pith. sign in

arxiv: 2606.12696 · v1 · pith:G6LXJNZUnew · submitted 2026-06-10 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Optical pulse-induced quantum geometric waves in graphene

Luis Fernando Cardenas Castillo , Wei Chen This is my paper

Pith reviewed 2026-06-27 08:06 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords graphenequantum metricBerry curvatureoptical pulseFloquet bandsDirac pointsFisher informationtime-dependent Schrödinger equation
0
0 comments X

The pith

A short optical pulse makes the quantum metric of graphene dynamic and wave-like near Dirac points.

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

The paper establishes that a brief optical pulse drives the quantum metric of Bloch states in graphene's momentum-time space into wave-like patterns near the Dirac points. This behavior directly mirrors the Floquet band structure created by the pulse. Solving the time-dependent Schrödinger equation shows that the metric's momentum and time components evolve differently and continue after the pulse ends. The same drive also produces a Berry curvature wave that does not exist in equilibrium graphene. Time-dependent occupation of the bands further creates a Fisher information wave that forms part of the metric wave and can be accessed experimentally.

Core claim

Under a short optical pulse, the quantum metric of Bloch states in the momentum-time (kx, ky, t) space of graphene becomes dynamic and exhibits a wave-like behavior near Dirac points. This quantum metric wave reflects the Floquet-band structure caused by the pulse. The momentum and temporal components of the metric have very distinct time dependence that persists even after the pulse has passed. In addition, the pulse also generates a Berry curvature wave that is otherwise absent in static graphene. The time-dependent electron densities in conduction and valence bands also give rise to a Fisher information wave that constitutes part of the quantum metric wave.

What carries the argument

The time-dependent quantum metric in (kx, ky, t) space obtained by solving the time-dependent Schrödinger equation for pulse-driven Bloch states.

If this is right

  • The momentum and temporal components of the metric evolve with distinct time dependence that survives after the pulse.
  • The pulse creates a Berry curvature wave absent from static graphene.
  • Time-dependent band densities produce a Fisher information wave as part of the quantum metric wave.
  • These waves directly encode the Floquet band structure induced by the pulse.

Where Pith is reading between the lines

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

  • Similar pulse-driven waves may appear in other Dirac materials if the same non-interacting approximation holds.
  • The persistence of the metric components after the pulse suggests a route to imprinting transient geometric phases for ultrafast control.
  • Pump-probe detection of the Fisher information wave offers a direct experimental handle on non-equilibrium quantum geometry without requiring full tomography.

Load-bearing premise

The calculation assumes correlations and out-of-equilibrium effects can be ignored when solving the time-dependent Schrödinger equation.

What would settle it

Pump-probe measurement of the time-dependent electron density or Berry curvature near the Dirac points under a short optical pulse that matches or deviates from the wave patterns predicted by the time-dependent Schrödinger equation solution.

Figures

Figures reproduced from arXiv: 2606.12696 by Luis Fernando Cardenas Castillo, Wei Chen.

Figure 1
Figure 1. Figure 1: Momentum profile of the elements of the dynamic quantum geometric tensor near [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Time dependence of the dynamic quantum geometric tensor along the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Momentum profile of the dynamic Fisher information matrix near the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time-varying band populations  |c1| 2 , |c2| 2 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The momentum-time pattern of the components of the dynamic quantum geometric [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

We show that, under a short optical pulse, the quantum metric of Bloch states in the momentum-time (kx, ky , t) of graphene becomes dynamic and exhibits a wave-like behavior near Dirac points. This quantum metric wave reflects the Floquet-band structure caused by the pulse, as revealed by solving the time-dependent Schr\"odinger equation assuming that correlations and out-of-equilibrium effects can be ignored. The momentum and temporal components of the metric have very distinct time dependence that persists even after the pulse has passed. In addition, the pulse also generates a Berry curvature wave that is otherwise absent in static graphene. The time-dependent electron densities in conduction and valence bands also give arise to a Fisher information wave that constitutes part of the quantum metric wave, and is readily measurable by pump-probe experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that a short optical pulse renders the quantum metric of Bloch states dynamic in the (kx, ky, t) space of graphene, producing wave-like behavior near the Dirac points that reflects the Floquet-band structure. This is obtained by direct solution of the time-dependent Schrödinger equation under the explicit assumption that correlations and out-of-equilibrium effects can be ignored. The pulse additionally generates a Berry curvature wave (absent in equilibrium graphene) and a Fisher information wave arising from the time-dependent conduction- and valence-band densities, the latter asserted to be measurable via pump-probe spectroscopy. Momentum and temporal metric components exhibit distinct post-pulse time dependence.

