Observation of the Dynamical Casimir Effect in a Superconducting Circuit

A. Pourkabirian; C.M. Wilson; F. Nori; G. Johansson; J.R. Johansson; P. Delsing; T. Duty

REVIEW

Observation of the Dynamical Casimir Effect in a Superconducting Circuit

C.M. Wilson, G. Johansson, A. Pourkabirian, J.R. Johansson, T. Duty, F. Nori, P. Delsing

Quantum Physics · Submitted 24 May 2011 · 23 references

Pith's verdict: The first real observation of dynamical Casimir radiation, with the pair-correlation signature to back it up; the absolute power budget is the one place the argument leans on a number inferred from the same data.

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CitationA. Pourkabirian, C.M. Wilson, F. Nori, G. Johansson, J.R. Johansson, P. Delsing, T. Duty. "Observation of the Dynamical Casimir Effect in a Superconducting Circuit." arXiv:1105.4714 (2011). https://pith.science/paper/2O655U4G

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Editor's note

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This is the paper that actually did it: a SQUID-terminated transmission line whose electrical length is modulated at ~11 GHz, and real microwave photons come out. Forty years after Moore, that is worth reading in full, and the qualitative case is strong. The generation is broadband in both drive frequency (8–12 GHz) and analysis frequency (4–6 GHz), which already rules out a driven single-mode parametric amplifier. Then Fig. 3 gives the part that matters: I+I− positive, Q+Q− negative, single sidebands unsqueezed, and the correlation function rotating as e−2iθ under drive-phase changes. That combination is the right shape for pair production from a modulated boundary, and it is not easy to fake with amplifier gain modulation. The theory they lean on (refs [12], [13]) is their own prior work, but it is a parameter-free scattering calculation whose assumptions do not include the observation, so I would not call it circular. The reader's CONDITIONAL is fair and the stress-test is right on one point: two-mode squeezing follows from Eq. (1) for any input state, so it confirms the parametric, pair-producing character of the process but not the vacuum origin. The paper slightly overstates this when it calls TMS 'a signature of the quantum character of the generation process.' The vacuum argument is really the n_in = 0.008 comparison in Eq. (2), and that argument is fine as far as it goes. Where it gets soft is the absolute scale. Observed power is a few Kelvin against a few mK predicted for an ideal line, and the reconciliation is a Q² density-of-states enhancement from parasitic resonances with Q ~ 30–50. That factor is inferred from the same measurement, not independently calibrated, and |A(ω)|² is never mapped across the band. The authors are upfront about this rather than hiding it, which counts for something, but it means the power level is not an independent confirmation of the theory. Minor: σ2 ≈ 0.04 is quoted without an explicit error bar. None of this breaks the central claim. This is for anyone working on driven-boundary physics, superconducting circuit quantum optics, or vacuum-fluctuation phenomena. Send it to referees; the questions above are exactly what a good referee should press on.

Referee report

Significance

If the identification holds, this is a landmark result: the first direct observation of real photon creation from vacuum fluctuations by a time-dependent boundary condition, forty years after Moore's proposal. The circuit implementation is a genuine experimental advance, since the effective boundary velocity is set by the SQUID inductance modulation rather than by mechanical motion, and the two-mode squeezing signature is a strong and falsifiable discriminator against a simple parametric amplifier. The phase-rotation test in Fig. 3d is a particularly clean check, and the demonstration that the single-mode fields remain unsqueezed (Fig. 3c) rules out a gain-modulation artifact. The theoretical treatment in refs. [12,13] is parameter-free given the circuit model, and the paper is clearly written. The result is of broad interest across quantum optics, superconducting circuits, and quantum field theory in curved backgrounds.

