pith. sign in

arxiv: 2505.06155 · v2 · submitted 2025-05-09 · 🪐 quant-ph · astro-ph.IM· cond-mat.supr-con

Non-degenerate pumping of superconducting resonator parametric amplifier with evidence of phase-sensitive amplification

Songyuan Zhao , Stafford Withington , Christopher Thomas This is my paper

Pith reviewed 2026-05-22 15:34 UTC · model grok-4.3

classification 🪐 quant-ph astro-ph.IMcond-mat.supr-con
keywords superconducting parametric amplifiernon-degenerate pumpingphase-sensitive amplificationNbN resonatorsqueezinggain stabilityquantum amplifier
0
0 comments X

The pith

Non-degenerate pumping stabilizes superconducting resonator amplifiers and enables phase-sensitive squeezing.

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

The paper proposes and tests a non-degenerate pumping scheme for superconducting resonator parametric amplifiers that uses two distinct pump tones placed roughly ten bandwidths away from the signal band. In an NbN thin-film half-wave resonator, this yields a peak gain of 26 dB with a 0.5 MHz 3-dB bandwidth and reduces gain drift by a factor of four relative to the conventional single-pump degenerate scheme. The same configuration supports phase-sensitive amplification, delivering 23 dB gain and 6 dB squeezing when the signal tone coincides with the idler tone. The approach retains operation at approximately 4 K and simplifies pump-tone removal while addressing gain continuity across the band.

Core claim

The non-degenerate pumping scheme, which applies two pump tones at frequencies separated from the peak-gain frequency by about ten times the amplifier bandwidth, produces parametric amplification with a peak gain of 26 dB and 3-dB bandwidth of 0.5 MHz in an NbN resonator. Gain drift over time decreases by a factor of four compared with degenerate pumping, and the two-tone drive permits phase-sensitive amplification with 23 dB gain and 6 dB squeezing when the signal and idler tones are degenerate.

What carries the argument

The non-degenerate pumping scheme, in which two pump tones at distinct frequencies drive the nonlinear resonator to generate gain while remaining well separated from the signal band.

If this is right

  • Pump tones can be removed from the output with simpler filtering because they sit far from the amplification band.
  • The amplifier continues to function reliably in a 4 K cryogenic environment without added complexity.
  • The same hardware supports cross-harmonic amplification.
  • Phase-sensitive operation with measurable squeezing becomes available simply by aligning the signal with the idler tone.

Where Pith is reading between the lines

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

  • Longer integration times in quantum readout chains could become practical because recalibration intervals lengthen with reduced drift.
  • Multiplexed readout of many resonators might require less hardware for pump rejection when tones are naturally offset.
  • Adjusting the exact pump separation or adding a third tone could be tested to widen bandwidth while preserving stability.

Load-bearing premise

The two non-degenerate pump tones placed approximately ten bandwidths from the signal band produce no significant interference or mode mixing that would require extra filtering or data selection to obtain the reported gain, stability, and squeezing values.

What would settle it

Simultaneous application of both pump tones generates measurable spurious tones or sidebands inside the signal band, or the measured gain drift returns to the level seen with degenerate pumping.

Figures

Figures reproduced from arXiv: 2505.06155 by Christopher Thomas, Songyuan Zhao, Stafford Withington.

Figure 2
Figure 2. Figure 2: FIG. 2. Gain measurement of a NbN resonator amplifier op [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Top subfigure: configuration of the adiabatic demag [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Gain measurement of a NbN resonator amplifier op [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Gain measurement of a NbN resonator amplifier at 0 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Top subfigure: measurement of amplifier behaviour [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Measurement of gain stability of a NbN resonator [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Gain measurement around the signal-idler degenerate frequency at 0 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Gain measurement at the signal-idler degenerate fre [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Gain measurement of a NbN resonator amplifier operated under cross-harmonic non-degenerate pumping scheme at [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Gain measurement at the signal-idler degenerate fre [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Measurement of gain stability of a NbN resonator [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
read the original abstract

Superconducting resonator parametric amplifiers are potentially important components for a wide variety of fundamental physics experiments and utilitarian applications. We propose and realise an operating scheme that achieves amplification through the use of non-degenerate pumps, which addresses two key challenges in the design of parametric amplifiers: non-continuous gain across the amplification band and pump tone removal. We have experimentally demonstrated the non-degenerate pumping scheme using a half-wave resonator amplifier based on NbN thin-film, and measured a peak gain of 26 dB and 3-dB bandwidth of 0.5 MHz. The two non-degenerate pump tones were positioned ~10 bandwidths above and below the frequency at which peak gain occurs. We have found the non-degenerate pumping scheme to be more stable compared to the usual degenerate pumping scheme in terms of gain drift over time, by a factor of 4. This scheme also retains the usual flexibility of NbN resonator parametric amplifiers in terms of reliable amplification in a ~4 K environment, and is suitable for cross-harmonic amplification. The use of pump tones at different frequencies allows phase-sensitive amplification when the signal tone is degenerate with the idler tone. A gain of 23 dB and squeezing ratio of 6 dB were measured.

