Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read Momentum-resolved two-dimensional spectroscopy of the quantum sine-Gordon model predicts asymmetric cross-peaks and an echo peak, giving ultracold-atom quantum simulators a nonlinear probe of many-body dynamics.

desk verdict A solid, well-worked proposal for momentum-resolved 2D spectroscopy of the sine-Gordon model, with a genuinely new asymmetric cross-peak prediction; the main caveat is that the showcase maps sit outside the benchmarked range of the Gaussian Ansatz. read the letter →

arxiv 2509.25147 v1 pith:V5GROPY6 submitted 2025-09-29 cond-mat.quant-gas nlin.PSquant-ph

Duilio De Santis , Alex Gómez Salvador , Nataliia Bazhan , Sebastian Erne , Maximilian Prüfer , Claudio Guarcello , Davide Valenti , Jörg Schmiedmayer
show 1 more author
Eugene Demler
This is my paper · ORCID
classification cond-mat.quant-gasnlin.PSquant-ph
keywords two-dimensionalspectroscopysine-Gordonmodelmomentum-resolvedultracoldatomsbreathersnonlinearresponsequantumsimulatorsecho
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 proposes combining the spatial resolution of ultracold atomic gases with the nonlinear probing power of two-dimensional spectroscopy to study collective excitations beyond linear response. Using the quantum sine-Gordon model as the test case, it claims that a sequence of two time-delayed modulations of the tunnel coupling between two one-dimensional condensates produces momentum-resolved two-dimensional spectra with two distinctive many-body signatures. First, the nonrephasing sector shows asymmetric cross-peaks that arise from the coupling between the isolated B2 breather and the continuum of B1-pair excitations. Second, the rephasing sector shows an echo peak that is absent for a harmonic system and that separates intrinsic damping from shot-to-shot density disorder. If these predictions hold, the protocol gives experimentalists a direct way to measure anharmonicity, interaction strengths, and disorder in quantum simulators.

What carries the argument

The central object is the momentum-resolved second-order response function chi^(2)_k(omega_1 + omega_2, omega_1), extracted from the variance of the relative phase after two time-delayed perturbations. The calculation is carried out with a self-consistent Gaussian Ansatz that replaces the cosine potential cos($\beta$ phi) by an effective quadratic term with a dynamically determined mass, together with a bubble resummation (random-phase approximation) that produces the B2 breather pole from the B1-pair continuum. The divergent bare coupling is regularized by renormalizing to the physical B1 mass, and the relevant integrals I1 and I2 are evaluated exactly at zero temperature. This machinery yields both the linear and nonlinear response functions entering the two-dimensional spectra.

What would settle it

Compute the second-order response at $beta^{2}$ = 2 pi using the exact integrable form factors of the sine-Gordon model, or measure the nonrephasing quadrant in a tunnel-coupled one-dimensional Bose gas at that coupling; if the predicted missing off-diagonal peak appears, or if no echo peak develops as $\beta$ is increased, the Gaussian-based prediction is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that momentum-resolved two-dimensional spectroscopy, applied to the sine-Gordon model realized by two tunnel-coupled one-dimensional Bose-Einstein condensates, reveals qualitative many-body features that ordinary linear-response probes cannot see. The external perturbation is a homogeneous modulation of the cosine coupling, which couples to even powers of the field and produces a finite second-order response. Within a self-consistent Gaussian approximation, the linear response already contains both a two-particle continuum of oppositely moving B1 breathers and an isolated zero-momentum B2 breather appearing as a pole in an RPA-type resummation. The second-order two-dimensional map then shows a nonrephasing quadrant with asymmetric cross-peaks: one off-diagonal peak is suppressed by the dephasing of the continuum, a signature the authors argue is unique to the many-body interplay of a continuum with an isolated mode. The rephasing quadrant contains an echo peak whose strength grows with the interaction parameter beta and whose lineshape is almond-shaped under shot-to-shot density fluctuations, allowing one to distinguish inhomogeneous disorder from homogeneous damping.

Load-bearing premise

The entire nonlinear response calculation treats the interacting cosine potential as an effective quadratic term whose mass is fixed self-consistently, and this approximation is only checked against the exact theory for the B2 mode up to $beta^{2}$ approximately pi, while the central asymmetric-cross-peak maps are computed at $beta^{2}$ = 2 pi.

Editorial extensions

If this is right

  • Atom-chip experiments on tunnel-coupled one-dimensional condensates can directly test the predicted asymmetric cross-peaks by modulating the barrier height and measuring momentum-resolved phase correlations.
  • The echo peak in the rephasing quadrant provides a direct experimental indicator of anharmonicity, since it is absent at small beta and grows as beta increases.
  • The distinct lineshapes of the nonrephasing and rephasing peaks allow one to separate intrinsic damping from shot-to-shot fluctuations in atom number, a common source of disorder in ultracold-atom experiments.
  • Momentum resolution gives access to the dispersion of the B1-pair continuum and the B2 bound state, enabling measurements of nonlinear matrix elements and form factors of the sine-Gordon model.
  • The same two-dimensional spectroscopy framework can be extended to other effective field theories realized in ultracold atoms and to engineered quantum devices such as superconducting resonators and trapped ions.