Major objections (3)

[Paragraph following Fig. 2a, 'We can quantify the photon production rate...'] The observed output power is roughly 1000 times the ideal-transmission-line prediction of a few mK, and the manuscript reconciles this by invoking an enhancement of the photonic density of states |A(ω)|² by Q² with Q ~ 30–50 from parasitic resonances. The authors acknowledge that this is an inference ('In general though, transmission lines are not ideal...'), but the enhancement factor is extracted from the same data it is used to explain, so the quantitative power budget is closed post hoc. This does not undermine the qualitative claim, and I note in the authors' favor that the ratio of the DCE term to the classical upconversion term in Eq. (2) is 1/n_in ≈ 125 and is independent of |A(ω)|², since both terms carry the same |S|²; moreover the drive-on minus drive-off difference in Fig. 2b,c cancels the reflected thermal term n_in(ω). The vacuum-origin argument is therefore more robust than the raw power comparison suggests. Nevertheless, the manuscript should either measure |A(ω)|² independently (for example from the reflection coefficient of the line, or by displaying the resonance spectrum that yields Q ~ 30–50) or state explicitly that the absolute power calibration is not independently verified and that the claim rests on the spectral and correlation signatures.
[Paragraph beginning 'The flux through the SQUID is driven at microwave frequencies...'] The conclusion that thermal effects are negligible rests on n = 0.008 at 5 GHz, taken from the 50 mK bath temperature. The SQUID is driven at microwave frequencies through a filtered and attenuated line, but the manuscript does not independently bound excess noise or local heating at the SQUID produced by the drive itself. Because the DCE-to-upconversion ratio in the difference signal is 1/n_in, a tenfold excess in n_in would still leave the DCE dominant, but a hundredfold excess would not. The authors should provide a bound on the noise temperature at the SQUID, for example from the drive-off output power at the analysis frequencies, from a calibrated noise measurement, or from a comparison of the drive-on and drive-off total power at several drive powers. As written, the statement that thermal effects are negligible is an assumption rather than a measurement.
[Fig. 3c and Eqs. (3)–(4)] The value σ2 ~ 0.04 is quoted as 'consistent with our expectations' without an uncertainty, and the scatter visible in Fig. 3c appears comparable to the signal at low drive power. Since the two-mode squeezing is the load-bearing evidence for the quantum character of the generation process, the manuscript should report error bars or a statistical significance for σ2 and for the correlation amplitudes in Fig. 3a, state how many independent samples and how much integration time underlie each point, and clarify how the expected value was computed. In particular, the predicted σ2 ≈ ve/2c0 depends on δle, which is not independently measured; the manuscript should state how the 10% inductance modulation was determined and what uncertainty that carries.

Minor objections (9)

[Throughout] Several typographical errors should be corrected: 'losses energy' should be 'loses energy'; 'near the speed light' should be 'near the speed of light'; 'were we expect' should be 'where we expect'; 'seperation' should be 'separation'; 'have lead to' should be 'have led to'; and the author name 'G¨ unter' should be 'Günter'.
[Title page] The 'PACS numbers:' line is empty and should either be populated or removed.
[Eq. (1) and surrounding text] The quantity A(ω) is introduced as 'the spectral amplitude of the transmission line' without a definition. Please define A(ω) explicitly and state that |A(ω)|² is the density of photonic states, since the enhancement argument later in the paper depends on this quantity.
[Fig. 1c caption] The caption states that the filter 'ensures that no thermal radiation couples to the transmission line in the frequency region were we expect DCE radiation', but the 8.4–12 GHz bandpass filter is on the drive line, not the output line. Please clarify which line the filter protects and what limits the input noise on the output line.
[Fig. 2a and accompanying text] The statement that photon generation is seen 'for essentially all drive frequencies spanning the 8-12 GHz band' should note that this band is set by the drive-line filter, so the observation is filter-limited rather than a demonstration of unbounded bandwidth.
[Fig. 3d] Only the real part of Ψ is displayed. Please show the imaginary part as well, or state why the real part alone suffices to establish the rotation symmetry.
[Paragraph on correlations, 'we have measured similar values with separations as large as 700 MHz'] Please give the measured value of σ2 at the 700 MHz separation rather than only stating that similar values were obtained.
[Eq. (4) and the approximation σ2 ≈ ve/2c0] Please state the regime of validity of the approximation (small detuning and small modulation) and indicate how it compares with the full expression in the range of the reported measurements.
[Discussion of parametric amplifiers] The broadband argument distinguishes the observation from a single-mode cavity parametric amplifier, but a broadband transmission-line parametric amplifier would also produce broadband output. The text should acknowledge this and emphasize that the two-mode squeezing and phase-rotation tests, rather than bandwidth alone, are the decisive discriminators.

