Pith. sign in

REVIEW 3 major objections 7 minor 51 references

Quantum sensitivity of parametric oscillators

T0 review · 3 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Quantum states imprint themselves on a classical phase choice

desk verdict A clean, useful extension of the vacuum bias result to arbitrary quantum states, but the Q-function reconstruction claim needs a stated lambda<=2 validity bound and a quantitative linearization condition. read the letter →

arxiv 2412.02887 v2 pith:F2IXJQ26 submitted 2024-12-03 quant-ph physics.optics

Alex Gu , Jamison Sloan , Charles Roques-Carmes , Seou Choi , Eric I. Rosenthal , Michael Horodynski , Yannick Salamin , Jelena Vučković
show 1 more author
Marin Soljačić
This is my paper · ORCID
classification quant-phphysics.optics
keywords quantumsensitivityparametricoscillationinitialconditionsbistablesteadystatesHusimiQ-functionreconstructionJosephsonoscillatordriven-dissipativesystemsnonlineardynamics
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

An optical parametric oscillator driven above threshold must choose between two steady phases, so its final condition is a macroscopic, apparently random decision. This paper claims that the probabilities of that decision are a filtered image of the quantum state that started in the cavity: the early parametric gain amplifies the initial $X$-quadrature distribution, cavity loss smooths it with a Gaussian of known width, and the sign at the moment of amplification decides the phase. The derived formula is Eq. (3), where the probability of the $\alpha^{(1)}$ outcome is the integral over a shifted half-line of the initial marginal convolved with that Gaussian. Because sweeping the coherent bias shifts the decision boundary, the measured bias-probability curve is the cumulative of the smoothed marginal; differentiating it and rotating the pump phase reconstructs the initial Husimi $Q$-function. The authors argue the same mechanism governs Josephson parametric oscillators, making the effect testable in superconducting circuits.

What carries the argument

The key machinery is the early-time linearization of the Heisenberg-Langevin equation, Eq. (1), into the decoupled stochastic quadrature equations (2): $\dot X = (\lambda-1)X + \sqrt{2}b + \sqrt{1+\xi(1-\lambda)}\,\eta_1(t)$ and $\dot Y = -(\lambda+1)Y + \sqrt{1+\xi(1+\lambda)}\,\eta_2(t)$, with $\eta_1,\eta_2$ independent standard-normal noises. Integrating the $X$ equation turns the initial marginal into a Gaussian-smoothed one whose width $\sigma^2 = (1+\xi(1-\lambda))/(2(\lambda-1))$ is the Green's function of the linearized amplifier; the sign of the smoothed trajectory at the decision time selects the steady state. The special value $\lambda=2$ in the Husimi $Q$ representation makes the noise term vanish, so the final phase is deterministic given the initial $X$ sign; for other parameters the Gaussian filter widens and washes out fine features of the initial distribution. Everything downstream in the paper -- the bias-probability curve, the reconstruction protocol, the JPO extension -- is this linear-filter picture transported to a measurable classical probability.

What would settle it

Prepare a non-Gaussian initial state, such as a cat state with appreciable amplitude near $X=0$, pump the oscillator just above threshold, and measure $p(b)$ for several bias values; Eq. (3) predicts precisely the smoothed cumulative marginal $p_{X_0} * g_\sigma$. The prediction would be falsified by observing a bias-probability curve that depends on the nonlinearity strength $g^2$ or that is sharper than the smoothed marginal, since either would show nonlinear saturation intervening before the linear filtering completed. A systematic scan of initial states with increasing separatrix weight would locate the boundary of the early-linearization regime.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes a quantitative 'quantum sensitivity': a closed relationship between an arbitrary initial quantum state and the steady-state probabilities of a degenerate biased OPO. In the regime $g^2 \ll \lambda - 1$, the steady-state probabilities are set during early-time linearized dynamics, before the nonlinear saturation term $g^2(a^\dagger a)a$ becomes important. The result is Eq. (3), $p(\alpha^{(1)}, b) = \int_{-\sqrt{2}b/(\lambda-1)}^{\infty} (p_{X_0} * g_\sigma)(x)\,dx$, with $p_{X_0}$ the $X$-marginal of the initial phase-space distribution and $g_\sigma$ a zero-mean Gaussian of variance $\sigma^2 = (1+\xi(1-\lambda))/(2(\lambda-1))$. The authors describe the content as: the steady-state distribution $p(\alpha^{(1)})$ is the initial $X$-quadrature marginal, smoothed by a Gaussian of variance $\sigma^2$, then integrated over the right of the decision boundary. The parameter $\xi$ selects the quasiprobability representation, with $\xi=1$ for the Husimi $Q$-function used in the simulations, $\xi=0$ for Wigner, and $\xi=-1$ for Glauber-Sudarshan $P$. The paper further shows numerically that the same bias-probability formula holds for vacuum, squeezed, Fock, cat, and arbitrary states, and that a Josephson parametric oscillator obeys the same Heisenberg-Langevin structure, so the same mapping applies there.