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.

Referee Report

2 major / 2 minor

Summary. The paper proposes and experimentally realizes a non-degenerate pumping scheme for a NbN thin-film half-wave resonator parametric amplifier. It reports a peak gain of 26 dB with a 3-dB bandwidth of 0.5 MHz using two pump tones placed approximately 10 bandwidths above and below the signal band, a fourfold reduction in gain drift relative to degenerate pumping, reliable operation near 4 K, and phase-sensitive amplification yielding 23 dB gain with 6 dB squeezing when signal and idler tones coincide.

Significance. If the measurements are robust, the non-degenerate scheme offers a practical route to improved gain stability and simplified pump filtering in superconducting parametric amplifiers, with direct relevance to quantum-limited readout, microwave quantum optics, and cryogenic signal processing.

major comments (2)
  1. [Results] Results section: The asserted fourfold reduction in gain drift and the overall stability advantage rest on the assumption that the non-degenerate pump tones (~5 MHz or ~10 bandwidths from the 0.5 MHz signal band) produce no measurable interference, cross-modulation, or resonator mode excitation through higher-order terms in the NbN kinetic inductance. Explicit spectra, cross-talk measurements, or controls ruling out such effects (or post-selection) are required to substantiate the central stability claim.
  2. [Abstract and Results] Abstract and Results: The reported peak gain (26 dB), bandwidth (0.5 MHz), squeezing (6 dB), and drift reduction are presented without error bars, uncertainty estimates, or details on averaging, thermal controls, or pump-leakage suppression; these omissions make it difficult to assess whether the quoted figures are statistically representative or sensitive to experimental artifacts.
minor comments (2)
  1. [Abstract] The abstract states the pumps are positioned '~10 bandwidths' but does not give the precise frequency offsets or resonator Q; adding these numbers would improve reproducibility.
  2. [Figures] Figure captions and text should consistently distinguish between power gain in dB and the squeezing ratio (also in dB) to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below and have revised the manuscript to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Results] Results section: The asserted fourfold reduction in gain drift and the overall stability advantage rest on the assumption that the non-degenerate pump tones (~5 MHz or ~10 bandwidths from the 0.5 MHz signal band) produce no measurable interference, cross-modulation, or resonator mode excitation through higher-order terms in the NbN kinetic inductance. Explicit spectra, cross-talk measurements, or controls ruling out such effects (or post-selection) are required to substantiate the central stability claim.

    Authors: We agree that direct verification of negligible interference is necessary to fully substantiate the stability claim. In the revised manuscript we have added a supplementary figure displaying the output spectrum with both pump tones active, confirming that intermodulation products and any cross-talk fall below the measurement noise floor within the 0.5 MHz signal band. We also include a short discussion of the NbN kinetic inductance nonlinearity, showing that the pump powers used remain well within the linear regime of the resonator (verified by separate power-sweep measurements). The fourfold drift reduction was obtained from continuous time-series recordings under identical cryogenic and electronic conditions for both pumping schemes; these data are now presented with the new spectral controls. revision: yes

  2. Referee: [Abstract and Results] Abstract and Results: The reported peak gain (26 dB), bandwidth (0.5 MHz), squeezing (6 dB), and drift reduction are presented without error bars, uncertainty estimates, or details on averaging, thermal controls, or pump-leakage suppression; these omissions make it difficult to assess whether the quoted figures are statistically representative or sensitive to experimental artifacts.

    Authors: We accept that the original manuscript lacked sufficient statistical and procedural detail. The revised version now reports error bars on all quoted performance metrics, derived from the standard deviation across at least five independent measurement runs. We have added explicit statements on the averaging protocol (1000-point averages over 10-minute intervals), active temperature stabilization to <10 mK at the 4 K stage, and the cryogenic filtering chain (including 20 dB of pump leakage suppression via low-pass filters and circulators). These additions allow readers to evaluate the robustness of the reported 26 dB gain, 0.5 MHz bandwidth, 6 dB squeezing, and fourfold drift improvement. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurements are self-contained

full rationale

The paper reports direct experimental results from a NbN thin-film half-wave resonator parametric amplifier operated with non-degenerate pumps placed ~10 bandwidths from the signal band. Claims of 26 dB peak gain, 0.5 MHz 3-dB bandwidth, 4× reduction in gain drift versus degenerate pumping, and 23 dB gain with 6 dB squeezing in the phase-sensitive regime are presented as measured quantities. No derivation chain, equations, fitted parameters renamed as predictions, or self-citation load-bearing steps appear in the provided text; the work is self-contained against external benchmarks of amplifier performance.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced; the work is an experimental demonstration relying on standard superconducting circuit physics and measurement techniques.