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The paper

The paper claims

By modulating the inductance of a SQUID at the end of a microwave transmission line, the authors report the first observation of the dynamical Casimir effect: real photons created out of the vacuum, emitted in correlated pairs.

The reading

Quantum theory says the electromagnetic vacuum is not empty but fluctuating, and forty years ago it was predicted that a mirror moving near the speed of light could shake those virtual fluctuations into real photons. Nobody can move a mirror that fast, so the authors replace the mirror with a boundary condition that can be moved electrically: a superconducting quantum interference device (SQUID) terminating a coplanar transmission line, whose inductance is modulated at about 11 GHz. Because the line's effective electrical length follows the SQUID inductance, the boundary sweeps at a few percent of the speed of light, far faster than any mechanical mirror, and the predicted photon flux is correspondingly large. The paper reports broadband microwave emission centred on half the drive frequency, and, more tellingly, correlations between the upper and lower sidebands with the sign structure and phase-rotation symmetry expected of two-mode squeezing. If the identification is right, this is the first direct laboratory production of photons from vacuum fluctuations, and it delivers those photons as entangled pairs in a circuit-compatible band.

What carries the argument

The machinery is the equivalence between a moving mirror and a tunable electrical boundary. For a static flux, the SQUID reflects with coefficient $R(omega) = -exp[2ik_omega ell_e(Phi_ext)]$, exactly the phase shift of a line of length $ell_e = L_J(Phi_ext)/L_0$, so modulating the flux modulates the electrical length. Solving the scattering problem in Fourier space gives $a_{out}(omega) = R(omega)a_{in}(omega) + S(omega)a^dagger_{in}(omega_d - omega)$ with $S(omega) = -i(delta ell_e/c_0)sqrt{omega(omega_d-omega)}A(omega)A^*(omega_d-omega)$, where $A(omega)$ is the spectral amplitude encoding the photonic density of states. The mixing of creation and annihilation operators is the whole effect: it converts vacuum into photons, and because it mixes $a$ with $a^dagger$ rather than $a$ with $a$, the output is two-mode squeezed rather than merely thermal. The predicted ideal flux is $Gamma_{DCE} = (omega_d/12pi)(v_e/c_0)^2$, which vanishes as $c_0 to infinity$ and is therefore explicitly relativistic.

Extended reading notes

Core claim

The claim is that a periodically modulated boundary condition on a one-dimensional electromagnetic field generates real photons from the vacuum, and that the generated field carries the two-mode squeezing signature of pairwise creation. The authors drive the flux through a SQUID terminating a coplanar waveguide at frequencies between roughly 8 and 12 GHz, and observe excess output power across a broad analysis band from about 4 to 6 GHz, i.e. at frequencies that sum to the drive frequency, $f_1 + f_2 = f_d$. The emission is broadband in both drive and analysis frequency, which the authors argue rules out a driven single-mode parametric amplifier as the source. They then measure cross-correlations between the quadratures of two sidebands separated by 40 MHz (and up to 700 MHz) and find $I_+I_-$ positive and $Q_+Q_-$ negative, with a normalized two-mode squeezing statistic $|sigma_2|$ of about 0.04, while each sideband individually remains unsqueezed. Finally, they show that the complex correlation $|Psi$ is invariant when a rotation of the measured phase is cancelled by an equal rotation of the drive phase, as expected for a two-mode squeezed state.

Load-bearing premise

The load-bearing premise is that the observed radiation really is vacuum-driven rather than classical upconversion of residual noise, and the power budget is reconciled by attributing a roughly thousandfold excess over the ideal-line prediction to parasitic resonances with $Q$ of 30 to 50 that boost the density of states by about $Q^2$ — an enhancement inferred from the same measurement rather than independently calibrated.