Reading between the lines

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

  • A testable extension of this reasoning is that the echo-peak amplitude could serve as a quantitative 'anharmonicity meter' for bosonic quantum simulators, with the echo strength calibrating the effective interaction strength in a model-independent way.
  • The asymmetry of the cross-peaks may be exploitable to extract the two-breather continuum edge directly from the data, giving a momentum-resolved measurement of the density of states of the B1-pair continuum.
  • Because the drive couples to the full cosine rather than to a single quadratic operator, the second-order response is generically nonzero even for harmonic systems; an experimental implementation would need to subtract this harmonic background carefully before attributing peaks to intrinsic nonlinearity.
  • The main cross-peak maps are presented at beta^2 = 2 pi, where the Gaussian Ansatz has not been benchmarked against the exact theory; checking the predicted asymmetry against integrable form-factor calculations at that coupling would either confirm or rule out this central signature.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes momentum-resolved two-dimensional spectroscopy (2DS) of the quantum sine-Gordon model, using a homogeneous cos(βφ) drive and detecting the momentum-resolved phase variance. Within a self-consistent Gaussian Ansatz, the authors derive perturbative expressions for the second-order response, present nonrephasing 2D maps showing asymmetric cross-peaks between the B2 breather and the B1-pair continuum at β²=2π, and show that the rephasing sector develops an echo peak as β increases. They further argue that inhomogeneous shot-to-shot density fluctuations, modeled as a Gaussian spread of the two-particle mass 2M_B1, broaden the nonrephasing peak symmetrically while producing a distinguishable almond-shaped rephasing signature, thereby separating damping from disorder. The protocol is motivated by tunnel-coupled 1D Bose gases with matter-wave interferometry readout, and the paper claims the predicted signatures are experimentally accessible with current technology.

Significance. If the central predictions survive the approximation checks described below, this is a useful proposal: it would provide a momentum-resolved nonlinear probe for ultracold-atom quantum simulators, with a concrete many-body signature (asymmetric cross-peaks) that is absent in coupled-oscillator models. The Supplemental Material contains a complete second-order perturbative calculation with exact T=0 evaluations of the integrals I1 and I2, and the linear-response B2 pole is benchmarked against the exact breather mass up to β²≈π. The predicted spectra depend only on the physical inputs β and M_B1 (plus the disorder width in Fig. 4), and the experimental connection to atom-chip interferometry is laid out explicitly. The main risk is quantitative, not structural: the showcase nonrephasing maps are computed at β²=2π, outside the validated range of the Gaussian Ansatz, and the off-diagonal vertex is unbenchmarked.

major comments (3)
  1. [Fig. 3(a)-(b), Fig. S1(b), Conclusions] The central asymmetric-cross-peak prediction is presented at β²=2π, but the only benchmark of the Gaussian Ansatz, Fig. S1(b), validates the B2 pole position only up to β²≈π. The cross-peak asymmetry is controlled by the q-dependent product of matrix elements entering Eq. (S25) through I1 and I2, and the authors themselves state in the Conclusions that the off-diagonal peak is proportional to the known form factor ⟨B2|cosβφ|B1(k)B1(−k)⟩. The prediction should therefore be benchmarked against exact integrable form factors, or the showcase maps should be moved to the validated β² regime, before the qualitative 'dice-4 minus one' signature is quoted as the paper's central result.
  2. [Supplemental Eqs. (S67)-(S68)] The heuristic derivation of the missing off-diagonal peak is not a derivation from the computed response function of Eq. (S25). Equation (S67) contains a sum over the q-continuum, but the presence of such a sum shows only that the contribution is spread over the continuum; whether the peak is suppressed, broadened, or restored depends on the q-dependence of the matrix elements, which is exactly the unbenchmarked quantity. I recommend either deriving the suppression directly from Eq. (S25) or evaluating the off-diagonal intensities with the exact sine-Gordon form factors, so that the asymmetry is a computed consequence rather than a plausibility argument.
  3. [Fig. 4 and preceding paragraph] The shot-to-shot disorder model is introduced as a Gaussian distribution of the two-particle mass 2M_B1 with σ/(2M_B1)=0.1 without derivation. Atom-number shot-to-shot fluctuations are discrete and would be expected to affect β and Δ in a correlated way, not simply to produce an independent Gaussian spread of the mass. Because the claim that the rephasing peak separates damping from shot-to-shot disorder rests on this mapping, the authors should either derive the mapping from the experimental noise sources or explicitly present the Gaussian mass spread as a phenomenological ansatz and temper the diagnostic claim accordingly.
minor comments (6)
  1. [Section '2D spectroscopy of fluctuation dynamics'] The phrase 'where the where the cosine potential has to be considered' contains a duplicated 'where the'; please fix.
  2. [Conclusions] The sentence 'proportional to well-known from factors' should read 'well-known form factors'.
  3. [Reference [55]] Reference [55] is a placeholder ('see Supplemental Material at [] for additional information on ...'); the actual link or reference should be supplied.
  4. [Fig. 3 caption] The bottom labels in Fig. 3 ('β²=π β²=0.5π k/(2MB)=01 k/(2MB)=31') do not align transparently with the caption's panel descriptions; please clarify the correspondence between panels, β² values, and k values.
  5. [References [78] and [87]] References [78] and [87] cite the same Shi-Demler-Cirac paper; the duplicate should be removed.
  6. [SM Eq. (S26) and main text] The regularization of the bare coupling through the equilibrium fluctuations is clear in the SM, but the main text refers to it only briefly; one or two sentences stating that Δ_0 is replaced by the renormalized mass scale would help readers who do not consult the SM.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 2D spectra are computed from the model inputs (beta, MB1, Gaussian-ansatz dynamics) and benchmarked against external exact results; no fitted parameter is relabeled as a prediction.

