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REVIEW 4 major objections 4 minor 1 cited by

Detecting the Unruh Effect via an Engineered Low-Mass Field in a Superconducting Qubit

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper shows that Unruh-induced excitation of massive fields is exponentially suppressed when M c² ≫ ℏa/c, and proposes a superconducting flux-qubit circuit with an engineered small effective mass that should display a linear excitation

desk verdict The exponential-suppression claim for massive fields is plausible and worth checking, but the circuit experiment as written is an asserted analogy with a fitted slope, not a derived test. read the letter →

arxiv 2512.17959 v2 pith:KARAG3ZN submitted 2025-12-18 gr-qc

Vladimir Toussaint This is my paper
classification gr-qc MSC 81T2083C47 PACS 04.62.+v85.25.-j
keywords UnruheffectUnruh-DeWittdetectorexponentialsuppressionmassivescalarfieldsuperconductingfluxqubitcircuitQEDeffectivemassanalogquantumsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that any attempt to detect the Unruh effect by exciting massive fields is blocked by an exponential suppression factor exp(−constant×Mc²/(ℏa/c)) once the field's rest energy exceeds the acceleration energy scale, and it derives this suppression in two independent models. It then shows that the way around this barrier is not to use massless fields but to engineer a system with a very small effective mass, where the optimal condition Meffc² ≪ ℏaeff/c is automatically satisfied by setting the detector gap to the mass threshold. The concrete proposal is a persistent-current flux qubit coupled to a microwave resonator, which should exhibit a linear relation Pe_signal ≈ Sδω between excitation probability and flux-modulation depth, a falsifiable prediction accessible with existing circuit technology. A sympathetic reader would care because this offers a practical in-laboratory test of a cornerstone quantum-field-theory prediction that has eluded direct observation.

What carries the argument

The carrying mechanism is the exponential suppression of the modified Bessel function K_{i∆E/a}(√(µ²+(M/a)²)) in the Unruh-DeWitt transition rate (Eq. 5) and the analogous decay-rate ratio Γ_acc/Γ_in ∼ exp(−2Mc²/(ℏa/c)) in the cavity model; both yield the universal exp(−constant×Mc²/(ℏa/c)) barrier. To bypass it, the paper introduces the superconducting persistent-current flux qubit (energy bias ϵ = 2Ip(Φ_ext − Φ₀/2), tunneling gap Δ) coupled to a microwave resonator (mass analog Meffc² = ℏωr) via the Jaynes-Cummings interaction ℏλ(σ₊a + σ₋a†). Time-dependent flux modulation Φ_ext(t) = Φ₀/2 + ΔΦ cos(Ωt) produces an effective Lorentz factor γ(t) = ℏωq(t)/Δ and, in the large-modulation limit 2

What would settle it

Measure Pe_signal as a function of δω (equivalently ΔΦ) at fixed T, λ, and ωr. If the background-subtracted excitation probability is not linear through the origin with slope S = K|λ|²T over the range where ωr ≪ δω, or if the slope does not scale as 1/ωr² when ωr is varied, the central prediction fails and the qubit response cannot be attributed to Unruh-like excitation. Conversely, confirming the linear relation and its frequency scaling would distinguish the Unruh-type mechanism from generic parametric heating.

Watch

Extended reading notes

Core claim

The paper's central claim is that Unruh-induced excitation of fields with rest energy M c² ≫ ℏa/c is exponentially suppressed, with the rate scaling as ∼ exp(−constant × Mc²/(ℏa/c)) in both a (3+1)-dimensional Unruh-DeWitt detector coupled to a massive scalar field and a (1+1)-dimensional cavity QED model of a confined massless Dirac field coupled to a massive external Dirac field. This universal suppression is the reason electron-mass fields are unobservable at achievable accelerations, and it implies detection requires either massless fields or engineered effective masses satisfying Meffc² ≲ ℏaeff/c. The paper further claims that in the optimal regime Meffc² ≪ ℏaeff/c, a massive field has

Load-bearing premise

The paper assumes that a flux-modulated persistent-current qubit coupled to a resonator behaves exactly as an Unruh-DeWitt detector with effective acceleration aeff = cδω; this mapping is drawn by analogy (Section IX) rather than derived from the circuit Hamiltonian or a coordinate transformation.