Significance. If the single-particle TDSE approximation remains valid, the work would establish a concrete route by which optical driving can induce propagating quantum-geometric waves in a Dirac material, thereby connecting Floquet engineering to time-resolved measurements of the quantum metric and Berry curvature. The derivation contains no free parameters and proceeds from an explicit TDSE solution rather than phenomenological fitting, which strengthens its internal consistency.

major comments (2)
  1. [Abstract / TDSE derivation] Abstract and the TDSE solution section: the reported wave-like propagation of the quantum metric and the induced Berry curvature wave are obtained under the assumption that correlations and out-of-equilibrium effects can be ignored. In graphene, electron-electron and electron-phonon scattering times are often comparable to or shorter than typical optical-pulse durations; without a quantitative estimate of the regime where the non-interacting evolution remains accurate, it is unclear whether the claimed wave-like features survive in a realistic many-body setting.
  2. [Post-pulse dynamics paragraph] Results on post-pulse dynamics: the manuscript states that the momentum and temporal components of the metric retain distinct time dependence even after the pulse has passed. Because the central claim of a persistent quantum metric wave rests on this persistence, an explicit check against the neglected scattering channels (or a statement of the relevant timescales) is required to establish that the wave-like behavior is not an artifact of the non-interacting approximation.
minor comments (2)
  1. [Abstract] Abstract: 'give arise to' should read 'give rise to'.
  2. [Introduction / Methods] Notation for the quantum geometric tensor in (kx, ky, t) should be introduced with a brief reminder of its relation to the standard quantum metric g_{\mu\nu} and Berry curvature \Omega, to aid readers unfamiliar with the time-dependent extension.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments. Our work is a single-particle TDSE study under the stated assumption of negligible correlations. We address the two major comments below and will make partial revisions to clarify timescales.

read point-by-point responses

  1. Referee: [Abstract / TDSE derivation] Abstract and the TDSE solution section: the reported wave-like propagation of the quantum metric and the induced Berry curvature wave are obtained under the assumption that correlations and out-of-equilibrium effects can be ignored. In graphene, electron-electron and electron-phonon scattering times are often comparable to or shorter than typical optical-pulse durations; without a quantitative estimate of the regime where the non-interacting evolution remains accurate, it is unclear whether the claimed wave-like features survive in a realistic many-body setting.

    Authors: The manuscript explicitly frames the calculation as a non-interacting TDSE solution (see abstract and derivation section). We will add a discussion of relevant timescales, noting that optical pulses are typically femtoseconds while electron-phonon scattering in graphene is often picoseconds (depending on doping and temperature), suggesting a window where coherent evolution dominates. A full many-body validation lies outside the present scope; the reported waves constitute the coherent baseline. This is a partial revision. revision: partial

  2. Referee: [Post-pulse dynamics paragraph] Results on post-pulse dynamics: the manuscript states that the momentum and temporal components of the metric retain distinct time dependence even after the pulse has passed. Because the central claim of a persistent quantum metric wave rests on this persistence, an explicit check against the neglected scattering channels (or a statement of the relevant timescales) is required to establish that the wave-like behavior is not an artifact of the non-interacting approximation.

    Authors: The distinct post-pulse time dependence of metric components follows directly from the phase evolution of the time-dependent Bloch states after the drive is off. We will insert a clarifying statement on timescales, indicating that the persistence is expected to hold for durations shorter than scattering times within the non-interacting model. An explicit scattering calculation would require an entirely different formalism and is not feasible here, but the result is not presented as an artifact. revision: partial

standing simulated objections not resolved
  • A quantitative estimate of the regime of validity for the non-interacting approximation, which would require many-body calculations beyond the manuscript's scope.