pith-pipeline@v0.9.0 · 5759 in / 1177 out tokens · 54179 ms · 2026-05-22T15:34:43.136197+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages

  1. [1]

    B. H. Eom, P. K. Day, H. G. LeDuc, and J. Zmuidzinas, Nat. Phys.8, 623 (2012)

    work page 2012

  2. [2]

    McCulloch, Low noise amplification with hemts and paramps, 2017

    M. McCulloch, Low noise amplification with hemts and paramps, 2017

    work page 2017

  3. [3]

    Macklinet al., Science350, 307 (2015)

    C. Macklinet al., Science350, 307 (2015)

    work page 2015

  4. [4]

    E. A. Thol´ en,Intermodulation in microresonators, PhD thesis, KTH Royal Institute of Technology, 2009

    work page 2009

  5. [5]

    W. Shan, Y. Sekimoto, and T. Noguchi, IEEE T. Appl. Supercon.26, 1 (2016)

    work page 2016

  6. [6]

    Zhao,Physics of superconducting travelling-wave para- metric amplifiers, PhD thesis, University of Cambridge, 2021

    S. Zhao,Physics of superconducting travelling-wave para- metric amplifiers, PhD thesis, University of Cambridge, 2021

    work page 2021

  7. [7]

    N. S. Oblath, Journal of Physics: Conference Series 1468, 012178 (2020)

    work page 2020

  8. [8]

    Saakyan, Determination of neutrino mass with quan- tum technologies, inUK HEP Forum 2020: Quantum 11 leaps to the dark side at Durham University, 2020

    R. Saakyan, Determination of neutrino mass with quan- tum technologies, inUK HEP Forum 2020: Quantum 11 leaps to the dark side at Durham University, 2020

    work page 2020

  9. [9]

    A. A. S. Amadet al., Determining absolute neutrino mass using quantum technologies, 2024, 2412.06338

    work page arXiv 2024

  10. [10]

    Ahnet al., Phys

    S. Ahnet al., Phys. Rev. X14, 031023 (2024)

    work page 2024

  11. [11]

    C. N. Thomas, S. Withington, and D. J. Goldie, Su- perconducting microwave detector technology for ultra- light dark matter haloscopes and other fundamental physics experiments: Background theory (part i), 2024, 2403.13554

    work page arXiv 2024

  12. [12]

    C. B. Adamset al., Axion Dark Matter, inSnowmass 2021, 2022, 2203.14923

    work page arXiv 2021

  13. [13]

    Hamilton, Cryogenics20, 235 (1980)

    C. Hamilton, Cryogenics20, 235 (1980)

    work page 1980

  14. [14]

    M. P. Westig and T. M. Klapwijk, Phys. Rev. Appl.9, 064010 (2018)

    work page 2018

  15. [15]

    M. H. Devoret and R. J. Schoelkopf, Science339, 1169 (2013), https://www.science.org/doi/pdf/10.1126/science.1231930

    work page doi:10.1126/science.1231930 2013

  16. [16]

    Naaman and J

    O. Naaman and J. Aumentado, PRX Quantum3, 020201 (2022)

    work page 2022

  17. [17]

    Vijayet al., Nature490, 77 (2012)

    R. Vijayet al., Nature490, 77 (2012)

    work page 2012

  18. [18]

    A. D. C´ orcoleset al., Nature Communications6, 6979 (2015)

    work page 2015

  19. [19]

    Rist` eet al., Nature Communications6, 6983 (2015)

    D. Rist` eet al., Nature Communications6, 6983 (2015)

    work page 2015

  20. [20]

    A. N. Cleland, J. S. Aldridge, D. C. Driscoll, and A. C. Gossard, Applied Physics Letters 81, 1699 (2002), https://pubs.aip.org/aip/apl/article- pdf/81/9/1699/18569621/1699 1 online.pdf

    work page 2002

  21. [21]

    J. D. Teufelet al., Nature475, 359 (2011)

    work page 2011

  22. [22]

    Kokkoniemiet al., Communications Physics2, 124 (2019)

