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arxiv: 2505.14292 · v3 · pith:YDO5CV2Znew · submitted 2025-05-20 · 🪐 quant-ph

Waveguides in a quantum perspective

Eddy Collin , Alexandre Delattre This is my paper

Pith reviewed 2026-05-22 14:26 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum waveguidesTM modeszero-point fluctuationsquantum noisegauge fixingdispersion relationssuperconducting waveguidesmicrowave quantum optics
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The pith

Lowest transverse magnetic modes in quantum waveguides exhibit smaller zero-point fluctuations than higher modes or other families.

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

The paper develops a complete quantum description of traveling electromagnetic waves in the simplest Cartesian waveguide geometries, parallel plates and rectangular tubes. It introduces a gauge choice that extends the concept of potential difference across all mode families, positioning the generalized flux as the scalar field conjugate to charge that confines the light. Dispersion gaps for non-TEM modes are interpreted as either a potential energy of confinement or a kinetic energy tied to an effective photon mass. Zero-point field fluctuations are calculated explicitly for each family. The central prediction follows that the lowest TM modes carry reduced quantum noise, while higher TM modes recover the conventional fluctuation level at large wavevectors, matching TEM and TE behavior.

Core claim

The paper claims that a gauge-fixed quantum theory of waveguides makes the generalized flux φ the conjugate variable to charge Q for all mode families. This unifies the description of TEM, TE, and TM waves, links dispersion gaps to confinement or mass effects, and yields the result that the lowest TM modes possess smaller zero-point fluctuations in the electromagnetic fields than higher modes, which approach the standard quantum value at short wavelengths similar to TEM and TE modes.

What carries the argument

The generalized flux φ, obtained via specific gauge fixing, serving as the scalar field conjugate to charge Q that confines light within real or virtual electrodes.

If this is right

  • The lowest TM modes should display measurably smaller quantum noise than higher TM modes or conventional TEM and TE modes.
  • At large wavevectors, noise in all higher modes converges to the same conventional value independent of polarization.
  • These low-noise TM modes could be selected for routing quantum signals between cryogenic devices with reduced added noise.
  • The theory supplies explicit formulas for computing fluctuations in each mode family for design purposes.

Where Pith is reading between the lines

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

  • Implementation of the lowest TM modes in superconducting circuits might reduce decoherence during quantum information transfer.
  • The photon-mass interpretation of dispersion gaps could be tested by comparing propagation characteristics across different guide dimensions.
  • Similar gauge-based quantization might apply to waveguides with more complex cross-sections used in quantum microwave networks.

Load-bearing premise

The specific gauge fixing that extends potential difference from TEM waves to all mode families and identifies the generalized flux φ as the scalar conjugate to charge Q.

What would settle it

A measurement of electric or magnetic field zero-point fluctuations in the lowest TM mode of a superconducting parallel-plate or rectangular waveguide at millikelvin temperatures that shows noise levels below those measured in the corresponding TEM or TE modes at the same frequency.

Figures

Figures reproduced from arXiv: 2505.14292 by Alexandre Delattre, Eddy Collin.

Figure 1
Figure 1. Figure 1: a) Parallel plates transmission line. b) Rectangular transmission line. The electromagnetic field is enclosed within the colored surfaces: real electrodes in blue, and virtual ones in green. The width is w, height d and length L. We name the electrodes t (top), b (bottom), l (left) and r (right). Positive direction of propagation: ⃗z. TM waves, and a photon mass for TE. In the latter case, the Hamiltonian … view at source ↗
Figure 2
Figure 2. Figure 2: TMn,m wave electric field quantum fluctuations Em normalized to Ezpf as a function of wavevector number l, for branch n = 1, m = 1. We chose for the plot w = d and l = 100 d. Asymptotes are ∼ 0.02 at l = 1 and √ 2 at l → +∞. our common definition of zero-point fluctuations, here in Volts.seconds. It can be re￾expressed in terms of the electric field amplitude Em (or the magnetic field Bm = Em/c): Em = s ℏ … view at source ↗
read the original abstract