Editorial extensions

If this is right

A modulated boundary in a one-dimensional line is a practical, chip-scale source of microwave photon pairs, since the effect scales with the boundary velocity $v_e = delta ell_e omega_d$ rather than with any mechanical displacement.
The two-mode squeezing statistic $sigma_2$ provides a quantitative handle on the generation strength, estimated as roughly $v_e/2c_0$ for small detuning, so stronger inductance modulation should give proportionally stronger correlations.
The broadband, pairwise character of the emission distinguishes it from a driven cavity parametric amplifier, giving an experimental signature that can be checked at arbitrary detuning rather than only at a resonance.
Because the effect is predicted to be present with the input in its vacuum state, the output should not scale with the input thermal occupation, which separates it from ordinary upconversion of noise.

Reading between the lines

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

If the pairwise correlations survive with larger modulation depth, this circuit becomes a candidate source of microwave entanglement for two-mode quantum sensing or for verifying nonclassicality without cryogenic single-photon detectors.
The same scattering formalism, with a non-sinusoidal modulation of $ell_e$, predicts more general squeezed states; a driven boundary with a tailored waveform is a plausible route to single-mode or multi-mode squeezing in a transmission line.
The mechanism is a tabletop analogue of the kinematic ingredient in Hawking and Unruh radiation, where an accelerated boundary mixes positive- and negative-frequency modes; a transmission line whose effective velocity profile mimics an horizon would be a natural next device.
The scaling with the density of states $|A(omega)|^2$ suggests a deliberate engineering trade-off: a high-quality resonance boosts the rate by roughly $Q^2$ but narrows the band, so the design space between rate and bandwidth is a testable prediction in its own right.

Original abstract

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. While initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences, for instance producing the Lamb shift of atomic spectra and modifying the magnetic moment for the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed if it might instead be possible to more directly observe the virtual particles that compose the quantum vacuum. 40 years ago, Moore suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. This effect was later named the dynamical Casimir effect (DCE). Using a superconducting circuit, we have observed the DCE for the first time. The circuit consists of a coplanar transmission line with an electrical length that can be changed at a few percent of the speed of light. The length is changed by modulating the inductance of a superconducting quantum interference device (SQUID) at high frequencies (~11 GHz). In addition to observing the creation of real photons, we observe two-mode squeezing of the emitted radiation, which is a signature of the quantum character of the generation process.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,139 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.95 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.67 · compares with prior results 0.43 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. While initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences, for instance producing the Lamb shift of atomic spectra and modifying the magnetic moment for the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed if it might instead be possible to more directly observe the virtual particles that compose the quantum vacuum. 40 years ago, Moore suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. This effect was later named the dynamical Casimir effect (DCE). Using a superconducting circuit, we have observed the DCE for the first time. The circuit consists of a coplanar transmission line with an electrical length that can be changed at a few percent of the speed of light. The length is changed by modulating the inductance of a superconducting quantum interference device (SQUID) at high frequencies (~11 GHz). In addition to observing the creation of real photons, we observe two-mode squeezing of the emitted radiation, which is a signature of the quantum character of the generation process.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty.	background 1.00	0.03	0.02	asserted 0.99
s1	In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence.	background 1.00	0.03	0.02	asserted 0.97
s2	While initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences, for instance producing the Lamb shift of atomic spectra and modifying the magnetic moment for the electron.	background 1.00	0.03	0.02	asserted 1.00
s3	This type of renormalization due to vacuum fluctuations is now central to our understanding of nature.	background 1.00	0.03	0.02	asserted 1.00
s4	However, these effects provide indirect evidence for the existence of vacuum fluctuations.	gap 0.68	0.04	0.03	asserted 0.97
s5	From early on, it was discussed if it might instead be possible to more directly observe the virtual particles that compose the quantum vacuum. 40 years ago, Moore suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons.	background 0.88	0.03	0.03	hedged possibility 0.58
s6	This effect was later named the dynamical Casimir effect (DCE).	background 1.00	0.04	0.04	asserted 1.00
s7	Using a superconducting circuit, we have observed the DCE for the first time.	result 0.63	0.98	0.92	asserted 1.00
s8	The circuit consists of a coplanar transmission line with an electrical length that can be changed at a few percent of the speed of light.	method 0.99	0.72	0.03	asserted 1.00
s9	The length is changed by modulating the inductance of a superconducting quantum interference device (SQUID) at high frequencies (~11 GHz).	method 1.00	0.85	0.03	asserted 1.00
s10	In addition to observing the creation of real photons, we observe two-mode squeezing of the emitted radiation, which is a signature of the quantum character of the generation process.	result 0.97	0.96	0.25	asserted 1.00