Load-bearing premise

The load-bearing premise is that the phase choice is fully determined during early linear growth, so the nonlinear saturation term can be ignored while the sign of the amplified quadrature is being decided; this requires the initial state to have negligible probability weight near the unstable separatrix and the saturation photon number to be large compared with the initial fluctuation scale.

Editorial extensions

If this is right

  • The derivative of the measured bias-probability curve gives the Gaussian-smoothed $X$-marginal of the initial quantum state, so a single sweep of the bias is a partial state-characterization measurement.
  • Rotating the pump phase before repeating the sweep reconstructs the full Husimi $Q$-function, which fully describes the initial state, from classical phase-choice statistics alone.
  • The theory predicts that each initial state's $X$-marginal shape, not just its center of mass, controls the phase-choice curve, so Fock and squeezed states produce visibly different $p(b)$ at fixed bias.
  • Because Josephson parametric oscillators obey the same equations, the prediction is testable in superconducting circuits where non-Gaussian states can be prepared and swapped into a parametric cavity.
  • The authors argue that the same early-linearization reasoning should generalize to other multistable driven-dissipative systems in the low-quantum-noise regime.

Reading between the lines

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

  • Editorial extension: with a calibrated Gaussian width, deconvolution of $p'(b)$ could recover the unsmoothed marginal, effectively performing quantum state tomography of non-Gaussian states without heterodyne detection, limited by how close to threshold the oscillator can run.
  • Editorial extension: the treatment suggests the classical bias acts as a movable decision boundary while the quantum state supplies the shape of the probability distribution; thus phase-choice statistics isolate the quantum contribution to the initial condition, which could be used to certify non-Gaussianity in a single macroscopic observable.
  • Editorial extension: operating near threshold ($\lambda$ close to 1) maximizes the sensitivity of the outcome to small differences in the initial state, pointing toward quantum-enhanced sensing of quadrature displacements, provided the early-linearization assumption remains valid.
  • Editorial extension: applying the same logic to multimode systems such as Kerr combs would require a multimode generalization of Eq. (3), but if that exists, the steady-state phase pattern could encode intermodal quantum correlations and enable tomography of multimode entangled states.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 7 minor

Summary. The paper analyzes a degenerate optical parametric oscillator (OPO) initialized in an arbitrary quantum state and claims that the steady-state probabilities of the two bistable phases are determined by the early-time linearized dynamics. The central formula, Eq. (3), expresses the probability p(α(1), b) as the integral over the right half of the initial X-quadrature marginal convolved with a Gaussian whose variance depends on the gain λ and the phase-space representation ξ. The authors validate Eq. (3) with stochastic simulations for vacuum, squeezed, Fock, cat, and arbitrary states, propose that rotating the pump phase reconstructs the initial Husimi Q-function, and extend the model to Josephson parametric oscillators (JPOs).