full rationale

The paper's central outputs—the nonrephasing asymmetric cross-peaks, the rephasing echo peak, and the disorder-broadened profiles—are obtained by solving the equations of motion for the two-point correlators under the stated Gaussian-Ansatz approximation (SM Eqs. (S13)-(S25)), not by fitting any parameter to the target spectra. The input parameters beta and the renormalized mass scale MB1 are set by the sine-Gordon description, and the B2 pole position is determined by the RPA condition 1+Re I1(omega_B2)=0 and explicitly benchmarked against the exact breather masses of Zamolodchikov up to beta^2 ≈ pi (SM Fig. S1(b)); the B1-pair continuum threshold 2MB1 is likewise an input, not a fit. The suppression of one off-diagonal peak is derived, in SM Eqs. (S67)-(S68), from the dephasing of the q-integral over the B1-pair continuum, while the surviving peak involves a discrete B2 intermediate state; this asymmetry is a consequence of the model's mode structure, not an output imposed by construction. The disorder analysis in Fig. 4 inserts a Gaussian distribution of 2MB1 with sigma/(2MB1)=0.1 and then exhibits the resulting line shapes; the claim that the echo-peak extent measures the variance is a forward-model statement of the standard inhomogeneous-broadening mechanism, not a circular fit. Self-citations (Refs. [30], [54], [75], [78], [79], [87]) supply the Gaussian-ansatz and resummation techniques and the coupled-condensate mapping, but the equations are rederived in the Supplemental Material, and the key validation (B2 mass vs exact result) is external; these citations are therefore not load-bearing in a circular sense. The main validity limitation—that the showcase beta^2=2pi maps lie beyond the beta^2≈pi range where the Gaussian-Ansatz B2 mass was benchmarked, and that the off-diagonal peak is only argued schematically to be proportional to known form factors <B2|cos(beta phi)|B1(k)B1(-k)> rather than evaluated exactly—is a correctness and approximation concern, not a circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central predictions rest on the SG low-energy mapping, the Gaussian-Ansatz closure, and the mass-renormalization choice. These are inputs inherited from prior literature or standard methods, not fitted to the target spectra; however, the validity of the Gaussian Ansatz at the showcased beta squared equal to 2 pi is not established. No invented entities appear.

free parameters (3)
  • Sine-Gordon coupling beta = beta squared = 2 pi in Fig. 3(a,b); beta squared = 0.5 pi and pi in Fig. 3(c,d); beta squared = pi in Fig. 4
    Model parameter carried over from the SG low-energy description; it sets the interaction strength and the breather masses. It is an input, not fitted to the predicted spectra.
  • Renormalized mass scale MB1 (or 2MB1) = Used as the frequency unit in all figures
    Introduced by regularizing the UV-divergent equilibrium fluctuations; sets the energy scale of the 2D maps. It is a renormalization input, and its value is not measured or fitted in this paper.
  • Shot-to-shot disorder width sigma = sigma/(2MB1) = 0.1 in Fig. 4
    Chosen by hand to illustrate the disorder diagnostic; the qualitative almond-vs-broadened contrast does not depend on the exact value.
assumptions (4)
  • domain assumption The low-energy dynamics of two weakly tunnel-coupled one-dimensional Bose condensates is governed by the quantum sine-Gordon Hamiltonian (Eq. 1)
    Standard mapping from Refs. [60,61], reproduced in the SM; the entire analysis is performed inside this model.
  • domain assumption The self-consistent Gaussian Ansatz captures the dominant two-point dynamics of the sine-Gordon model, including the B1-pair continuum and B2 pole
    Invoked in Eq. (3) and the SM. The linear B2 mass is benchmarked against exact results only up to beta squared approximately pi (SM Fig. S1b); validity at beta squared equal to 2 pi is assumed.
  • domain assumption UV-divergent equilibrium fluctuations can be regularized by replacing the bare coupling Delta0 with the physical mass MB1
    Standard mass renormalization, but it introduces MB1 as an external energy scale; see SM 'Equilibrium correlators'.
  • ad hoc to paper Shot-to-shot atom-number fluctuations are equivalent to a Gaussian distribution of the two-particle mass 2MB1
    Used to generate Fig. 4; no microscopic derivation from the experimental density distribution is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics." pith.science (2026). https://pith.science/paper/V5GROPY6

@misc{pith2026250925147,
  author       = {Pith},
  title        = {Pith review of: Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V5GROPY6}},
  note         = {Machine review of arXiv:2509.25147}
}
abstract