Circularity Check

0 steps flagged

No significant circularity; derivation is direct TDSE solution

full rationale

The paper's central claim follows from numerically or analytically solving the time-dependent Schrödinger equation for single-particle Bloch states in graphene under a short optical pulse, then computing the quantum geometric tensor (including metric and Berry curvature components) in (kx, ky, t) space from the evolved states. This procedure is presented as a first-principles computation under the explicit assumption that correlations and out-of-equilibrium effects can be ignored; no parameters are fitted to data and then relabeled as predictions, no quantities are defined in terms of each other, and no load-bearing self-citations or imported uniqueness theorems are invoked in the abstract or described method. The resulting wave-like behavior in the metric and induced Berry curvature are direct consequences of the Floquet-like structure generated by the pulse, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on solving the time-dependent Schrödinger equation while explicitly ignoring correlations and out-of-equilibrium effects; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption correlations and out-of-equilibrium effects can be ignored
    Explicitly stated in the abstract as the assumption under which the TDSE is solved to reveal the quantum metric wave.

pith-pipeline@v0.9.1-grok · 5658 in / 1249 out tokens · 21352 ms · 2026-06-27T08:06:56.829127+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references

  1. [1]

    J. P. Provost and G. Vallee. Riemannian structure on manifolds of quantum states.Comm. Math. Phys., 76(3):289–301, 1980

    1980

  2. [2]

    M. V. Berry. Quantal phase factors accompanying adiabatic changes.Proc. R. Soc. A, 392(1802):45–57, 1984

    1984

  3. [3]

    Berry phase effects on electronic properties.Rev

    Di Xiao, Ming-Che Chang, and Qian Niu. Berry phase effects on electronic properties.Rev. Mod. Phys., 82:1959–2007, July 2010

    1959

  4. [4]

    Extracting the quantum metric tensor through periodic driving.Phys

    Tomoki Ozawa and Nathan Goldman. Extracting the quantum metric tensor through periodic driving.Phys. Rev. B, 97:201117, May 2018

    2018

  5. [5]

    Riemannian geometry of resonant optical responses.Nat

    Junyeong Ahn, Guang-Yu Guo, Naoto Nagaosa, and Ashvin Vishwanath. Riemannian geometry of resonant optical responses.Nat. Phys., 18(3):290–295, Mar 2022

    2022

  6. [6]

    The quantum geometric origin of capacitance in insulators.Nature Communications, 15(1):4621, May 2024

    Ilia Komissarov, Tobias Holder, and Raquel Queiroz. The quantum geometric origin of capacitance in insulators.Nature Communications, 15(1):4621, May 2024

    2024

  7. [7]

    Dielectric and optical markers originating from quantum geometry.Phys

    Wei Chen. Dielectric and optical markers originating from quantum geometry.Phys. Rev. B, 111:085202, Feb 2025

    2025

  8. [8]

    De Grandi, V

    C. De Grandi, V. Gritsev, and A. Polkovnikov. Quench dynamics near a quantum critical point.Phys. Rev. B, 81:012303, Jan 2010

    2010

  9. [9]

    De Grandi, V

    C. De Grandi, V. Gritsev, and A. Polkovnikov. Quench dynamics near a quantum critical point: Application to the sine-gordon model.Phys. Rev. B, 81:224301, Jun 2010

    2010

  10. [10]

    Shengshi Pang and Andrew N. Jordan. Optimal adaptive control for quantum metrology with time-dependent hamiltonians.Nature Communications, 8(1):14695, Mar 2017

    2017

  11. [11]

    Jafari and Alireza Akbari

    R. Jafari and Alireza Akbari. Dynamics of quantum coherence and quantum fisher informa- tion after a sudden quench.Phys. Rev. A, 101:062105, Jun 2020

    2020

  12. [12]

    Universal critical dynamics of quantum geometry, 2024

    Shuohang Wu, Zhengxin Guo, Zijian Xiong, Yuan Yao, and Zi Cai. Universal critical dynamics of quantum geometry, 2024. arXiv:2401.17885

    arXiv 2024

  13. [13]

    Hernández, and J

    Bogar Díaz, Diego Gonzalez, Marcos J. Hernández, and J. David Vergara. Time-dependent quantum geometric tensor and some applications, 2025. arXiv:2502.01788

    arXiv 2025

  14. [14]