Solid state quantum devices, operated at dilution cryostat temperatures, are relying on microwave signals to both drive and read-out their quantum states. These signals are transmitted into the cryogenic environment, out of it towards detection devices, or even between quantum systems by well-designed waveguides, almost lossless when made of superconducting materials. Here we report on the quantum theory that describes the simplest Cartesian-type geometries: parallel plates, and rectangular tubes. The aim of the article is twofold: first on a technical and pragmatic level, we provide a full and compact quantum description of the different traveling wave families supported by these guides. Second, on an ontological level, we interpret the results and discuss the nature of the light fields corresponding to each mode family. The concept of potential difference is extended from transverse electric-magnetic (TEM) waves to all configurations, by means of a specific gauge fixing. The generalized flux $\phi$ introduced in the context of quantum electronics becomes here essential: it is the scalar field, conjugate of a charge $Q$, that confines light within the electrodes, let them be real or virtual. The gap in the dispersion relations of non-TEM waves turns out to be linked either to a potential energy necessary for the photon confinement, or to a kinetic energy arising from a photon mass. We finally compute the field zero-point fluctuations in every configuration. The theory is predictive: the lowest transverse magnetic (TM) modes should have smaller quantum noise than the higher ones, which at large wavevectors recover a conventional value similar to TEM and transverse electric (TE) ones. Such low-noise modes might be particularly useful for the routing of quantum information.

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 develops a quantum theory for traveling electromagnetic waves in Cartesian waveguide geometries (parallel plates, rectangular tubes). It supplies mode expansions for TEM, TE, and TM families, extends the TEM potential-difference concept to all modes via a specific gauge choice, defines a generalized flux φ as the scalar field conjugate to a confining charge Q, reinterprets the dispersion cutoff as confinement potential energy or photon mass, and computes zero-point field fluctuations. The central prediction is that the lowest TM modes exhibit reduced quantum noise relative to higher TM modes and to TEM/TE modes, with the latter recovering conventional values at large wavevectors.

Significance. If the quantization procedure is shown to be consistent with standard QED, the work could supply a compact quantum description useful for superconducting microwave circuits and quantum-information routing. The explicit prediction of lower-noise fundamental TM modes is falsifiable and, if confirmed, would be of practical interest for minimizing decoherence in waveguide-mediated quantum links.

major comments (2)
  1. [Gauge-fixing and mode-expansion section] The gauge-fixing procedure that extends the potential difference to TM modes and makes φ the canonical conjugate to Q is load-bearing for the fluctuation spectrum. The manuscript provides no explicit demonstration that this choice preserves the transverse boundary conditions and the [A, Π] algebra after projection onto the TM basis (see the skeptic note on TM modes with cutoff).
  2. [Zero-point fluctuation calculation] The claim that lowest TM modes have smaller zero-point fluctuations (recovering conventional values only at large k) is obtained by reinterpreting the dispersion gap. Without the explicit field-operator expressions, the resulting noise integral, or any numerical verification, it is impossible to confirm that the k-dependent suppression follows rigorously rather than from the gauge choice itself.
minor comments (2)
  1. [Abstract and results section] The abstract states that derivations and zero-point calculations are performed, yet the main text should include at least one worked example of the mode expansion and the noise integral for a concrete geometry.
  2. [Dispersion-relation interpretation] Clarify whether the invented photon-mass interpretation for non-TEM modes is an auxiliary picture or a necessary ingredient of the quantization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment below and will revise the text to include the requested explicit derivations and verifications.

read point-by-point responses

  1. Referee: The gauge-fixing procedure that extends the potential difference to TM modes and makes φ the canonical conjugate to Q is load-bearing for the fluctuation spectrum. The manuscript provides no explicit demonstration that this choice preserves the transverse boundary conditions and the [A, Π] algebra after projection onto the TM basis (see the skeptic note on TM modes with cutoff).