Emergent collective excitations constitute a hallmark of interacting quantum many-body systems, yet in solid-state platforms their study has been largely limited by the constraints of linear-response probes and by finite momentum resolution. We propose to overcome these limitations by combining the spatial resolution of ultracold atomic systems with the nonlinear probing capabilities of two-dimensional spectroscopy (2DS). As a concrete illustration, we analyze momentum-resolved 2DS of the quantum sine-Gordon model describing the low energy dynamics of two weakly coupled one-dimensional Bose-Einstein condensates. This approach reveals distinctive many-body signatures, most notably asymmetric cross-peaks reflecting the interplay between isolated ($B_2$ breather) and continuum ($B_1$ pair) modes. The protocol further enables direct characterization of anharmonicity and disorder, establishing momentum-resolved 2DS as both a powerful diagnostic for quantum simulators and a versatile probe of correlated quantum matter.

Figures

Figures reproduced from arXiv: 2509.25147 by the authors.

Figure 1
Figure 1. FIG. 1. Schematics of a 2DS protocol. Two perturbations, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Pictorial representation of the external modula [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a)-(b) The (normalized) [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), symmetrically broadens with a shape indistin￾guishable from that of a damped mode. The echo peak instead presents a characteristic almond signature, see [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Emergent Fermi polarons in Dirac materials

    cond-mat.mtrl-sci 2026-07 accept novelty 7.0 of 10

    Impurities in Dirac materials form robust Dirac-Fermi polarons from dressing by excitations near the Dirac point, visible as a third branch in absorption spectra for both attractive and repulsive interactions.

Reference graph

Works this paper leans on

90 extracted references · 57 canonical work pages · cited by 1 Pith paper

  1. [1]

    D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two- dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett.48, 1559 (1982)

    1982

  2. [2]

    R. B. Laughlin, Anomalous quantum hall effect: An in- compressible quantum fluid with fractionally charged ex- citations, Phys. Rev. Lett.50, 1395 (1983)

    1983

  3. [3]

    F. D. M. Haldane, Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids, Phys. Rev. Lett.47, 1840 (1981)

    1981

  4. [4]

    F. D. M. Haldane, ’luttinger liquid theory’ of one- dimensional quantum fluids. i. properties of the luttinger model and their extension to the general 1d interact- ing spinless fermi gas, Journal of Physics C: Solid State Physics14, 2585 (1981)

    1981

  5. [5]

    Giamarchi,Quantum physics in one dimension (Clarendon press, 2003)

    T. Giamarchi,Quantum physics in one dimension (Clarendon press, 2003)

    2003

  6. [6]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys.80, 885 (2008)

    2008

  7. [7]

    M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, One dimensional bosons: From condensed mat- ter systems to ultracold gases, Rev. Mod. Phys.83, 1405 (2011)

    2011

  8. [8]

    Langen, R

    T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold atoms out of equilibrium, Annu. Rev. Condens. Matter Phys.6, 201 (2015)

    2015

Show all 90 references
  1. [9]

    Gross and I

    C. Gross and I. Bloch, Quantum simulations with ultra- cold atoms in optical lattices, Science357, 995 (2017)

    2017

  2. [10]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano,et al., Programmable quantum sim- ulations of spin systems with trapped ions, Reviews of Modern Physics93, 025001 (2021)

    2021

  3. [11]

    A. D. King, S. Suzuki, J. Raymond, A. Zucca, T. Lanting, F. Altomare, A. J. Berkley, S. Ejtemaee, E. Hoskinson, S. Huang,et al., Coherent quantum annealing in a pro- grammable 2,000 qubit ising chain, Nature Physics18, 1324 (2022)

    2022

  4. [12]

    Guinier,X-ray diffraction in crystals, imperfect crys- tals, and amorphous bodies(Courier Corporation, 1994)

    A. Guinier,X-ray diffraction in crystals, imperfect crys- tals, and amorphous bodies(Courier Corporation, 1994)

    1994

  5. [13]

    Comin and A

    R. Comin and A. Damascelli, Resonant x-ray scattering studies of charge order in cuprates, Annual Review of Condensed Matter Physics7, 369 (2016)

    2016

  6. [14]

    Jimenez and J

    J. Jimenez and J. W. Tomm, Basics of optical spec- troscopy: Transmission and reflection measurements, their analysis, and related techniques, inSpectroscopic Analysis of Optoelectronic Semiconductors(Springer In- ternational Publishing, Cham, 2016) pp. 49–76

    2016

  7. [15]

    Robson, R

    R. Robson, R. White, and M. Hildebrandt,Fundamentals 6 of Charged Particle Transport in Gases and Condensed Matter(CRC Press, 2017)

    2017

  8. [16]

    J. P. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021)

    2021

  9. [17]

    Gupta, Z

    S. Gupta, Z. Hadzibabic, M. W. Zwierlein, C. A. Stan, K. Dieckmann, C. H. Schunck, E. G. M. van Kempen, B. J. Verhaar, and W. Ketterle, Radio-frequency spec- troscopy of ultracold fermions, Science300, 1723 (2003), https://www.science.org/doi/pdf/10.1126/science.1085335

    2003 doi

  10. [18]