Editorial extensions

If this is right

  • Any existing or future experiment that relies on exciting a massive field (e.g., electron mass) at accelerations up to 10²⁰ m/s² will see unmeasurable Unruh signals; the suppression exponent C/a ~ 2.3×10⁹ leaves no room for incremental technical improvement.
  • The effective-mass strategy converts the problem from achieving astronomically large acceleration to fabricating a low-frequency resonator (ωr ≪ δω) and a qubit with large persistent current and moderate gap, both within current circuit-QED capabilities.
  • The linear relation Pe_signal = Sδω provides a clean, background-subtracted observable (control with ΔΦ = 0) that can be checked directly in a single experiment at fixed λ, T, and ωr.
  • The interplay of mass threshold and acceleration energy means the optimal regime is self-calibrating: no fine-tuning of the detector gap is needed, unlike the massless-field case.
  • If the slope S is measured to scale as 1/ωr² (Eq. 20), that would corroborate the effective-mass model of the resonator.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The analogy between the flux-modulated qubit and an Unruh-DeWitt detector is the hinge of the proposal; a rigorous derivation from a coordinate transformation or an effective metric would either confirm the aeff identification or reveal corrections that change the predicted slope.
  • The same effective-mass logic could be applied to other analog platforms (e.g., trapped ions, optomechanics) where a low-frequency bosonic mode acts as the field and a two-level system as the detector; the predicted linearity would be a general signature of Unruh-type responses.
  • Because K is left as a free parameter, the cleanest experimental falsification is not the absolute value of Pe but the linearity and the 1/ωr² scaling; a test could be conducted without knowing K.
  • The exponential-suppression result suggests that proposals to detect Unruh radiation from accelerated electrons via massive-field channels are even more strongly ruled out than previously appreciated.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper argues that exciting massive fields in Unruh-type processes is exponentially suppressed when M c^2 ≫ ℏ a/c, and claims to derive this suppression in a (3+1)-dimensional Unruh-DeWitt model and a (1+1)-dimensional cavity QED model, obtaining exponents (π+2)M/a and 2M/a. It then proposes to bypass the suppression by using a superconducting persistent-current qubit coupled to a microwave resonator, with an effective mass M_eff c²=ℏω_r and an effective acceleration a_eff≈cδω from flux modulation. The main experimental prediction is P_e^signal(δω;T)≈K|λ|²T δω, a linear dependence of qubit excitation probability on modulation depth, where K is an undetermined constant. The paper acknowledges that K needs future determination and that the gravity mimicry is not fully explored.

Significance. If the derivation of the exponential suppression were made fully explicit, it would provide a useful quantitative statement of a known energy-scale barrier. The two-model comparison is a reasonable pedagogical contribution, and the proposed parameter regime (ω_r≪δω with accessible microwave components) is concrete and falsifiable in principle. However, the experimental central claim is not yet a test of the Unruh effect: the circuit-to-Rindler mapping is asserted rather than derived, and the slope contains an undetermined constant K. The paper therefore does not currently meet the standard for a self-contained result in quantum field theory or circuit QED.