    Authors: We agree that an explicit verification strengthens the argument. The gauge is chosen to enforce the Coulomb condition ∇·A=0 while respecting the TM boundary conditions (vanishing tangential E on the walls). Mode orthogonality then ensures the projected fields satisfy the same conditions. In the revision we will add an appendix that explicitly computes the commutator [A_i(r), Π_j(r')] for the TM basis functions, confirming it reduces to the standard transverse delta function after summation over the discrete transverse indices. revision: yes

  2. Referee: The claim that lowest TM modes have smaller zero-point fluctuations (recovering conventional values only at large k) is obtained by reinterpreting the dispersion gap. Without the explicit field-operator expressions, the resulting noise integral, or any numerical verification, it is impossible to confirm that the k-dependent suppression follows rigorously rather than from the gauge choice itself.

    Authors: The mode expansions and field operators are stated in Section III; the zero-point energy for each family follows from the standard integral of (ħω/2) weighted by the normalized mode functions. For TM modes the dispersion ω(k)=√(c²k²+ω_c²) enters the spectral density, and the lowest mode (m=1,n=1) carries an extra factor arising from the confinement potential that suppresses the long-wavelength contribution. We will insert the explicit noise integral, derive its k-dependence analytically, and add a numerical plot comparing the lowest TM mode to higher TM and to TEM/TE modes, showing the asymptotic recovery at large k. revision: yes

Circularity Check

1 steps flagged

Gauge fixing for generalized flux φ ties confinement to definition, affecting TM noise prediction

specific steps
  1. self definitional [Abstract]
    "The concept of potential difference is extended from transverse electric-magnetic (TEM) waves to all configurations, by means of a specific gauge fixing. The generalized flux φ introduced in the context of quantum electronics becomes here essential: it is the scalar field, conjugate of a charge Q, that confines light within the electrodes, let them be real or virtual. The gap in the dispersion relations of non-TEM waves turns out to be linked either to a potential energy necessary for the photon confinement, or to a kinetic energy arising from a photon mass."

    φ is introduced via gauge fixing and immediately defined as the confining scalar field conjugate to Q; the dispersion gap is then stated to be the potential energy of that same confinement. The link is therefore definitional rather than independently derived from the Maxwell operator or the [A, Π] algebra after projection onto the TM basis.

full rationale

The paper's technical quantization of waveguide modes follows standard QED procedures for TEM/TE/TM families in Cartesian geometries, with explicit mode expansions and zero-point fluctuation calculations that do not reduce to fitted parameters or prior self-citations. The predictive claim for k-dependent suppression of noise in lowest TM modes arises from projecting the fields onto the chosen basis after gauge fixing. However, the ontological step that reinterprets the dispersion gap as confinement potential energy (or photon mass) is directly enabled by defining φ as the scalar conjugate to confining charge Q. This creates a moderate self-definitional element in the interpretation without rendering the entire fluctuation spectrum tautological. No equations are shown to equal their inputs by construction, and the framework remains falsifiable via boundary conditions and commutation relations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard quantum electrodynamics for traveling waves plus one domain-specific modeling choice (gauge fixing) and an optional interpretive entity (photon mass). No free parameters are mentioned.

axioms (2)
  • standard math Quantum electrodynamics governs the traveling-wave modes inside the waveguides
    The entire treatment is framed as a quantum-field description of photons in confined geometries.
  • domain assumption A specific gauge fixing extends the potential-difference concept to non-TEM families
    Invoked to define voltage and flux for TE and TM modes.
invented entities (1)
  • Photon mass for non-TEM modes no independent evidence
    purpose: Alternative explanation for the gap in the dispersion relation as kinetic energy
    Presented as one possible physical origin of the cutoff; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5813 in / 1539 out tokens · 67369 ms · 2026-05-22T14:26:48.969029+00:00 · methodology

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Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    Yu, Jay Gambetta, A

    Charge-insensitive qubit design derived from the Cooper pair box, Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf, Phys. Rev. A Vol. 76, 042319 (2007)

    work page 2007

  2. [2]

    Wieck, Matias Urdampilleta, Christopher Bäuerle and Tristan Meunier, Nature Nanotechnology Vol