    Endres, T

    M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauβ, C. Gross, E. Demler, S. Kuhr, and I. Bloch, The ‘higgs’ amplitude mode at the two-dimensional superfluid/mott insulator transition, Nature487, 454 (2012)

    2012

  11. [19]

    M. L. Prichard, Z. Ba, I. Morera, B. M. Spar, D. A. Huse, E. Demler, and W. S. Bakr, Magnon-polarons in the fermi–hubbard model, Nature Physics 10.1038/s41567- 025-03004-6 (2025)

    2025 doi

  12. [20]

    Autere, H

    A. Autere, H. Jussila, A. Marini, J. R. M. Saavedra, Y. Dai, A. S¨ ayn¨ atjoki, L. Karvonen, H. Yang, B. Amir- solaimani, R. A. Norwood, N. Peyghambarian, H. Lipsa- nen, K. Kieu, F. J. G. de Abajo, and Z. Sun, Optical har- monic generation in monolayer group-vi transition meta...

    2018

  13. [21]

    Seibold, M

    G. Seibold, M. Udina, C. Castellani, and L. Benfatto, Third harmonic generation from collective modes in dis- ordered superconductors, Phys. Rev. B103, 014512 (2021)

    2021

  14. [22]

    M.-J. Kim, S. Kovalev, M. Udina, R. Haenel, G. Kim, M. Puviani, G. Cristiani, I. Ilyakov, T. V. A. G. de Oliveira, A. Ponomaryov, J.-C. Deinert, G. Logvenov, B. Keimer, D. Manske, L. Benfatto, and S. Kaiser, Tracing the dynamics of supercon- ducting order via transient teraher...

    2024 doi

  15. [23]

    Liu, Multidimensional terahertz probes of quantum materials, npj Quantum Materials10, 18 (2025)

    A. Liu, Multidimensional terahertz probes of quantum materials, npj Quantum Materials10, 18 (2025)

    2025

  16. [24]

    Huang, M

    C. Huang, M. Mootz, L. Luo, I. E. Perakis, and J. Wang, Unlocking quantum control and multi-order correlations via terahertz two-dimensional coherent spec- troscopy (2025), arXiv:2507.02116 [cond-mat.supr-con]

    2025

  17. [25]

    Mootz, L

    M. Mootz, L. Luo, J. Wang, and l. E. Perakis, Visu- alization and quantum control of light-accelerated con- densates by terahertz multi-dimensional coherent spec- troscopy, Communications Physics5, 47 (2022)

    2022

  18. [26]

    A. Liu, D. Pavi´ cevi´ c, M. H. Michael, A. G. Salvador, P. E. Dolgirev, M. Fechner, A. S. Disa, P. M. Lozano, Q. Li, G. D. Gu, E. Demler, and A. Cavalleri, Probing inhomo- geneous cuprate superconductivity by terahertz joseph- son echo spectroscopy, Nature Physics20, 1751 (2024)

    2024

  19. [27]

    Katsumi, J

    K. Katsumi, J. Fiore, M. Udina, R. Romero, D. Barbalas, J. Jesudasan, P. Raychaudhuri, G. Seibold, L. Benfatto, and N. P. Armitage, Revealing novel aspects of light- matter coupling by terahertz two-dimensional coherent spectroscopy: The case of the amplitude mode in super- co...

    2024

  20. [28]

    Puviani, Theory of symmetry-resolved quench-drive spectroscopy: Nonlinear response of phase-fluctuating superconductors, Phys

    M. Puviani, Theory of symmetry-resolved quench-drive spectroscopy: Nonlinear response of phase-fluctuating superconductors, Phys. Rev. B109, 214515 (2024)

    2024

  21. [29]

    Katsumi, J

    K. Katsumi, J. Liang, R. R. III, K. Chen, X. Xi, and N. P. Armitage, Amplitude mode in a multi-gap supercon- ductor mgb 2 investigated by terahertz two-dimensional coherent spectroscopy (2024), arXiv:2411.10852 [cond- mat.supr-con]

    2024 arXiv

  22. [30]

    G´ omez Salvador, P

    A. G´ omez Salvador, P. E. Dolgirev, M. H. Michael, A. Liu, D. Pavicevic, M. Fechner, A. Cavalleri, and E. Demler, Principles of two-dimensional terahertz spec- troscopy of collective excitations: The case of josephson plasmons in layered superconductors, Phys. Rev. B110, 0945...

    2024

  23. [31]

    Barbalas, R

    D. Barbalas, R. Romero III, D. Chaudhuri, F. Mahmood, H. P. Nair, N. J. Schreiber, D. G. Schlom, K. Shen, and N. Armitage, Energy relaxation and dynamics in the correlated metal sr 2 ruo 4 via thz two-dimensional coherent spectroscopy, arXiv preprint arXiv:2312.13502 (2023)

    2023 arXiv

  24. [32]

    Chen and P

    J. Chen and P. Werner, Multidimensional coher- ent spectroscopy of correlated lattice systems (2024), arXiv:2411.02389 [cond-mat.str-el]

    2024 arXiv

  25. [33]

    J. Lu, X. Li, H. Y. Hwang, B. K. Ofori-Okai, T. Kurihara, T. Suemoto, and K. A. Nelson, Coherent two-dimensional terahertz magnetic resonance spectroscopy of collective spin waves, Phys. Rev. Lett.118, 207204 (2017)