major comments (4)
  1. [Section IX, Eqs. (15)-(18)] The central experimental prediction rests on the identification of the flux-modulated qubit-resonator system with a uniformly accelerated UDW detector. The text defines γ(t)=ℏω_q(t)/Δ and a_eff≈cδω 'by analogy with Unruh-DeWitt theory' without deriving a detector worldline, a Rindler coordinate transformation, or the effective mass from the circuit Hamiltonian. Equation (18) then replaces the UDW matrix element by |q|²=4π²K|λ|², with K explicitly left for future work or fitting. The result is that P_e^signal≈K|λ|²T δω is an assumed functional form, not a derived consequence of Eqs. (12)-(14). Standard resonant flux driving generically produces Rabi-type oscillations scaling as (δωT)² at short times, so the predicted linearity does not discriminate the Unruh mechanism from ordinary parametric excitation unless the mapping is established.
  2. [Section IV, Eq. (5) and Section V, Eq. (8)] The claimed derivation of the exponential suppression is not self-contained. Equation (5) is quoted from Ref. [5], and the Bessel-integral evaluation leading to Eq. (6) is stated without showing the integral or the precise conditions on ΔE, M, and a. Equation (8) is imported from the author's previous arXiv paper [22]. Since the paper's stated purpose is to fill the gap in the literature with an explicit derivation, this omission is load-bearing: a reader cannot verify the quoted constants (π+2 and 2) or the claim of universality from the material presented.
  3. [Section IX, Eqs. (17)-(21)] The quantitative prediction is internally inconsistent. Equation (18) gives P_e≈K|λ|²T δω with no ω_r dependence, yet Eq. (20) asserts S∝1/ω_r² and defines C'=ω_r²K; this is only consistent if K itself depends on ω_r, which is not stated. Consequently the numerical estimate in Eq. (21) (P≈0.0226 C') is uninterpretable because C' is undetermined and the ω_r-scaling is not derived. The predicted slope S=K|λ|²T therefore has no predictive content beyond a linear fit parameter.
  4. [Section VI] The conclusion that the exponential suppression is a 'fundamental barrier' and 'applies to all detection methods and field types' goes beyond the evidence. Only two specific models are considered: a point-like UDW detector coupled to a massive scalar field, and a particular (1+1)-dimensional cavity interaction. Other couplings, observables (e.g., decoherence, vacuum friction), or finite-size effects are not analyzed. The two models support the energy-scale argument for those couplings, but not the stated universality across all detection schemes.
minor comments (4)
  1. [Abstract and Section I] The phrase 'Detecting the Unruh effect' overstates the analog nature of the proposal; Section IX later correctly describes it as an analog simulation. The title and abstract should reflect this distinction.
  2. [Equations (14)-(15)] The notation δω is used as both a frequency and an angular frequency. Since a_eff≈cδω requires δω in rad/s, please state this explicitly and keep units consistent throughout, including the numerical example δω/(2π)=50 GHz.
  3. [Section IX, text] There are several typos: 'as as coming from', 'the the correct', and 'defined the frequency modulation depth' should read 'defines'. A careful proofreading pass is needed.
  4. [General] The paper contains no figures. A schematic of the circuit and a plot of the predicted P_e versus δω (for a fixed K) would make the proposal substantially easier to follow.

Circularity Check

3 steps flagged · score 6.0 of 10

The central experimental prediction is constructed rather than derived: a_eff is set equal to cδω and |q|² is redefined via the free constant K, so P_e≈K|λ|²Tδω follows by definition; the second suppression framework is imported from the author's own prior paper.

  1. fitted input called prediction [Section IX, Eq. (18) and following paragraph; Eq. (15)]
    "In our analogue model, this signal is interpreted as being generated by the effective massive rate, such that P_e = R_{eff,massive}T = (|q|^2 a_{eff,max}/(4π^2 c))T. In this context, |q|^2 is not the UDW matrix element; it is related to the qubit-resonator coupling strength, λ by |q|^2 = 4π^2K|λ|^2, where K is a constant that depends on the interaction details with dimensions of time squared."

    Combined with Eq. (15), a_{eff,max}≈cδω, this substitution gives exactly P_e≈K|λ|²Tδω, Eq. (18). The paper later states: 'The fact that we rely on an unknown parameter is a limitation that future studies must fix... or by fitting experimental data.' Thus the central quantitative prediction has a free slope S=K|λ|²T, to be fitted to data; the linear-in-δω signal is not computed from the circuit Hamiltonian but is obtained by defining |q|² and a_eff so that the UDW formula becomes P_e=K|λ|²Tδω. A line with adjustable slope does not uniquely test the Unruh mechanism.

  2. self definitional [Section IX, Eq. (15)]
    "We define an effective Lorentz factor γ(t)=ℏω_q(t)/Δ and a peak effective acceleration a_{eff,max} from the maximum rate of change of γ(t). By setting the modulation frequency to match the qubit's gap, Δ/ℏ=Ω, and under the large modulation condition 2I_p∆Φ≫Δ, we get: a_{eff,max} ≈ c 2I_p∆Φ/ℏ = cδω"

    The 'effective acceleration' is not obtained from a Rindler trajectory or a coordinate transformation of the circuit; it is defined so that a_eff equals c times the already-defined modulation depth δω=2I_p∆Φ/ℏ. Since the UDW optimal-regime rate is proportional to a (Eq. 11), every later 'linear in a_eff' prediction is automatically linear in δω. The analogy is asserted ('by analogy with Unruh-DeWitt theory'), not derived, making this mapping the load-bearing, unverified step.

