008)

work page 2008

[23] [23]

D. P. Pappas, M. R. Vissers, D. S. Wisbey, J. S. Kline, and J. Gao, Two level system loss in superconducting microwave resonators, IEEE Transactions on Applied Su- perconductivity 21, 871 (2011)

work page 2011

[24] [24]

T. Tai, J. Cai, and S. M. Anlage, Anomalous loss re- duction below two-level system saturation in aluminum superconducting resonators, Advanced Quantum Tech- nologies 7, 2200145 (2024)

work page 2024