Significance. If Eq. (3) is correct and its validity range is properly stated, the paper provides a simple analytical map from an initial quantum state's X-marginal to a macroscopic bistable outcome probability, with potential applications in quantum state reconstruction and in controlling driven-dissipative systems. The analytical derivation from Eq. (2) to Eq. (3) is straightforward, and the simulation agreement shown in Figs. 2 and 3 supports the result in the tested parameter regimes. The JPO proposal connects the theory to an existing superconducting-circuit platform, which strengthens the practical relevance. However, the Q-function reconstruction claim is presently stated without a necessary stability bound in λ, and the linearization assumption lacks a quantitative validity condition, so the central claim is not yet established in the full generality claimed.

major comments (3)
  1. [Results, Eq. (3) and Fig. 3] For the Husimi Q representation (ξ=1), the variance in Eq. (3) is σ²=(2−λ)/(2(λ−1)), which is positive only for 1<λ<2, vanishes at λ=2, and is negative for λ>2. The text states the Q-function dynamics generically and refers to λ=2 as the 'noiseless regime', but it never restricts the Q-function claim to λ≤2. For λ>2, Eq. (2) itself has an imaginary noise coefficient for the Q representation, so the stochastic differential equation is not a real SDE and the Gaussian-smoothing interpretation of Eq. (3) is undefined. The paper must either explicitly restrict the Q-function reconstruction claim to 1<λ≤2 (treating λ=2 as a limiting case) or provide a Wigner-based version (ξ=0) for λ>2 and state that the Q-function reconstruction is not valid there.
  2. [Results, before Eq. (2)] The derivation of Eq. (2) drops the nonlinear term g²(a†a)a under the assumption g²≪λ−1, with the argument that steady-state probabilities are decided by early-time linearized dynamics. The manuscript does not state a quantitative condition on the initial state that makes this approximation valid. If the initial X-marginal has significant support near the separatrix (X≈0) or if the initial fluctuation amplitude is comparable to the saturation photon number, the nonlinearity can act before the sign decision is complete and bias the outcome away from Eq. (3). Please provide a concrete validity criterion (for example, a bound on the initial-state width relative to the saturation amplitude, or an estimate of the nonlinear correction during the decision time) and test Eq. (3) for initial states that approach that boundary, such as large-amplitude displaced states or states with substantial weight near X=0.
  3. [Results, Q-function reconstruction claim] The statement that 'rotating the pump phase and repeating this procedure across various phases reconstructs the entire initial Q-function' requires inverting the Gaussian convolution in Eq. (3). For λ close to 1, the smoothing variance σ² can be large, making the deconvolution ill-conditioned; the paper does not describe the deconvolution procedure, its achievable fidelity, or its noise sensitivity. Figure 3(d) only shows reconstruction of the smoothed marginal at λ=2.0 and λ=1.2, and for λ=1.2 the derivative p'(b) still contains the Gaussian filter. Please specify the reconstruction protocol (including the deconvolution step and its resolution limits) or revise the claim to state that the measured quantity is a smoothed marginal rather than the exact initial Q-function.
minor comments (7)
  1. [Fig. 2 caption] The caption says 'Marginal Q-function (integrated along Y quadrature)' but does not state that this is the X-marginal Q(X)=∫dY Q(X+iY); please make that explicit.
  2. [Fig. 3(d)] The label p'(b) is not defined in the text or caption; clarify whether it is a numerical derivative of p(b) and how the Gaussian deconvolution (if any) was applied to obtain the reconstructed quadrature.
  3. [Eq. (4)] The JPO Langevin equation uses +ig²(a†a)a while the OPO equation (1) has −g²(a†a)a; if this sign difference is intentional (e.g., a different Kerr convention), state it explicitly; otherwise it appears to be a typo.
  4. [Fig. 3 and main text] Calling λ=2 the 'noiseless regime' is potentially confusing: the physical system is not noiseless; rather, the noise coefficient in the Q-representation SDE vanishes. Please clarify this wording.
  5. [Introduction] The phrase 'high sensitivity to initial conditions' may be misread as classical chaos; the paper actually addresses the dependence of bistable-outcome probabilities on the initial quantum state. A sentence distinguishing this from exponential divergence of trajectories would improve readability.
  6. [Data and code availability] The statement that data and codes are 'available from the corresponding authors upon reasonable request' is weaker than a public repository; please provide a repository link for reproducibility.
  7. [Eq. (2) derivation] Eq. (2) is the foundation for the central result, but its derivation is relegated to SI Section S1, which was not available for inspection; please include at least a concise derivation sketch in the main text or supplement the main text with the key steps.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Eq. (3) is solved from the linearized SDE with the initial X-marginal as an independent input; self-citations are peripheral, and the lambda>2 caveat is a validity issue, not circularity.