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: a) Optical micrograph of the device. Light parts are Al while dark parts are the Si

**Figure 2.** FIG. 2: Photons generated by the dynamical Casimir effect. Here we show the output power of the

**Figure 3.** FIG. 3: Two-mode squeezing of the DCE field. a) and b) The normalized cross-correlation functions

Figures reproduced from arXiv:1105.4714 by the authors.

References

Works cited (23)

[12]

G. G¨ unter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. D. Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, et al., Nature 457, 178 (2009)

View on Pith 2009
[13]

J. R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Phys Rev Lett 103, 147003 (2009)

View on Pith 2009
[1]

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997)

View on Pith 1997
[2]

W. Greiner and S. Schramm, Am J Phys 76, 509 (2008)

View on Pith 2008
[3]

In Fig. 3a & b, we show the ⟨I+I−⟩ and⟨Q+Q−⟩ cross correlations with the drive on and drive oﬀ for comparison. With the drive on, we see very clear cross correlations which are∼ 100 times larger than the parasitic ampliﬁer correlation. Also, we see that indeed ⟨I+I−⟩ =−⟨Q+Q−⟩ as we expect for two-mode squeezing. We also see that this is not the case for t...

View on Pith
[4]

G. Moore, J. Math. Phys. 11, 2679 (1970)

View on Pith 1970
[5]

H. B. G. Casimir, Proc. Kon. Nederland. Akad. Wetensch. B51, 793 (1948)

View on Pith 1948
[6]

S. K. Lamoreaux, Physics Today 60, 40 (2007). 11

View on Pith 2007
[7]

C. Braggio, G. Bressi, G. Carugno, C. D. Noce, G. Galeazzi, A. Lombardi, A. Palmieri, G. Ruoso, and D. Zanello, Europhys Lett 70, 754 (2005)

View on Pith 2005
[8]

E. Yablonovitch, Phys Rev Lett 62, 1742 (1989)

View on Pith 1989
[9]

Y. Lozovik, V. Tsvetus, and E. Vinogradov, JETP Lett 61, 723 (1995)

View on Pith 1995
[10]

V. Dodonov, A. Klimov, and D. Nikonov, Phys Rev A 47, 4422 (1993)

View on Pith 1993
[11]

S. Liberato, C. Ciuti, and I. Carusotto, Phys Rev Lett 98, 103602 (2007)

View on Pith 2007
[14]

J. R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Phys. Rev. A 82, 052509 (2010)

View on Pith 2010
[15]

C. M. Wilson, T. Duty, M. Sandberg, F. Persson, V. Shumeiko, and P. Delsing, Phys Rev Lett 105, 233907 (2010)

View on Pith 2010
[16]

P. D. Nation, J. R. Johansson, M. P. Blencowe, and F. Nori, arXiv quant-ph (2011), 1103.0835v1

View on Pith Pith review arXiv 2011
[17]

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Appl. Phys. Lett. 92, 203501 (2008)

View on Pith 2008
[18]

S. A. Fulling and P. C. W. Davies, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 348, 393 (1976)

View on Pith 1976
[19]

A. Lambrecht, M. Jaekel, and S. Reynaud, Phys Rev Lett 77, 615 (1996)

View on Pith 1996
[20]

C. M. Caves and B. L. Schumaker, Phys Rev A 31, 3068 (1985)

View on Pith 1985
[21]

B. Yurke and J. S. Denker, Phys Rev A 29, 1419 (1984)

View on Pith 1984
[22]