1 more flagged steps
  1. self citation load bearing [Section V.A, Eq. (8), reference [22]]
    "Our analysis [22] shows that for M c^2 ≫ℏa/c, the decay rate of the confined excited field is always dominated by an exponential factor, regardless of cavity size: Γ_acc/Γ_in ∼exp(−2M c^2/(ℏa/c)), where Γ_in is the inertial decay rate."

    This is the quantitative result for the second of the two frameworks used to claim universality of the exponential suppression, but it is not derived in the present paper; it is imported from a paper by the same author ([22], arXiv:2510.11460). The 'universal barrier' argument therefore leans on a load-bearing self-citation for one of its two pillars, rather than a derivation contained in this text.

full rationale

The UDW suppression part of the paper is not circular: Eq. (5) is taken from the standard Crispino-Higuchi-Matsas review and the Bessel-function asymptotic is a standard mathematical result. The circularity is concentrated in the experimental prediction of Section IX. Equation (15) defines a_eff so that a_eff≈cδω, and |q|² is redefined as 4π²K|λ|² with K undetermined and explicitly allowed to be fitted to data; substituting these into the UDW rate yields Eq. (18), P_e≈K|λ|²Tδω, identically. Thus the headline linear signal is a rearrangement of the chosen parameters, not a consequence derived from the circuit Hamiltonian or from an independently established Unruh-worldline mapping. The cavity-QED suppression result is also imported from the author's own prior paper [22], which is load-bearing for the claimed universality. The linearity of P_e in δω could in principle be falsified experimentally, so the paper is not fully degenerate, but the quantitative content as written reduces to a free linear fit with an asserted analogy.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The derivation rests on a known UDW rate formula and Bessel asymptotics, a self-cited cavity result, and an asserted circuit-to-Rindler mapping. The only explicit free parameter is the proportionality constant K, which sets the amplitude of the predicted signal and is left to future fitting.

free parameters (1)
  • K = not determined
    Introduced in Section IX to relate |q|² to the circuit coupling |λ|² (|q|² = 4π²K|λ|²); the predicted slope S=K|λ|²T and hence the quantitative signal depend on it. The conclusion says its value requires a QED calculation or fitting to experimental data.
assumptions (5)
  • domain assumption The UDW excitation rate for a massive scalar field is given by Eq. (5) from Crispino et al. [5].
    The suppression calculation in Model 1 starts from this literature formula; if it is incorrect or misapplied, the derived (π+2) exponent fails.
  • standard math The modified Bessel asymptotic Kν(z)≈sqrt(π/(2z))e^{-z} for z≫1 controls the integral in Eq. (5), giving the e^{-2M/a} factor.
    Standard DLMF asymptotics; the paper does not show the integration steps but relies on it.
  • domain assumption The cavity QED result Γ_acc/Γ_in ∼ exp(-2Mc²/(ℏa/c)) from the author's previous paper [22] is correct and relevant.
    Eq. (8) is quoted, not derived; the universality claim depends on it.
  • ad hoc to paper The flux-modulated qubit-resonator system behaves as a UDW detector with effective Lorentz factor γ(t)=ℏω_q(t)/Δ and effective acceleration a_eff≈c(2IpΔΦ/ℏ).
    Asserted by analogy in Section IX; no derivation from the circuit Hamiltonian or a coordinate transformation.
  • domain assumption Single-mode approximation and rotating-wave approximation for qubit-resonator coupling are valid.
    Standard in circuit QED but imports the Jaynes-Cummings model as a given mapping; location Section IX.
invented entities (1)
  • Effective mass field M_eff=ℏωr assigned to the resonator mode
    purpose: Allows the optimal condition ωr ≪ δω to be satisfied with realistic parameters, bypassing the massive-field suppression.
    It is a bookkeeping identification of the resonator frequency as a field mass, not an independently detected particle or force; no handle outside the model.