full rationale

The central result, Eq. (3), is obtained by integrating the linearized stochastic differential equation Eq. (2) for the X quadrature. The initial X-marginal pX0 is an independent input, and no parameter is fitted to the steady-state probabilities being predicted. The reconstruction protocol (differentiating p(b) with respect to b and rotating the pump phase) is a linear inversion of Eq. (3), not a re-labeling of the result, and the paper demonstrates it on simulated cat, Fock, squeezed, and arbitrary states in Figs. 2 and 3. The cited prior work [30] is used only for the existence of bistable steady states and [32] for the completeness of Q-function tomography; neither carries the derivation, and the paper's own stochastic simulations, plus the standard textbook reference [31], provide independent support. Thus the self-citations are not load-bearing. The main caveat is a correctness/validity issue rather than circularity: for the Husimi Q representation (xi=1), sigma^2 = (1+xi(1-lambda))/(2(lambda-1)) = (2-lambda)/(2(lambda-1)), which is negative for lambda>2. The paper states, 'For the Q-function, the semi-classical stochastic trajectories has a noise coefficient which vanishes at lambda = 2,' and later claims, 'In principle, we could also rotate the pump phase and repeat this procedure across various phases—thereby reconstructing the entire initial Q-function,' without explicitly restricting lambda to the domain where the Gaussian variance is nonnegative. Figs. 2 and 3 only show lambda = 1.2 and lambda = 2.0. This missing bound does not make Eq. (3) circular, because within its domain of validity the formula is still a direct solution of the linearized SDE with the initial state as an external input. Overall, I find no significant circularity; the score of 1 reflects only the presence of minor self-citations that do not support the central claim.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters were fitted; lambda, b, and g are physical control parameters. The derivation rests on the linearized early-time approximation and on the validity of the phase-space representation; these are assumptions, not fitted constants. No new entities are introduced.

assumptions (4)
  • domain assumption The OPO is accurately described by the single-mode Heisenberg-Langevin equation Eq. (1) with Markovian noise.
    Standard cavity QED treatment; assumes single mode, rotating wave, weak coupling to bath; cited refs [31].
  • ad hoc to paper In the low quantum noise regime g^2 << lambda-1, steady-state basin probabilities are set by early-time linearized dynamics before nonlinear saturation.
    This is the key approximation that lets the authors drop the nonlinear term and integrate Eq. (2); stated in the paragraph before Eq. (2), not proven from the master equation.
  • domain assumption For the chosen phase-space representation, Eq. (2) with representation-dependent noise coefficient sqrt(1+xi(1-lambda)) is a valid stochastic description; the diffusion coefficient must be nonnegative for the chosen representation.
    Needed for Eq. (3); for xi=1 it requires lambda <= 2, a restriction not stated.
  • domain assumption The probability of reaching the alpha(1) steady state equals the probability that the long-time amplified X quadrature is positive.
    Assumes the separatrix is at X=0 and no additional phase-space rotations occur during saturation for the OPO case; the JPO case is treated as a rotation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum sensitivity of parametric oscillators." pith.science (2026). https://pith.science/paper/F2IXJQ26

@misc{pith2026241202887,
  author       = {Pith},
  title        = {Pith review of: Quantum sensitivity of parametric oscillators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F2IXJQ26}},
  note         = {Machine review of arXiv:2412.02887}
}
read the original abstract

Many quantum systems exhibit high sensitivity to their initial conditions, where microscopic quantum fluctuations can significantly influence macroscopic observables. Understanding how quantum states may influence the behavior of nonlinear dynamic systems may open new avenues in controlling light-matter interactions. To explore this issue, we analyze the sensitivity of a fundamental quantum optical process - parametric oscillation - to quantum initializations. Focusing on optical parametric oscillators (OPOs), we demonstrate that the quantum statistics of arbitrary initial states are imprinted in the early-stage dynamics and can persist in the steady-state probabilities. We derive the "quantum sensitivity" of parametric oscillators, linking the initial quantum state to the system's steady-state outcomes, highlighting how losses and parametric gain govern the system's quantum sensitivity. Moreover, we show that these findings extend beyond OPOs to a broader class of nonlinear systems, including Josephson junction based superconducting circuits. Our work opens the way to a new class of experiments that can test the sensitivity of macroscopic systems to quantum initial conditions and offers a pathway for controlling systems with quantum degrees of freedom.