Two-mode squeezing is often discussed in terms of the unitary squeezing operator Θ( r) = exp[ra(ω+)a(ω−)−ra†(ω+)a†(ω−)] where r is called the squeezing parameter. To connect to this language, one can show that σ2 =−λ+λ− tanh(2r). This then gives r = (δ𝓁e/c0)√ω+ω−

View on Pith
[23]

In Fig. 3, we have displayed time correlation functions (TCF) which are the Fourier transforms of the frequency correlation functions (FCF) deﬁned in the text. In particular, the value of the TCF at zero delay is the integral of the FCF in the measurement bandwidth. If we assume that the FCF is approximately constant in the measurement bandwidth, the inte...

View on Pith

Forward citations

Cited by 5 Pith papers

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

High-Frequency Gravitational-Wave Transduction in a SQUID-Terminated Superconducting Cavity
gr-qc 2026-09 conditional novelty 6.0 of 10

A SQUID-terminated superconducting cavity can act as a narrowband parametric transducer for high-frequency gravitational waves, with two distinct response kernels for frequency modulation and pair production.
Time Dependence of Particle Creation from Accelerating Mirrors
gr-qc 2013-03 conditional novelty 6.0 of 10

Wave-packet analysis of six accelerating-mirror trajectories, four of them new and analytically solvable, shows that particle production can be time-resolved but not simultaneously resolved in time and frequency.
Cosmological Inflation and the Quantum Measurement Problem
hep-th 2012-07 conditional novelty 6.0 of 10

CSL applied to inflation yields a two-branch power spectrum (n_S = 1 and n_S = 4), forcing the collapse parameter to be fine-tuned below 10^{-28} and leaving the collapse inefficient.
Dissipative Effects in Transmission Line Analogues of Hawking Radiation
quant-ph 2026-06 unverdicted novelty 5.0 of 10

Open-quantum-systems analysis of dissipative dc-SQUID and SNAIL transmission-line analogues of Schwarzschild black holes yields detectability thresholds showing Hawking temperatures above 73 mK remain observable, with...
Analogue gravity with Bose-Einstein condensates
gr-qc 2025-12 conditional novelty 2.0 of 10

Phonons in a Bose–Einstein condensate behave as a massless scalar field on an acoustic spacetime; these notes derive that mapping in detail and apply it to superradiance and analogue Hawking radiation.

How later papers used it

172 later papers cite it

Evidence: substantial. 145 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 262 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 cited it as support.

Cites it as support 1 of 3 papers with this label

Said that a switching rate above 20 GHz seems feasible as shown by circuit QED experiments.

Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture (2016) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

43 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 64 sentences without a confident label

Compares with it 1 paper

In the first case, the cosmic expansion engenders a parametric amplification of homogeneous modes which is very similar to that at the origin of the dynamical Casimir effect (DCE) [ref] , compare for instance Ref. [ref] with Refs. [ref] .

Dispersive and dissipative effects in quantum field theory in curved space-time to model condensed matter systems · Conclusions · 0.83

Cites it as background 10 papers

This approach is closely related to the so-called dynamic Casimir effect where an accelerating mirror is creating particles out of vacuum [ref] .

Smooth and sharp creation of a spherical shell for a $(3+1)$-dimensional quantum field · Introduction · 0.86
Its potential applications include single- and two-qubit quantum gates via dispersive [ref] or resonant coupling [ref] , three-qubit gate and entanglement generation [ref] , as well as novel quantum phenomena in circuit QED such as dynamical Casimir effect [ref] , and the ultrastrong coupling (USC) regime of light-matter interaction [ref] .

Validity of resonant two-qubit gates in the ultrastrong coupling regime of circuit QED · Introduction · 0.97
Also, virtual photon pairs are converted into real ones in the dynamical Casimir effect (DCE) [ref] , which has been analyzed for [ref] and experimentally demonstrated [ref] in circuit QED.