    2017

  26. [34]

    H.-W. Lin, G. Mead, and G. A. Blake, Mapping linbo 3 phonon-polariton nonlinearities with 2d thz-thz-raman spectroscopy, Phys. Rev. Lett.129, 207401 (2022)

    2022

  27. [35]

    Zhang, F

    Z. Zhang, F. Y. Gao, Y.-C. Chien, Z.-J. Liu, J. B. Cur- tis, E. R. Sung, X. Ma, W. Ren, S. Cao, P. Narang, A. von Hoegen, E. Baldini, and K. A. Nelson, Terahertz- field-driven magnon upconversion in an antiferromagnet, Nature Physics20, 788 (2024)

    2024

  28. [36]

    Zhang, F

    Z. Zhang, F. Y. Gao, J. B. Curtis, Z.-J. Liu, Y.-C. Chien, A. von Hoegen, M. T. Wong, T. Kurihara, T. Suemoto, P. Narang, E. Baldini, and K. A. Nelson, Terahertz field- induced nonlinear coupling of two magnon modes in an antiferromagnet, Nature Physics20, 801 (2024)

    2024

  29. [37]

    S. A. Parameswaran and S. Gopalakrishnan, Asymptot- ically exact theory for nonlinear spectroscopy of random quantum magnets, Phys. Rev. Lett.125, 237601 (2020)

    2020

  30. [38]

    T. G. H. Blank, K. A. Grishunin, K. A. Zvezdin, N. T. Hai, J. C. Wu, S.-H. Su, J.-C. A. Huang, A. K. Zvezdin, and A. V. Kimel, Two-dimensional terahertz spectroscopy of nonlinear phononics in the topological insulator mnbi2te4, Phys. Rev. Lett.131, 026902 (2023)

    2023

  31. [39]

    Wan and N

    Y. Wan and N. P. Armitage, Resolving continua of frac- tional excitations by spinon echo in thz 2d coherent spec- troscopy, Phys. Rev. Lett.122, 257401 (2019)

    2019

  32. [40]

    Liebman, J

    O. Liebman, J. Curtis, I. Petrides, and P. Narang, Mul- tiphoton spectroscopy of a dynamical axion insulator (2023), arXiv:2306.00064 [cond-mat.str-el]

    2023

  33. [41]

    W. Choi, K. H. Lee, and Y. B. Kim, Theory of two- dimensional nonlinear spectroscopy for the kitaev spin liquid, Phys. Rev. Lett.124, 117205 (2020)

    2020

  34. [42]

    McGinley, M

    M. McGinley, M. Fava, and S. A. Parameswaran, Sig- natures of fractional statistics in nonlinear pump-probe spectroscopy, Phys. Rev. Lett.132, 066702 (2024)

    2024

  35. [43]

    McGinley, M

    M. McGinley, M. Fava, and S. A. Parameswaran, Anoma- lous thermal relaxation and pump-probe spectroscopy of two-dimensional topologically ordered systems, Phys. Rev. B109, 075108 (2024)

    2024

  36. [44]

    Potts, R

    M. Potts, R. Moessner, and O. Benton, Signatures of spinon dynamics and phase structure of dipolar- octupolar quantum spin ices in two-dimensional coherent spectroscopy (2024), arXiv:2406.01472 [cond-mat.str-el]

    2024 arXiv

  37. [45]

    Lomsadze and S

    B. Lomsadze and S. T. Cundiff, Frequency combs en- able rapid and high-resolution multidimensional coherent 7 spectroscopy, Science357, 1389 (2017)

    2017

  38. [46]

    A. Liu, D. B. Almeida, W. K. Bae, L. A. Padilha, and S. T. Cundiff, Non-markovian exciton-phonon interac- tions in core-shell colloidal quantum dots at femtosecond timescales, Phys. Rev. Lett.123, 057403 (2019)

    2019

  39. [47]

    J. B. Muir, J. Levinsen, S. K. Earl, M. A. Conway, J. H. Cole, M. Wurdack, R. Mishra, D. J. Ing, E. Estrecho, Y. Lu, D. K. Efimkin, J. O. Tollerud, E. A. Ostrovskaya, M. M. Parish, and J. A. Davis, Interactions between fermi polarons in monolayer ws2, Nature Communications13, ...

    2022

  40. [48]

    K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, Two-quantum 2d ft electronic spectroscopy of biexcitons in gaas quantum wells, Science 324, 1169 (2009)

    2009

  41. [49]

    K. Hao, L. Xu, F. Wu, P. Nagler, K. Tran, X. Ma, C. Sch¨ uller, T. Korn, A. H. MacDonald, G. Moody,et al., Trion valley coherence in monolayer semiconductors, 2D Materials4, 025105 (2017)

    2017

  42. [50]

    K. Hao, J. F. Specht, P. Nagler, L. Xu, K. Tran, A. Singh, C. K. Dass, C. Sch¨ uller, T. Korn, M. Richter, A. Knorr, X. Li, and G. Moody, Neutral and charged inter-valley biexcitons in monolayer mose2, Nature Communications 8, 15552 (2017)

    2017

  43. [51]

    Bristow, T

    A. Bristow, T. Zhang, M. Siemens, S. Cundiff, and R. Mirin, Separating homogeneous and inhomogeneous line widths of heavy- and light-hole excitons in weakly disordered semiconductor quantum wells, The Journal of Physical Chemistry B115, 5365–5371 (2011)

    2011

  44. [52]

    Moody, C

    G. Moody, C. Kavir Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Bergh¨ auser, E. Malic, A. Knorr, and X. Li, Intrinsic homoge- neous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides, Nature Communicatio...