Figures

Figures reproduced from arXiv: 2412.02887 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a) shows one way of setting up a superconducting microwave version of this experiment, making use of the de￾vice demonstrated in Ref. [45]. First, a quantum state is pre￾pared in a readout resonator using standard techniques from circuit quantum dynamics. Next, this s…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 48 canonical work pages

  1. [30]

    Biasing the quantum vacuum to control macro- scopic probability distributions,

    C. Roques-Carmes, Y . Salamin, J. Sloan, S. Choi, G. Velez, E. Koskas, N. Rivera, S. E. Kooi, J. D. Joannopoulos, and M. Solja ˇci´c, “Biasing the quantum vacuum to control macro- scopic probability distributions,” Science, vol. 381, no. 6654, pp. 205–209, 2023

    work page 2023

  2. [1]

    Haken, Advanced synergetics: Instability hierarchies of self- organizing systems and devices , vol

    H. Haken, Advanced synergetics: Instability hierarchies of self- organizing systems and devices , vol. 20. Springer Science & Business Media, 2012

    work page 2012

  3. [2]

    F. T. Arecchi and R. G. Harrison, Instabilities and chaos in quantum optics, vol. 34. Springer Science & Business Media, 2012

    work page 2012

  4. [3]

    Chaos and generalized multistability in quantum optics,

    F. Arecchi, “Chaos and generalized multistability in quantum optics,” Physica Scripta, vol. 1985, no. T9, p. 85, 1985

    work page 1985

  5. [4]

    Quantum crit- icality as a resource for quantum estimation,

    P. Zanardi, M. G. Paris, and L. Campos Venuti, “Quantum crit- icality as a resource for quantum estimation,” Physical Review A—Atomic, Molecular , and Optical Physics , vol. 78, no. 4, p. 042105, 2008

    work page 2008

  6. [5]

    Critical parametric quantum sensing,

    R. Di Candia, F. Minganti, K. Petrovnin, G. Paraoanu, and S. Felicetti, “Critical parametric quantum sensing,” npj Quan- tum Information, vol. 9, no. 1, p. 23, 2023

    work page 2023

  7. [6]

    Microwave photon detection at parametric critical- ity,

    K. Petrovnin, J. Wang, M. Perelshtein, P. Hakonen, and G. S. Paraoanu, “Microwave photon detection at parametric critical- ity,” PRX Quantum, vol. 5, no. 2, p. 020342, 2024

    work page 2024

  8. [7]

    Opti- mality and noise resilience of critical quantum sensing,

    U. Alushi, W. G ´orecki, S. Felicetti, and R. Di Candia, “Opti- mality and noise resilience of critical quantum sensing,” Physi- cal Review Letters, vol. 133, no. 4, p. 040801, 2024

    work page 2024

Show all 51 references
  1. [8]

    Criticality-enhanced quantum sensing with a parametric superconducting resonator,

    G. Beaulieu, F. Minganti, S. Frasca, M. Scigliuzzo, S. Felicetti, R. Di Candia, and P. Scarlino, “Criticality-enhanced quantum sensing with a parametric superconducting resonator,” arXiv preprint arXiv:2409.19968, 2024

    2024

  2. [9]

    Quantum metrology with a squeezed kerr oscillator,

    J. Guo, Q. He, and M. Fadel, “Quantum metrology with a squeezed kerr oscillator,” Physical Review A , vol. 109, no. 5, p. 052604, 2024

    2024

  3. [10]

    Superradiance: An essay on the theory of collective spontaneous emission,

    M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Physics reports , vol. 93, no. 5, pp. 301–396, 1982