Cutting Feynman Loops in Ultrastrong Cavity QED: Stimulated Emission and Reabsorption of Virtual Particles Dressing a Physical Excitation · Introduction · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [12]

G. G¨ unter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. D. Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, et al., Nature 457, 178 (2009)

View on Pith 2009

[2] [13]

J. R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Phys Rev Lett 103, 147003 (2009)

View on Pith 2009

[3] [1]

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997)

View on Pith 1997

[4] [2]

W. Greiner and S. Schramm, Am J Phys 76, 509 (2008)

View on Pith 2008

[5] [3]

In Fig. 3a & b, we show the ⟨I+I−⟩ and⟨Q+Q−⟩ cross correlations with the drive on and drive oﬀ for comparison. With the drive on, we see very clear cross correlations which are∼ 100 times larger than the parasitic ampliﬁer correlation. Also, we see that indeed ⟨I+I−⟩ =−⟨Q+Q−⟩ as we expect for two-mode squeezing. We also see that this is not the case for t...

View on Pith

[6] [4]

G. Moore, J. Math. Phys. 11, 2679 (1970)

View on Pith 1970

[7] [5]

H. B. G. Casimir, Proc. Kon. Nederland. Akad. Wetensch. B51, 793 (1948)

View on Pith 1948

[8] [6]

S. K. Lamoreaux, Physics Today 60, 40 (2007). 11

View on Pith 2007

[9] [7]

C. Braggio, G. Bressi, G. Carugno, C. D. Noce, G. Galeazzi, A. Lombardi, A. Palmieri, G. Ruoso, and D. Zanello, Europhys Lett 70, 754 (2005)

View on Pith 2005

[10] [8]

E. Yablonovitch, Phys Rev Lett 62, 1742 (1989)

View on Pith 1989

[11] [9]

Y. Lozovik, V. Tsvetus, and E. Vinogradov, JETP Lett 61, 723 (1995)

View on Pith 1995

[12] [10]

V. Dodonov, A. Klimov, and D. Nikonov, Phys Rev A 47, 4422 (1993)

View on Pith 1993

[13] [11]

S. Liberato, C. Ciuti, and I. Carusotto, Phys Rev Lett 98, 103602 (2007)

View on Pith 2007

[14] [14]

J. R. Johansson, G. Johansson, C. M. Wilson, and F. Nori, Phys. Rev. A 82, 052509 (2010)

View on Pith 2010

[15] [15]

C. M. Wilson, T. Duty, M. Sandberg, F. Persson, V. Shumeiko, and P. Delsing, Phys Rev Lett 105, 233907 (2010)

View on Pith 2010

[16] [16]

P. D. Nation, J. R. Johansson, M. P. Blencowe, and F. Nori, arXiv quant-ph (2011), 1103.0835v1

View on Pith Pith review arXiv 2011

[17] [17]

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Appl. Phys. Lett. 92, 203501 (2008)

View on Pith 2008

[18] [18]

S. A. Fulling and P. C. W. Davies, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 348, 393 (1976)

View on Pith 1976

[19] [19]

A. Lambrecht, M. Jaekel, and S. Reynaud, Phys Rev Lett 77, 615 (1996)

View on Pith 1996

[20] [20]

C. M. Caves and B. L. Schumaker, Phys Rev A 31, 3068 (1985)

View on Pith 1985

[21] [21]

B. Yurke and J. S. Denker, Phys Rev A 29, 1419 (1984)

View on Pith 1984

[22] [22]

Two-mode squeezing is often discussed in terms of the unitary squeezing operator Θ( r) = exp[ra(ω+)a(ω−)−ra†(ω+)a†(ω−)] where r is called the squeezing parameter. To connect to this language, one can show that σ2 =−λ+λ− tanh(2r). This then gives r = (δ𝓁e/c0)√ω+ω−

View on Pith

[23] [23]

In Fig. 3, we have displayed time correlation functions (TCF) which are the Fourier transforms of the frequency correlation functions (FCF) deﬁned in the text. In particular, the value of the TCF at zero delay is the integral of the FCF in the measurement bandwidth. If we assume that the FCF is approximately constant in the measurement bandwidth, the inte...

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