    2015

  45. [53]

    Huang, K

    D. Huang, K. Sampson, Y. Ni, Z. Liu, D. Liang, K. Watanabe, T. Taniguchi, H. Li, E. Martin, J. Levin- sen, M. M. Parish, E. Tutuc, D. K. Efimkin, and X. Li, Quantum dynamics of attractive and repulsive polarons in a doped mose 2 monolayer, Phys. Rev. X13, 011029 (2023)

    2023

  46. [54]

    A. G. Salvador, I. Morera, M. H. Michael, P. E. Dol- girev, D. Pavicevic, A. Liu, A. Cavalleri, and E. Demler, Two-dimensional spectroscopy of bosonic collective exci- tations in disordered many-body systems, arXiv preprint arXiv:2501.16856 (2025)

    2025 arXiv

  47. [55]

    (2024), see Supplemental Material at [] for additional in- formation on

    2024

  48. [56]

    Dauxois and M

    T. Dauxois and M. Peyrard,Physics of Solitons(Cam- bridge University Press, 2006)

    2006

  49. [57]

    Torrielli,Integrability using the Sine-Gordon and Thirring Duality, 2053-2563 (IOP Publishing, 2024)

    A. Torrielli,Integrability using the Sine-Gordon and Thirring Duality, 2053-2563 (IOP Publishing, 2024)

    2024

  50. [58]

    Coleman, Quantum sine-Gordon equation as the mas- sive Thirring model, Phys

    S. Coleman, Quantum sine-Gordon equation as the mas- sive Thirring model, Phys. Rev. D11, 2088 (1975)

    1975

  51. [59]

    Benfatto, C

    L. Benfatto, C. Castellani, and T. Giamarchi, Sine- gordon description of beresinskii-kosterlitz-thouless vor- tices in superconductors immersed in an external mag- netic field, Phys. Rev. Lett.99, 207002 (2007)

    2007

  52. [60]

    Schweigler, V

    T. Schweigler, V. Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges, and J. Schmiedmayer, Experimental characterization of a quantum many-body system via higher-order correla- tions, Nature545, 323 (2017)

    2017

  53. [61]

    Schweigler, M

    T. Schweigler, M. Gluza, M. Tajik, S. Sotiriadis, F. Catal- dini, S.-C. Ji, F. S. Møller, J. Sabino, B. Rauer, J. Eisert, et al., Decay and recurrence of non-Gaussian correlations in a quantum many-body system, Nat. Phys.17, 559 (2021)

    2021

  54. [62]

    Cuevas-Maraver, P

    J. Cuevas-Maraver, P. G. Kevrekidis, and F. Williams, The sine-Gordon Model and its Applications(Springer, 2014)

    2014

  55. [63]

    M. H. Michael, D. De Santis, E. A. Demler, and P. A. Lee, Giant dynamical paramagnetism in the driven pseudogap phase of yba 2cu3o6+x, arXiv preprint arXiv:2410.12919 (2024)

    2024 arXiv

  56. [64]

    De Santis, D

    D. De Santis, D. Valenti, B. Spagnolo, G. Di Fresco, A. Carollo, and C. Guarcello, Noisy sine-gordon breather dynamics: A short review, Chaos, Solitons & Fractals 199, 116641 (2025)

    2025

  57. [65]

    P. Lee, T. Rice, and P. Anderson, Conductivity from charge or spin density waves, Solid State Communica- tions14, 703 (1974)

    1974

  58. [66]

    M. J. Rice, A. R. Bishop, J. A. Krumhansl, and S. E. Trullinger, Weakly pinned fr¨ ohlich charge-density-wave condensates: A new, nonlinear, current-carrying elemen- tary excitation, Phys. Rev. Lett.36, 432 (1976)

    1976

  59. [67]

    Asano, H

    T. Asano, H. Nojiri, Y. Inagaki, J. Boucher, T. Sakon, Y. Ajiro, and M. Motokawa, Esr investigation on the breather mode and the spinon-breather dynamical crossover in cu benzoate, Physical Review Letters84, 5880 (2000)

    2000

  60. [68]

    A. C. Tiegel, A. Honecker, T. Pruschke, A. Ponomaryov, S. A. Zvyagin, R. Feyerherm, and S. R. Manmana, Dy- namical properties of the sine-gordon quantum spin mag- net cu-pm at zero and finite temperature, Physical Re- view B93, 104411 (2016)

    2016

  61. [69]

    A. M. Visuri, M. Lebrat, S. H¨ ausler, L. Corman, and T. Giamarchi, Spin transport in a one-dimensional quan- tum wire, Phys. Rev. Res.2, 023062 (2020)

    2020

  62. [70]