    Coherent control of individual electron spins in a two-dimensional quantum dot array, Pierre- André Mortemousque, Emmanuel Chanrion, Baptiste Jadot, Hanno Flentje, Arne Ludwig, Andreas D. Wieck, Matias Urdampilleta, Christopher Bäuerle and Tristan Meunier, Nature Nanotechnology Vol. 16, p. 296–301 (2021)

    work page 2021

  3. [3]

    Schuster, Nature Comm

    Coupling a single electron on superfluid helium to a superconducting resonator, Gerwin Koolstra, Ge Yang and David I. Schuster, Nature Comm. Vol. 10, 5323 (2019)

    work page 2019

  4. [4]

    349, Issue 6246, pp

    Coherent coupling between a ferromagnetic magnon and a superconducting qubit, Yutaka Tabuchi, Seiichiro Ishino, Atsushi Noguchi, Toyofumi Ishikawa, Rekishu Yamazaki, Koji Usami, and Yasunobu Nakamura, Science Vol. 349, Issue 6246, pp. 405-408 (2015)

    work page 2015

  5. [5]

    Stabilized entanglement of massive mechanical oscillators, C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley and M. A. Sillanpää, Nature Vol. 556, pp. 478–482 (2018)

    work page 2018

  6. [6]

    Brubaker, J.M

    Optomechanical Ground-State Cooling in a Continuous and Efficient Electro-Optic Transducer, B.M. Brubaker, J.M. Kindem, M.D. Urmey, S. Mittal, R.D. Delaney, P.S. Burns, M.R. Vissers, K.W. Lehnert, and C.A. Regal, Phys. Rev. X Vol. 12, 021062 (2022)

    work page 2022

  7. [7]

    Clerk, M.H

    Introduction to Quantum Noise, Measurement and Amplification, A.A. Clerk, M.H. Devoret, S.M. Girvin, Florian Marquardt, and R.J. Schoelkopf, Rev. Mod. Phys. Vol. 82, 1155 (2010). Waveguides in a quantum perspective - Collin and Delattre 31

    work page 2010

  8. [8]

    Grimsmo, S

    Circuit Quantum Electrodynamics, Alexandre Blais, Arne L. Grimsmo, S. M. Girvin, Andreas Wallraff, Rev. Mod. Phys. Vol. 93, 025005 (2021)

    work page 2021

  9. [9]

    Stimulating Uncertainty: Amplifying the Quantum Vacuum with Superconducting Circuits, P. D. Nation, J. R. Johansson, M. P. Blencowe, Franco Nori, Rev. Mod. Phys. Vol. 84, 1-27 (2012)

    work page 2012

  10. [10]

    718–719,pp

    Microwave photonics with superconducting quantum circuits, Xiu Gu, Anton Frisk Kockum, Adam Miranowicz , Yu-xi Liu, Franco Nori, Physics Reports Vols. 718–719,pp. 1–102 (2017)

    work page 2017

  11. [11]

    Gardiner, P

    Quantum Noise, C.W. Gardiner, P. Zoller, Springer Series in Synergetics, Third Ed. (2004)

    work page 2004

  12. [12]

    Fragner, M

    Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift, A. Fragner, M. Göppl, J. M. Fink, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, A. Wallraff, Science Vol. 322, p. 1357 (2008)

    work page 2008

  13. [13]

    Korotkov, Nature Phys

    Experimental violation of a Bell’s inequality in time with weak measurement, Agustin Palacios- Laloy, François Mallet, François Nguyen, Patrice Bertet, Denis Vion, Daniel Estève and Alexander N. Korotkov, Nature Phys. Vol. 6, 442 (2010)

    work page 2010

  14. [14]

    Norris, Andrés Rosario, Ferran Martin, José Martinez, Waldimar Amaya, Morgan W

    Loophole-free Bell inequality violation with superconducting circuits, Simon Storz, Josua Schär, Anatoly Kulikov, Paul Magnard, Philipp Kurpiers, Janis Lütolf, Theo Walter, Adrian Copetudo, Kevin Reuer, Abdulkadir Akin, Jean-Claude Besse, Mihai Gabureac, Graham J. Norris, Andrés Rosario, Ferran Martin, José Martinez, Waldimar Amaya, Morgan W. Mitchell, Ca...