    Dawlaty, Shriram Shivaraman, Mvs Chandrashekhar, Farhan Rana, and Michael G

    Jahan M. Dawlaty, Shriram Shivaraman, Mvs Chandrashekhar, Farhan Rana, and Michael G. Spencer. Measurement of ultrafast carrier dynamics in epitaxial graphene.Appl. Phys. Lett., 92(4):042116, 01 2008

    2008

  15. [15]

    Strait, Paul A

    Haining Wang, Jared H. Strait, Paul A. George, Shriram Shivaraman, Virgil B. Shields, Mvs Chandrashekhar, Jeonghyun Hwang, Farhan Rana, Michael G. Spencer, Carlos S. Ruiz-Vargas, and Jiwoong Park. Ultrafast relaxation dynamics of hot optical phonons in graphene.Appl. Phys. Lett., 96(8):081917, 02 2010

    2010

  16. [16]

    Breusing, S

    M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser. Ultrafast nonequilibrium carrier dynamics in a single graphene layer.Phys. Rev. B, 83:153410, Apr 2011

    2011

  17. [17]

    Strait, Haining Wang, Shriram Shivaraman, Virgil Shields, Michael Spencer, and Farhan Rana

    Jared H. Strait, Haining Wang, Shriram Shivaraman, Virgil Shields, Michael Spencer, and Farhan Rana. Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy.Nano Lett., 11(11):4902–4906, Nov 2011. Optical pulse-induced quantum geometric waves in graphene 14

    2011

  18. [18]

    Winnerl, M

    S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm. Carrier relaxation in epitaxial graphene photoexcited near the dirac point.Phys. Rev. Lett., 107:237401, Nov 2011

    2011

  19. [19]

    K. J. Tielrooij, J. C. W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Zurutuza Elorza, M. Bonn, L. S. Levitov, and F. H. L. Koppens. Photoexcitation cascade and multiple hot-carrier generation in graphene.Nat. Phys., 9(4):248–252, Apr 2013

    2013

  20. [20]

    Jens Christian Johannsen, Søren Ulstrup, Federico Cilento, Alberto Crepaldi, Michele Zacchigna, Cephise Cacho, I. C. Edmond Turcu, Emma Springate, Felix Fromm, Christian Raidel, Thomas Seyller, Fulvio Parmigiani, Marco Grioni, and Philip Hofmann. Direct view of hot carrier dynamics in graphene.Phys. Rev. Lett., 111:027403, Jul 2013

    2013

  21. [21]

    Petersen, Matteo Mitrano, Cephise Cacho, I

    Isabella Gierz, Jesse C. Petersen, Matteo Mitrano, Cephise Cacho, I. C. Edmond Turcu, Emma Springate, Alexander Stöhr, Axel Köhler, Ulrich Starke, and Andrea Cavalleri. Snap- shots of non-equilibrium dirac carrier distributions in graphene.Nat. Mater., 12(12):1119– 1124, Dec 2013

    2013

  22. [22]

    Brida, A

    D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini. Ultrafast collinear scattering and carrier multiplication in graphene.Nat. Commun., 4(1):1987, Jun 2013

    1987

  23. [23]

    Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: relaxation dynamics and saturation behavior.J

    S Winnerl, F Göttfert, M Mittendorff, H Schneider, M Helm, T Winzer, E Malic, A Knorr, M Orlita, M Potemski, M Sprinkle, C Berger, and W A de Heer. Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: relaxation dynamics and saturation behavior.J. Phys. Condens. Matter, 25(5):054202, jan 2013

    2013

  24. [24]

    Plötzing, T

    T. Plötzing, T. Winzer, E. Malic, D. Neumaier, A. Knorr, and H. Kurz. Experimental verification of carrier multiplication in graphene.Nano Lett., 14(9):5371–5375, Sep 2014

    2014

  25. [25]

    McLeod, Aleksandr S

    Martin Wagner, Zhe Fei, Alexander S. McLeod, Aleksandr S. Rodin, Wenzhong Bao, Eric G. Iwinski, Zeng Zhao, Michael Goldflam, Mengkun Liu, Gerardo Dominguez, Mark Thiemens, Michael M. Fogler, Antonio H. Castro Neto, Chun Ning Lau, Sergiu Amarie, Fritz Keilmann, and D. N. Basov. Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by ...