    1982

  4. [11]

    Siegman, Lasers

    A. Siegman, Lasers. University Science Books, 1986

    1986

  5. [12]

    The physics of x- ray free-electron lasers,

    C. Pellegrini, A. Marinelli, and S. Reiche, “The physics of x- ray free-electron lasers,” Reviews of Modern Physics , vol. 88, no. 1, p. 015006, 2016

    2016

  6. [13]

    Enhancing cavity quan- tum electrodynamics via antisqueezing: Synthetic ultrastrong coupling,

    C. Leroux, L. Govia, and A. Clerk, “Enhancing cavity quan- tum electrodynamics via antisqueezing: Synthetic ultrastrong coupling,” Physical review letters , vol. 120, no. 9, p. 093602, 2018

    2018

  7. [14]

    High-harmonic generation driven by quantum light,

    A. Gorlach, M. E. Tzur, M. Birk, M. Kr ¨uger, N. Rivera, O. Co- hen, and I. Kaminer, “High-harmonic generation driven by quantum light,” Nature Physics, vol. 19, no. 11, pp. 1689–1696, 2023

    2023

  8. [15]

    Multiphoton electron emis- sion with non-classical light,

    J. Heimerl, A. Mikhaylov, S. Meier, H. H ¨ollerer, I. Kaminer, M. Chekhova, and P. Hommelhoff, “Multiphoton electron emis- sion with non-classical light,” Nature Physics, pp. 1–6, 2024

    2024

  9. [16]

    Strong-field ionization of hydrogen atoms with quantum light,

    Y . Fang, F.-X. Sun, Q. He, and Y . Liu, “Strong-field ionization of hydrogen atoms with quantum light,” Physical Review Let- ters, vol. 130, no. 25, p. 253201, 2023

    2023

  10. [17]

    Compton scattering driven by intense quantum light,

    M. Khalaf and I. Kaminer, “Compton scattering driven by intense quantum light,” Science Advances , vol. 9, no. 1, p. eade0932, 2023

    2023

  11. [18]

    Squeezed states of light from an optical parametric oscillator,

    L.-A. Wu, M. Xiao, and H. Kimble, “Squeezed states of light from an optical parametric oscillator,” JOSA B, vol. 4, no. 10, pp. 1465–1475, 1987

    1987

  12. [19]

    New type of Einstein-Podolsky- Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,

    Y . Shih and C. O. Alley, “New type of Einstein-Podolsky- Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Physical Review Let- ters, vol. 61, no. 26, p. 2921, 1988

    1988

  13. [20]

    Few-cycle vacuum squeezing in nanophoton- ics,

    R. Nehra, R. Sekine, L. Ledezma, Q. Guo, R. M. Gray, A. Roy, and A. Marandi, “Few-cycle vacuum squeezing in nanophoton- ics,” Science, vol. 377, no. 6612, pp. 1333–1337, 2022

    2022

  14. [21]

    Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,

    Y . Shaked, Y . Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,”Nature communications, vol. 9, no. 1, p. 609, 2018

    2018

  15. [22]

    Integrated photonics on thin-film lithium niobate,

    D. Zhu, L. Shao, M. Yu, R. Cheng, B. Desiatov, C. Xin, Y . Hu, J. Holzgrafe, S. Ghosh, A. Shams-Ansari, et al. , “Integrated photonics on thin-film lithium niobate,”Advances in Optics and Photonics, vol. 13, no. 2, pp. 242–352, 2021

    2021

  16. [23]

    Integrated lithium niobate electro-optic modulators operating at CMOS- compatible voltages,

    C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lon ˇcar, “Integrated lithium niobate electro-optic modulators operating at CMOS- compatible voltages,” Nature, vol. 562, no. 7725, pp. 101–104, 2018

    2018

  17. [24]

    Cavity electro-optics in thin-film lithium niobate for efficient microwave-to-optical transduction,

    J. Holzgrafe, N. Sinclair, D. Zhu, A. Shams-Ansari, M. Colan- gelo, Y . Hu, M. Zhang, K. K. Berggren, and M. Lon ˇcar, “Cavity electro-optics in thin-film lithium niobate for efficient microwave-to-optical transduction,” Optica, vol. 7, no. 12, pp. 1714–1720, 2020