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Cite this review

Pith. "Pith review of Detecting the Unruh Effect via an Engineered Low-Mass Field in a Superconducting Qubit." pith.science (2026). https://pith.science/paper/KARAG3ZN

@misc{pith2026251217959,
  author       = {Pith},
  title        = {Pith review of: Detecting the Unruh Effect via an Engineered Low-Mass Field in a Superconducting Qubit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KARAG3ZN}},
  note         = {Machine review of arXiv:2512.17959}
}
abstract

Detecting the Unruh effect is a major challenge in fundamental physics. It is known that exciting massive fields with the Unruh thermal bath is heavily suppressed when the field's rest energy is much larger than the acceleration energy scale, $Mc^2 \gg\hbar a/c$. However, the standard literature lacks an explicit quantitative derivation of this suppression. In this work, we first fill this gap by deriving the exponential suppression, $\sim \exp(-\text{constant}\times Mc^2/(\hbar a/c))$, in two different frameworks: a (3+1)-dimensional Unruh-DeWitt detector and a (1+1)-dimensional cavity QED setup. This shows the suppression is universal and sets an insurmountable barrier for any detection method that relies on exciting massive fields. For an electron-mass field at achievable accelerations ($a \sim 10^{20}$ m/s$^2$), the suppression exceeds $10^9$ orders of magnitude. To avoid this suppression, the field's rest energy must be less than or of the order of the acceleration energy scale, $M c^2 \lesssim \hbar a / c$. Achieving this condition, however, requires astronomically high accelerations. For example, detecting the effect for an electron-mass field would require accelerations of $a \gtrsim 4.6\times 10^{29}$ m/s$^2$, which is far beyond experimental reach. While using a massless field avoids this suppression, we show the best strategy is not to avoid mass, but to engineer a small effective mass that satisfies the optimal condition $\hbar a / c \gg M_{\text{eff}} c^2$. We propose a concrete implementation using a superconducting circuit with a Josephson persistent-current qubit (the analog of a UDW detector) coupled to a microwave resonator (the analog of the scalar field). For this system, the optimal condition is $2I_p\Delta\Phi \gg \Delta$, where $I_p$ is the persistent current, $\Delta\Phi$ is the magnetic flux swing, and $\Delta$ is the qubit's tunneling energy gap....

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Probing Unruh Effect from Enhanced Decoherence

    gr-qc 2026-03 unverdicted novelty 6.0 of 10

    Decoherence rate of an Unruh-DeWitt detector scales as a^{2Δ-1} in the long-time limit, increasing with the scaling dimension Δ of the coupled field and offering a more sensitive probe of the Unruh effect.

Reference graph

Works this paper leans on

40 extracted references · 3 linked inside Pith · cited by 1 Pith paper

  1. [5]

    The Unruh effect and its applications,

    L. C. B. Crispino, A. Higuchi and G. E. A. Matsas, “The Unruh effect and its applications,” Rev. Mod. Phys.80, 787-838 (2008)

    2008

  2. [22]

    Exponential Suppression of the Unruh Effect and Geometric Enhancement in a Fermionic Cavity QED Setup,

    V. Toussaint, “Exponential Suppression of the Unruh Effect and Geometric Enhancement in a Fermionic Cavity QED Setup,” [arXiv:2510.11460 [gr-qc]] (2025)

    arXiv 2025

  3. [1]

    Notes on black hole evaporation,

    W. G. Unruh, “Notes on black hole evaporation,” Phys. Rev. D14, 870 (1976)

    1976

  4. [2]

    Scalar particle production in Schwarzschild and Rindler metrics,

    P. C. W. Davies, “Scalar particle production in Schwarzschild and Rindler metrics,” J. Phys. A8, 609-616 7 (1975)

    1975

  5. [3]

    Nonuniqueness of canonical field quan- tization in Riemannian space-time,

    S. A. Fulling, “Nonuniqueness of canonical field quan- tization in Riemannian space-time,” Phys. Rev. D7, 2850-2862 (1973)

    1973

  6. [4]