    work page 2023

  15. [15]

    Pozar, John Wiley & Sons Inc., Fourth Ed

    Microwave Engineering, David M. Pozar, John Wiley & Sons Inc., Fourth Ed. (2012)

    work page 2012

  16. [16]

    Michel Devoret, in Quantum Fluctuations (Les Houches Session LXIII) (Elsevier, Amsterdam), pp. 351-86. (1997)

    work page 1997

  17. [17]

    Staelin, MIT LibreTexts (2011)

    Electromagnetics and Applications, David H. Staelin, MIT LibreTexts (2011)

    work page 2011

  18. [18]

    KGaA, Weinheim (2004)

    Photons and Atoms, Claude Cohen-Tannoudji, Jacques Dupont-Roc, Gilbert Grynberg, Wiley- VCH Verlag GmbH & Co. KGaA, Weinheim (2004)

    work page 2004

  19. [19]

    Why Gauge?, Carlo Rovelli, Foundations of Physics Vol. 44, pp. 91–104 (2014)

    work page 2014

  20. [20]

    Quantum Electrodynamics, Vol. 4 of L. Landau and E. Lifshitz series, by V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, 2d Ed. Oxford Pergamon Press (1982)

    work page 1982

  21. [21]

    On light by light interactions in QED, Joel Thiescheffer P.h.D., Faculty of Science and Engineering, University of Groningen, The Netherlands (2017)

    work page 2017

  22. [22]

    Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions, Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, and Gabriel Molina-Terriza, Phys. Rev. A 86, 042103 (2012)

    work page 2012

  23. [23]

    EfficientSortingofOrbitalAngularMomentumStatesofLight, GregoriusC.G.Berkhout, Martin P. J. Lavery, Johannes Courtial, Marco W. Beijersbergen, and Miles J. Padgett, Phys. Rev. Lett. Vol. 105, 153601 (2010)

    work page 2010

  24. [24]

    Quantum mechanical description of waveguides, Zhi-Yong Wang, Cai-Dong Xiong, Bing He, Chin. Phys. B 17 (11), 3985 (2008)

    work page 2008

  25. [25]

    Marinescu and M

    Quantum-Mechanical concepts in the waveguides theory, N. Marinescu and M. Apostol, Z. Naturforsh. Vol. 47a, pp. 935-940 (1992)

    work page 1992

  26. [26]

    Franson, Phys

    Entanglement from longitudinal and scalar photons, J.D. Franson, Phys. Rev. A Vol. 84, 033809 (2011)

    work page 2011

  27. [27]

    Transparency, nonclassicality, and nonreciprocity in chiral waveguide quantum electrodynamics, Qingtian Miao and G. S. Agarwal, Phys. Rev. Research Vol. 7, 013138 (2025)

    work page 2025

  28. [28]

    Casimir, Kon

    On the attraction between two perfectly conducting plates, H.B.G. Casimir, Kon. Ned. Akad. Wetensch. Proc. Vol. 51(7), 793-795 (1948)

    work page 1948

  29. [29]

    The Casimir force: background, experiments, and applications, Steven K Lamoreaux, Rep. Prog. Phys. Vol.68, 201 (2005)

    work page 2005

  30. [30]

    Springer Berlin Heidelberg New York (2007)

    Photonics, Ralf Menzel, 2d Ed. Springer Berlin Heidelberg New York (2007)

    work page 2007

  31. [31]

    Quantum field theory for spin operator of the photon, Li-Ping Yang, Farhad Khosravi, and Zubin Jacob, Phys. Rev. Research Vol. 4, 023165 (2022). Waveguides in a quantum perspective - Collin and Delattre 32

    work page 2022

  32. [32]

    Input-Output Theory with Quantum Pulses, Alexander Holm Kiilerich and Klaus Mølmer, Phys. Rev. Lett. Vol. 123, 123604 (2019)

    work page 2019