    2020

  18. [25]

    Ultrashort pulse biphoton source 6 in lithium niobate nanophotonics at 2 µm,

    J. Williams, R. Nehra, E. Sendonaris, L. Ledezma, R. M. Gray, R. Sekine, and A. Marandi, “Ultrashort pulse biphoton source 6 in lithium niobate nanophotonics at 2 µm,” Nanophotonics, no. 0, 2024

    2024

  19. [26]

    4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics,

    D. M. Lukin, C. Dory, M. A. Guidry, K. Y . Yang, S. D. Mishra, R. Trivedi, M. Radulaski, S. Sun, D. Vercruysse, G. H. Ahn, et al., “4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics,” Nature Photonics , vol. 14, no. 5, pp. 330–334, 2020

    2020

  20. [27]

    Integrated quan- tum photonics with silicon carbide: challenges and prospects,

    D. M. Lukin, M. A. Guidry, and J. Vuˇckovi´c, “Integrated quan- tum photonics with silicon carbide: challenges and prospects,” PRX quantum, vol. 1, no. 2, p. 020102, 2020

    2020

  21. [28]

    Quantum optics of soliton microcombs,

    M. A. Guidry, D. M. Lukin, K. Y . Yang, R. Trivedi, and J. Vuˇckovi´c, “Quantum optics of soliton microcombs,” Nature Photonics, vol. 16, no. 1, pp. 52–58, 2022

    2022

  22. [29]

    Parametric amplification of a quantum pulse,

    O. Tziperman, V . R. Christiansen, I. Kaminer, and K. Mølmer, “Parametric amplification of a quantum pulse,”Physical Review A, vol. 110, no. 5, p. 053712, 2024

    2024

  23. [31]

    D. F. Walls and G. J. Milburn, Quantum optics. Springer Sci- ence & Business Media, 2007

    2007

  24. [32]

    Observing the dynamics of quan- tum states generated inside nonlinear optical cavities,

    S. Choi, Y . Salamin, C. Roques-Carmes, J. Sloan, M. Horo- dynski, and M. Solja ˇci´c, “Observing the dynamics of quan- tum states generated inside nonlinear optical cavities,” arXiv preprint arXiv:2412.01772, 2024

    2024 arXiv

  25. [33]

    Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,

    J. Fink, M. G ¨oppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature, vol. 454, no. 7202, pp. 315–318, 2008

    2008

  26. [34]

    Generation of Fock states in a superconducting quantum circuit,

    M. Hofheinz, E. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. O’connell, H. Wang, J. M. Martinis, and A. Cle- land, “Generation of Fock states in a superconducting quantum circuit,” Nature, vol. 454, no. 7202, pp. 310–314, 2008

    2008

  27. [35]

    Synthesizing arbitrary quan- tum states in a superconducting resonator,

    M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. O’connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, “Synthesizing arbitrary quan- tum states in a superconducting resonator,” Nature, vol. 459, no. 7246, pp. 546–549, 2009

    2009

  28. [36]

    Experimental state tomography of itinerant single microwave photons,

    C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, “Experimental state tomography of itinerant single microwave photons,” Physical Review Letters, vol. 106, no. 22, p. 220503, 2011

    2011

  29. [37]

    Deterministically encoding quantum information using 100-photon Schr ¨odinger cat states,

    B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frun- zio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schr ¨odinger cat states,” Science, vol. 342, no. 6158, pp. 607–610, 2013

    2013

  30. [38]

    Superconducting cir- cuits for quantum information: an outlook,

    M. H. Devoret and R. J. Schoelkopf, “Superconducting cir- cuits for quantum information: an outlook,” Science, vol. 339, no. 6124, pp. 1169–1174, 2013

    2013

  31. [39]

    Superconducting parametric amplifiers: The state of the art in Josephson parametric amplifiers,

    J. Aumentado, “Superconducting parametric amplifiers: The state of the art in Josephson parametric amplifiers,” IEEE Mi- crowave magazine, vol. 21, no. 8, pp. 45–59, 2020