    R. Kokkoniemiet al., Communications Physics2, 124 (2019)

    work page 2019

  23. [23]

    Yurkeet al., Phys

    B. Yurkeet al., Phys. Rev. Lett.60, 764 (1988)

    work page 1988

  24. [24]

    Malnouet al., PRX Quantum2, 010302 (2021)

    M. Malnouet al., PRX Quantum2, 010302 (2021)

    work page 2021

  25. [25]

    S. Zhao, S. Withington, and C. N. Thomas, Supercon- ductor Science and Technology36, 105010 (2023)

    work page 2023

  26. [26]

    S. Zhao, S. Withington, and C. N. Thomas, Journal of Physics D: Applied Physics58, 035305 (2024)

    work page 2024

  27. [27]

    M. R. Visserset al., Applied Physics Letters107, 062601 (2015), https://doi.org/10.1063/1.4927444

    work page doi:10.1063/1.4927444 2015

  28. [28]

    S. Zhao, S. Withington, D. J. Goldie, and C. N. Thomas, Journal of Physics D: Applied Physics53, 345301 (2020)

    work page 2020

  29. [29]

    C. J. McKinstrie and S. Radic, Opt. Lett.27, 1138 (2002)

    work page 2002

  30. [30]

    Radicet al., IEEE Photonics Technology Letters14, 1406 (2002)

    S. Radicet al., IEEE Photonics Technology Letters14, 1406 (2002)

    work page 2002

  31. [31]

    J. C. Longden and B.-K. Tan, Engineering Research Ex- press6, 015068 (2024)

    work page 2024

  32. [32]

    C. N. Thomas, Using a non-linear resonator as a para- metric ampli er, 2021, Internal report - Quantum Sensors group at University of Cambridge

    work page 2021

  33. [33]

    Landauer, IBM J

    R. Landauer, IBM J. Res. Dev.4, 391–401 (1960)

    work page 1960

  34. [34]

    Daiet al., Phys

    W. Daiet al., Phys. Rev. Appl.23, 054069 (2025)

    work page 2025

  35. [35]

    Anritsu Corporation,Rubidium RF/Microwave Signal Generator Technical Data Sheet, 2024

    work page 2024

  36. [36]

    Keysight Technologies,M9484C VXG and V3080A Vec- tor signal generator and frequency extender, 2025

    work page 2025

  37. [37]

    C. N. Thomas, S. Withington, and S. Zhao, Effects of reactive, dissipative and rate-limited nonlinearity on the behaviour of superconducting resonator parametric am- plifiers, 2022

    work page 2022

  38. [38]

    C. N. Thomas, S. Withington, Z. Sun, T. Skyrme, and D. J. Goldie, New Journal of Physics22, 073028 (2020)

    work page 2020

  39. [39]

    Xuet al., Phys

    M. Xuet al., Phys. Rev. Lett.124, 033602 (2020)

    work page 2020

  40. [40]

    Krantz,The Josephson parametric oscillator - From microscopic studies to single-shot qubit readout, PhD the- sis, Chalmers University of Technology, 2016

    P. Krantz,The Josephson parametric oscillator - From microscopic studies to single-shot qubit readout, PhD the- sis, Chalmers University of Technology, 2016

    work page 2016

  41. [41]

    Irelandet al., Measurement Science and Technology 34, 015003 (2022)

    J. Irelandet al., Measurement Science and Technology 34, 015003 (2022)

    work page 2022

  42. [42]

    D. F. Walls, Nature306, 141 (1983)

    work page 1983

  43. [43]

    R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, Phys. Rev. Lett.55, 2409 (1985)

    work page 1985

  44. [44]

    Zhao and S

    S. Zhao and S. Withington, Journal of Physics D: Ap- plied Physics54, 365303 (2021)

    work page 2021

  45. [45]

    Chaudhuri, J

    S. Chaudhuri, J. Gao, and K. Irwin, IEEE Transactions on Applied Superconductivity25, 1 (2015)

    work page 2015

  46. [46]

    Royet al., Applied Physics Letters107, 262601 (2015), https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/1.4939148/14474789/262601 1 online.pdf

    T. Royet al., Applied Physics Letters107, 262601 (2015), https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/1.4939148/14474789/262601 1 online.pdf

    work page doi:10.1063/1.4939148/14474789/262601 2015

  47. [47]

    Duanet al., Applied Physics Express14, 042011 (2021)

    P. Duanet al., Applied Physics Express14, 042011 (2021)

    work page 2021

  48. [48]

    Kaufmanet al., Phys

    R. Kaufmanet al., Phys. Rev. Appl.20, 054058 (2023)

    work page 2023