    Cosmological event horizons, thermodynamics, and particle creation,

    G. W. Gibbons and S. W. Hawking, “Cosmological event horizons, thermodynamics, and particle creation,” Phys. Rev. D15, 2738–2751 (1977)

    1977

  7. [6]

    Particle Creation by Black Holes,

    S. W. Hawking, “Particle Creation by Black Holes,” Com- mun. Math. Phys.43, 199-220 (1975) [erratum: Commun. Math. Phys.46, 206 (1976)]

    1975

  8. [7]

    The Unruh Effect and Quantum Fluctuations of Electrons in Storage Rings,

    J. S. Bell and J. M. Leinaas, “The Unruh Effect and Quantum Fluctuations of Electrons in Storage Rings,” Nucl. Phys. B284, 488 (1987)

    1987

Show all 40 references
  1. [8]

    Unruh effect in storage rings,

    J. M. Leinaas, “Unruh effect in storage rings,” [arXiv:hep- th/0101054 [hep-th]]

  2. [9]

    On polarization and spin effects in the theory of synchrotron radiation

    A. A. Sokolov and I. M. Ternov, “On polarization and spin effects in the theory of synchrotron radiation”, Dokl. Akad. Nauk SSSR153, 1052 (1963) [Sov. Phys. Dokl.8, 1203 (1964)]

    1963

  3. [10]

    Polarization kinetics of particles in storage rings

    Ya. S. Derbenev and A. M. Kondratenko, “Polarization kinetics of particles in storage rings”, Zh. Eksp. Teor. Fiz. 64, 1918 (1973) [Sov. Phys.–JETP37, 968 (1973)]

    1918

  4. [11]

    Thermal Excitations of Accelerated Elec- trons

    V. N. Baier, “Thermal Excitations of Accelerated Elec- trons”, Usp. Fiz. Nauk105, 441 (1971) [Sov. Phys.–Usp. 14, 695 (1972)]

    1971

  5. [12]

    Testing Unruh radiation with ultraintense lasers,

    P. Chen and T. Tajima, “Testing Unruh radiation with ultraintense lasers,” Phys. Rev. Lett.83, 256-259 (1999)

    1999

  6. [13]

    Us- ing Berry’s phase to detect the Unruh effect at lower accelerations,

    E. Martin-Martinez, I. Fuentes and R. B. Mann, “Us- ing Berry’s phase to detect the Unruh effect at lower accelerations,” Phys. Rev. Lett.107(2011), 131301 doi:10.1103/PhysRevLett.107.131301 [arXiv:1012.2208 [quant-ph]]

    2011 arXiv

  7. [14]

    Experimental Black-Hole Evaporation?

    W. G. Unruh, “Experimental Black-Hole Evaporation?”, Phys. Rev. Lett.46, 1351–1353 (1981)

    1981

  8. [15]

    Black holes in Bose-Einstein condensates,

    L. J. Garay, J. R. Anglin, J. I. Cirac and P. Zoller, “Black holes in Bose-Einstein condensates,” Phys. Rev. Lett.85, 4643-4647 (2000)

    2000

  9. [16]

    Fiber-optical analogue of the event horizon,

    T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig and U. Leonhardt, “Fiber-optical analogue of the event horizon,” Science319, 1367-1370 (2008)

    2008

  10. [17]

    Analogue Hawking Radiation in a dc-SQUID Array Copla- nar Waveguide,

    P. D. Nation, M. P. Blencowe, A. J. Rimberg and E. Buks, “Analogue Hawking Radiation in a dc-SQUID Array Copla- nar Waveguide,” Phys. Rev. Lett.103, 087004 (2009)

    2009

  11. [18]

    A New Extended Model of Hadrons,

    A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn and V. F. Weisskopf, “A New Extended Model of Hadrons,” Phys. Rev. D9, 3471-3495 (1974)

    1974

  12. [19]

    Kinematic entanglement degradation of fermionic cav- ity modes,

    N. Friis, A. R. Lee, D. E. Bruschi and J. Louko, “Kinematic entanglement degradation of fermionic cav- ity modes,” Phys. Rev. D85(2012), 025012

    2012

  13. [20]

    Scalar, spinor, and photon fields under relativistic cavity motion,

    N. Friis, A. R. Lee and J. Louko, “Scalar, spinor, and photon fields under relativistic cavity motion,” Phys. Rev. D88(2013) no.6, 064028