    2020

  32. [40]

    Parametric resonance in tun- able superconducting cavities,

    W. Wustmann and V . Shumeiko, “Parametric resonance in tun- able superconducting cavities,”Phys. Rev. B, vol. 87, p. 184501, May 2013

    2013

  33. [41]

    Parametric effects in circuit quantum electrodynamics,

    W. Wustmann and V . Shumeiko, “Parametric effects in circuit quantum electrodynamics,” Low Temperature Physics, vol. 45, p. 848, 2019

    2019

  34. [42]

    In- vestigation of nonlinear effects in Josephson parametric oscil- lators used in circuit quantum electrodynamics,

    P. Krantz, Y . Reshitnyk, W. Wustmann, J. Bylander, S. Gustavs- son, W. D. Oliver, T. Duty, V . Shumeiko, and P. Delsing, “In- vestigation of nonlinear effects in Josephson parametric oscil- lators used in circuit quantum electrodynamics,” New J. Phys. , vol. 15, p. 105002, 2013

    2013

  35. [43]

    Josephson parametric phase- locked oscillator and its application to dispersive readout of su- perconducting qubits,

    Z. R. Lin, K. Inomata, K. Koshino, W. D. Oliver, Y . Nakamura, J. S. Tsai, and T. Yamamoto, “Josephson parametric phase- locked oscillator and its application to dispersive readout of su- perconducting qubits,” Nature communications, vol. 5, p. 4480, 2014

    2014

  36. [44]

    Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator,

    P. Krantz, A. Bengtsson, M. Simoen, S. Gustavsson, V . Shumeiko, W. D. Oliver, C. M. Wilson, P. Delsing, and B. Bylander, “Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator,” Nature communica- tions, vol. 7, p. 11417, 2016

    2016

  37. [45]

    Efficient and low-backaction quantum measurement using a chip-scale detector,

    E. I. Rosenthal, C. M. Schneider, M. Malnou, Z. Zhao, F. Led- itzky, B. J. Chapman, W. Wustmann, X. Ma, D. A. Palken, M. F. Zanner, et al. , “Efficient and low-backaction quantum measurement using a chip-scale detector,” Physical review let- ters, vol. 126, no. 9, p. 090503, 2021

    2021

  38. [46]

    High-efficiency measurement of an artificial atom embedded in a parametric amplifier,

    A. Eddins, J. M. Kreikebaum, D. M. Toyli, E. M. Levenson- Falk, A. Dove, W. P. Livingston, B. A. Levitan, L. C. G. Govia, A. A. Clerk, and I. Siddiqi, “High-efficiency measurement of an artificial atom embedded in a parametric amplifier,” Phys. Rev. X, vol. 9, p. 011004, Jan 2019

    2019

  39. [47]

    Measurement of the entanglement of two su- perconducting qubits via state tomography,

    M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Measurement of the entanglement of two su- perconducting qubits via state tomography,” Science, vol. 313, no. 5792, pp. 1423–1425, 2006

    2006

  40. [48]

    Multimode entanglement in reconfigurable graph states using optical frequency combs,

    Y . Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,”Nature communications, vol. 8, no. 1, p. 15645, 2017

    2017

  41. [49]

    Multimode squeezing in soliton crystal microcombs,

    M. A. Guidry, D. M. Lukin, K. Y . Yang, and J. Vu ˇckovi´c, “Multimode squeezing in soliton crystal microcombs,” Optica, vol. 10, no. 6, pp. 694–701, 2023

    2023

  42. [50]

    Emerging quadrature lattices of Kerr combs,

    E. Lustig, M. A. Guidry, D. M. Lukin, S. Fan, and J. Vuckovic, “Emerging quadrature lattices of Kerr combs,” arXiv preprint arXiv:2407.13049, 2024

    2024 arXiv

  43. [51]

    Multimode amplitude squeezing through cascaded nonlinear optical processes,

    S. Pontula, Y . Salamin, C. Roques-Carmes, and M. Soljacic, “Multimode amplitude squeezing through cascaded nonlinear optical processes,” arXiv preprint arXiv:2405.05201, 2024

    2024 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.