    E. Wybo, M. Knap, and A. Bastianello, Quantum sine- Gordon dynamics in coupled spin chains, Phys. Rev. B 106, 075102 (2022)

    2022

  63. [71]

    E. Wybo, A. Bastianello, M. Aidelsburger, I. Bloch, and M. Knap, Preparing and Analyzing Solitons in the Sine- Gordon Model with Quantum Gas Microscopes, PRX Quantum4, 030308 (2023)

    2023

  64. [72]

    S. M. Girvin and A. H. MacDonald, Multi-component quantum hall systems: The sum of their parts and more (1995), arXiv:cond-mat/9505087 [cond-mat]

    1995 arXiv

  65. [73]

    Zharnitsky, I

    V. Zharnitsky, I. Mitkov, and M. Levi, Parametrically forced sine-gordon equation and domain wall dynamics in ferromagnets, Phys. Rev. B57, 5033 (1998)

    1998

  66. [74]

    T. I. Andersenet al., Nature638, 79 (2024)

    2024

  67. [75]

    Gritsev, A

    V. Gritsev, A. Polkovnikov, and E. Demler, Linear re- sponse theory for a pair of coupled one-dimensional con- densates of interacting atoms, Phys. Rev. B75, 174511 (2007)

    2007

  68. [76]

    Malard, Sine-Gordon Model: Renormalization Group Solution and Applications, Braz

    M. Malard, Sine-Gordon Model: Renormalization Group Solution and Applications, Braz. J. Phys.43, 182 (2013)

    2013

  69. [77]

    We also note that while our subsequent results are derived for a genericδ∆ 0(t), for plotting pur- poses we mostly focus on impulsive (delta-like) forcing profiles

    A generalization to spatially dependent scenarios [75] is straightforward. We also note that while our subsequent results are derived for a genericδ∆ 0(t), for plotting pur- poses we mostly focus on impulsive (delta-like) forcing profiles

  70. [78]

    T. Shi, E. Demler, and J. Ignacio Cirac, Variational study of fermionic and bosonic systems with non-gaussian states: Theory and applications, Annals of Physics390, 245 (2018). 8

    2018

  71. [79]

    Gritsev, E

    V. Gritsev, E. Demler, M. Lukin, and A. Polkovnikov, Spectroscopy of collective excitations in interacting low- dimensional many-body systems using quench dynamics, Physical review letters99, 200404 (2007)

    2007

  72. [80]

    Hamm and M

    P. Hamm and M. Zanni,Concepts and Methods of 2D In- frared Spectroscopy(Cambridge University Press, 2011)

    2011

  73. [81]

    Watanabe, S

    Y. Watanabe, S. Trebst, and C. Hickey, Revealing quadrupolar excitations with nonlinear spectroscopy, Phys. Rev. Lett.134, 106703 (2025)

    2025

  74. [82]

    E. L. Hahn, Spin echoes, Phys. Rev.80, 580 (1950)

    1950

  75. [83]

    Cetina, M

    M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, De- coherence of impurities in a fermi sea of ultracold atoms, Phys. Rev. Lett.115, 135302 (2015)

    2015

  76. [84]

    3(c)-(d) presents the system’s response summed over allk, where the bound state is expected to dominate (as indicated by the linear response)

    We note that Fig. 3(c)-(d) presents the system’s response summed over allk, where the bound state is expected to dominate (as indicated by the linear response). This ac- counts for the appearance of only a sub-2B 1 peak in this case. Rephasing phenomena are observed, in a simi...

  77. [85]

    M. E. Siemens, G. Moody, H. Li, A. D. Bristow, and S. T. Cundiff, Resonance lineshapes in two-dimensional fourier transform spectroscopy, Opt. Express18, 17699 (2010)

    2010

  78. [86]

    3 we plot the absolute-value peak, but both real and imaginary parts are in principle experimen- tally accessible, enabling their full characterization

    Note that in Fig. 3 we plot the absolute-value peak, but both real and imaginary parts are in principle experimen- tally accessible, enabling their full characterization

  79. [87]

    T. Shi, E. Demler, and J. Ignacio Cirac, Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications, Annals of Physics390, 245 (2018)

    2018

  80. [88]

    Maki and H

    K. Maki and H. Takayama, Breathers in the sine-gordon system at finite temperatures, Phys. Rev. B22, 5302 (1980)

    1980

  81. [89]

    A. B. Zamolodchikov, Mass scale in the sine–gordon model and its reductions, International Journal of Mod- ern Physics A10, 1125 (1995)

    1995

  82. [90]

    β4∆eq 2L Dφ q,1∗ X k Dφ k,1 ! − β6∆eq 8L2 Dφ q,0 X k Dφ k,1∗ X k Dφ k,1 ! −β 2 δ ˜∆(ω)∗D φ q,1 + +β4 2LDφ q,0 δ ˜∆(ω)∗ X k Dφ k,1 !#  0 1 0   +

    S. Mukamel,Principles of Nonlinear Optical Spec- troscopy, Oxford series in optical and imaging sciences (Oxford University Press, 1995). S1 Supplemental Material Coupled 1D condensates as a sine-Gordon experimental realization A prototypal experimental realization of the quan...

    1995

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.