    2013

  14. [21]

    NIST Digital Library of Mathematical Functions, https: //dlmf.nist.gov/, Release 1.1.10 of 2023-09-15

    2023

  15. [23]

    Relativistic Quantum Tele- portation with superconducting circuits,

    N. Friis, A. R. Lee, K. Truong, C. Sabin, E. Solano, G. Johansson and I. Fuentes, “Relativistic Quantum Tele- portation with superconducting circuits,” Phys. Rev. Lett. 110, no.11, 113602 (2013)

    2013

  16. [24]

    Cavity Optomechanics,

    M. Aspelmeyer, T. J. Kippenberg and F. Marquardt, “Cavity Optomechanics,” Rev. Mod. Phys.86, 1391 (2014)

    2014

  17. [25]

    Superconducting persistent-current qubit,

    T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd and J. J. Mazo, “Superconducting persistent-current qubit,” Phys. Rev. B6015398–15413 (1999)

    1999

  18. [26]

    Josephson persistent-current qubit,

    J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, “Josephson persistent-current qubit,” Science285, 1036–1039 (1999)

    1999

  19. [27]

    Quantum coding,

    B. Schumacher, “Quantum coding,” Phys. Rev. A51 (1995) no.4, 2738

    1995

  20. [28]

    Coherent control of macroscopic quantum states in a single-Cooper- pair box,

    Y. Nakamura, Y. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum states in a single-Cooper- pair box,” Nature398, 786–788 (1999)

    1999

  21. [29]

    A quantum engineer’s guide to superconducting qubits,

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson and W. D. Oliver, “A quantum engineer’s guide to superconducting qubits,” Appl. Phys. Rev.6(2019) no.2, 021318

    2019

  22. [30]

    Su- perconducting qubits: A short review,

    M. H. Devoret, A. Wallraff, and J. M. Martinis, “Su- perconducting qubits: A short review,”arXiv preprint arXiv:cond-mat/0411174 [cond-mat.mes-hall](2004)

    2004 arXiv

  23. [31]

    F. G. Paauw,Superconducting flux qubits: Quantum chains and tunable qubits, Doctoral Thesis, Delft University of Technology, Delft, Netherlands, 2009. Promotors: J. E. Mooij and C. J. P. M. Harmans. https://resolver.tudelft.nl/uuid: 9ed11bb5-0d00-4d33-96f7-b7a6c60d79b2

    2009

  24. [32]

    Quantum information processing with su- perconducting circuits: a review,

    G. Wendin, “Quantum information processing with su- perconducting circuits: a review,” Rept. Prog. Phys.80 (2017) no.10, 106001

    2017

  25. [33]

    Circuit quantum electrodynamics,

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Circuit quantum electrodynamics,” Rev. Mod. Phys.77, 1225–1260 (2005)

    2005

  26. [34]

    Charge-insensitive qubit design derived from the Cooper pair box,

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,”Phys. Rev. A76, 042319 (2007)

    2007

  27. [35]

    Low-loss superconducting transmission line resonators with high internal quality factors,

    M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and J. A. B. Jr., “Low-loss superconducting transmission line resonators with high internal quality factors,”Appl. Phys. Lett.93, 123508 (2008)

    2008

  28. [36]

    D. M. Pozar,Microwave Engineering, 4th ed. (Wiley, Hoboken, NJ, 2011)

    2011

  29. [37]

    Superconducting quantum bits,

    J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,”Nature453(7198), 1031–1042 (2008)

    2008

  30. [38]

    Comparison of quan- tum and semiclassical radiation theories with application to the beam maser,

    E. T. Jaynes and F. W. Cummings, “Comparison of quan- tum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE51, 89–109 (2004)

    2004

  31. [39]

    The Jaynes-Cummings model,

    B. W. Shore and P. L. Knight, “The Jaynes-Cummings model,” Journal of Modern Optics40, 1195–1238 (1993)

    1993

  32. [40]

    C. C. Gerry and P. L. Knight,Introductory Quantum Optics(Cambridge University Press, Cambridge, England, 2005)

    2005

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.