    2014

  26. [26]

    Gierz, F

    I. Gierz, F. Calegari, S. Aeschlimann, M. Chávez Cervantes, C. Cacho, R. T. Chapman, E.Springate, S.Link, U.Starke, C.R.Ast, andA.Cavalleri. Trackingprimarythermalization events in graphene with photoemission at extreme time scales.Phys. Rev. Lett., 115:086803, Aug 2015

    2015

  27. [27]

    M. A. Sentef, M. Claassen, A. F. Kemper, B. Moritz, T. Oka, J. K. Freericks, and T. P. Devereaux. Theory of floquet band formation and local pseudospin textures in pump-probe photoemission of graphene.Nature Communications, 6(1):7047, May 2015

    2015

  28. [28]

    Michael Schüler and Michael A. Sentef. Theory of subcycle time-resolved photoemission: Application to terahertz photodressing in graphene.J. Electron Spectrosc. Relat. Phenom., 253:147121, 2021

    2021

  29. [29]

    Manmana, Michael A

    Marco Merboldt, Michael Schüler, David Schmitt, Jan Philipp Bange, Wiebke Bennecke, Karun Gadge, Klaus Pierz, Hans Werner Schumacher, Davood Momeni, Daniel Steil, Salvatore R. Manmana, Michael A. Sentef, Marcel Reutzel, and Stefan Mathias. Observation of floquet states in graphene.Nat. Phys., 21(7):1093–1099, Jul 2025. Optical pulse-induced quantum geomet...

    2025

  30. [30]

    Driven quantum tunneling.Physics Reports, 304(5):229– 354, 1998

    Milena Grifoni and Peter Hänggi. Driven quantum tunneling.Physics Reports, 304(5):229– 354, 1998

    1998

  31. [31]

    Amari.Information Geometry and Its Applications

    S. Amari.Information Geometry and Its Applications. Springer, February 2016

    2016

  32. [32]

    R. A. Fisher. Theory of statistical estimation.Math. Proc. Camb. Philos. Soc., 22(5):700–725, 1925

    1925

  33. [33]

    Man’ko, Giuseppe Marmo, E.C.G

    Paolo Facchi, Ravi Kulkarni, V.I. Man’ko, Giuseppe Marmo, E.C.G. Sudarshan, and Franco Ventriglia. Classical and quantum fisher information in the geometrical formulation of quantum mechanics.Physics Letters A, 374(48):4801–4803, 2010

    2010

  34. [34]

    A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim. The electronic properties of graphene.Rev. Mod. Phys., 81:109–162, Jan 2009

    2009

  35. [35]

    Model spin-orbit coupling hamiltonians for graphene systems.Phys

    Denis Kochan, Susanne Irmer, and Jaroslav Fabian. Model spin-orbit coupling hamiltonians for graphene systems.Phys. Rev. B, 95:165415, Apr 2017

    2017

  36. [36]

    Measurement of topological order based on metric- curvature correspondence.Phys

    Gero von Gersdorff and Wei Chen. Measurement of topological order based on metric- curvature correspondence.Phys. Rev. B, 104:195133, Nov 2021

    2021

  37. [37]

    Measurement of the berry curvature of solids using high-harmonic spectroscopy.Nat

    Tran Trung Luu and Hans Jakob Wörner. Measurement of the berry curvature of solids using high-harmonic spectroscopy.Nat. Commun., 9(1):916, Mar 2018

    2018

  38. [38]

    Measurement of interaction-dressed berry curvature and quantum metric in solids by optical absorption.SciPost Phys

    Wei Chen and Gero von Gersdorff. Measurement of interaction-dressed berry curvature and quantum metric in solids by optical absorption.SciPost Phys. Core, 5:040, 2022

    2022

  39. [39]

    Neves, Linda Ye, Junseo Jung, Denny Puntel, Federico Mazzola, Shiang Fang, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Jun Fuji, Ivana Vobornik, Jae-Hoon Park, Joseph G

    Mingu Kang, Sunje Kim, Yuting Qian, Paul M. Neves, Linda Ye, Junseo Jung, Denny Puntel, Federico Mazzola, Shiang Fang, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Jun Fuji, Ivana Vobornik, Jae-Hoon Park, Joseph G. Checkelsky, Bohm-Jung Yang, and Riccardo Comin. Measurements of the quantum geometric tensor in solids.Nat. Phys., 21(1):110–117, Jan 2025

    2025