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A first-order cumulant expansion reduces the interacting Mössbauer ensemble to three nonlinear equations and predicts a measurable, excitation-dependent phase shift of the nuclear dipole moment at high excitation.

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2026-08-04 12:57 UTC pith:J4NM6A3D

load-bearing objection Useful cumulant-based method and a concrete nonlinear phase signature for Mössbauer ensembles, but the 'arbitrary excitation' claim is not yet backed by the uncontrolled closure or the missing exact benchmark.

arxiv 2510.00970 v2 pith:J4NM6A3D submitted 2025-10-01 quant-ph

Cumulant expansion approach to the decay dynamics of interacting M\"ossbauer nuclei after strong impulsive excitation

Miriam Gerharz , J\"org Evers This is my paper
classification quant-ph
keywords Mössbauer nucleicumulant expansionnonlinear nuclear decaysuperradiancenuclear dipole phasex-ray free-electron laserfinite-size effectsinterferometric phase measurement
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Strong X-ray sources are beginning to excite Mössbauer nuclei far beyond the single-photon level, but the interacting many-body decay that follows has resisted efficient theoretical treatment. This paper establishes that a first-order cumulant expansion—treating correlations between different nuclei as small—closes the hierarchy into equations that scale linearly with particle number, and that for translationally invariant lattices the whole ensemble reduces to three nonlinear equations governed by a single tunable coupling parameter K. Within this model, the nuclear dipole phase develops a nonlinear, excitation-dependent time evolution at higher pulse areas, a signature the authors propose to detect interferometrically using two nuclear chains. The same framework also reveals finite-size effects, with K oscillating as a function of chain length and nuclear position, suggesting a route to studying small Mössbauer samples.

Core claim

The paper claims that the decay of an interacting ensemble of Mössbauer nuclei after impulsive excitation can be described, to leading order in inter-nuclear correlations, by a closed set of equations obtained from a first-order cumulant expansion. For a translationally invariant lattice under homogeneous plane-wave excitation, these equations reduce to three real, nonlinear, population- and time-dependent equations that depend on the system only through a single complex coupling parameter K, whose real part gives superradiant broadening and whose imaginary part gives an interaction-induced shift. Solving them shows that the phase of the nuclear dipole moment acquires a nonlinear, excitation

What carries the argument

The central object is the first-order cumulant truncation, which replaces two-atom expectation values by products of single-atom expectation values, thereby closing the many-body hierarchy into equations whose cost scales linearly with the number of nuclei. The coherence is then decomposed into a magnitude and a phase, and a translational invariance assumption turns the sum over neighbors into a single complex constant K: its real part describes superradiant broadening, while its imaginary part drives the nonlinear phase evolution. K is evaluated using free-space dipole-dipole couplings and polylogarithmic sums, yielding an explicit geometry-dependent expression in terms of the incidence ang

Load-bearing premise

The load-bearing premise is that first-order cumulant truncation is accurate—i.e., that correlations between different nuclei remain small enough to factor two-particle expectation values into products of single-particle expectation values—which the paper supports only qualitatively, for a small system without internal conversion.

What would settle it

Perform the proposed two-chain interferometry with a 57Fe sample, sweeping the excitation pulse area A from about 0.1π to 0.9π at a fixed incidence angle near 5 mrad; the quantum-beat minima should shift monotonically with sin^2(A/2) by a predictable amount. If the shift is absent or has the wrong sign or magnitude, the first-order cumulant truncation is invalid in this regime. A complementary decisive check is a numerically exact master-equation simulation for N≈10 nuclei at the same incidence angle, comparing the phase evolution to the cumulant equations.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • For large, translationally invariant ensembles, the full many-body decay dynamics reduces to three real nonlinear equations whose solution no longer depends on the number of nuclei, making large-scale parameter scans feasible.
  • The nuclear dipole phase evolves nonlinearly at higher excitation, with the nonlinear contribution proportional to K_I sin^2(A/2), vanishing as the population decays and leaving a residual excitation-dependent offset.
  • Because K can be tuned by the incidence angle of the driving x-ray beam, the size and sign of the nonlinear phase shift can be controlled experimentally.
  • In a two-chain interferometer with one detuned reference chain, the nonlinear phase shift appears as shifts of the quantum-beat minima by a few nanoseconds, within current time-resolved nuclear forward scattering capabilities.
  • Finite chains show oscillatory deviations of K from the infinite-chain value, both with chain length and with the position of the nucleus, providing a handle for studying finite-size effects in small Mössbauer samples.

Where Pith is reading between the lines

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

  • The geometry-tunability of K_I suggests the same scheme could be used to map the inter-nuclear interaction landscape by rotating the sample, effectively performing interaction tomography.
  • The cumulant closure is not specific to Mössbauer nuclei; the same three-equation structure might describe other dense radiating ensembles, though the paper confines its claims to nuclei.
  • The finite-size oscillations of K imply that the position of a nucleus within a small chain affects its decay; this could be probed with focused beams and might enable position-resolved Mössbauer spectroscopy.
  • The proposed measurement effectively isolates K_I from the background decay rate Γ, so the two-chain interferometer could serve as a precision probe of collective level shifts in nuclear systems.

Editorial analysis

A structured set of objections, weighed in public.

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

Circularity Check

0 steps flagged

No circularity: the nonlinear phase prediction follows from the stated cumulant closure with K computed from free-space dipole couplings; there are no fitted parameters and no load-bearing self-citations.

full rationale

The derivation chain is self-contained. Starting from the microscopic master equation (1)–(3), the authors close the hierarchy by the explicit first-order factorization (6), ⟨A_n B_m⟩ ≈ ⟨A_n⟩⟨B_m⟩. This is a stated approximation/input, not a hidden redefinition; the output equations (7)–(13) are its mathematical consequences. The central quantity K is not fitted: it is computed from free-space dipole-dipole couplings via Eq. (16) (and the finite-chain Eq. (17)) using material parameters for 57Fe. The nonlinear phase Eq. (15) is obtained by integrating Eq. (12) with an explicit approximate population decay; it is not imposed or tuned to experimental data. The interferometric proposal uses only this derived φ(t). Self-citations (e.g., [39], [51], [52]) appear as background, motivation, or as approaches the authors do not rely on; no load-bearing step is justified solely by a same-author citation. The independent cross-check against the external truncated-Wigner approach [44] supports the calculation, and the paper itself flags the limited range of that check. The main caveat—that the first-order cumulant truncation (6) is uncontrolled and may fail for strong correlations, e.g., near full inversion—is an approximation-validity concern, not circularity: the prediction is not equivalent to its input by construction. Therefore no circular step is identified.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The central claim rests on a standard master equation plus a first-order factorization of two-atom correlations. No data were fitted; the only adjustable inputs are physical parameters and experimental control angles. The main burden is the factorization closure and the infinite-chain idealization, neither of which carries a quantitative error estimate in the paper.

axioms (6)
  • domain assumption Master equation (1)-(3) with dipole-dipole couplings J_mn and dissipative rates Gamma_mn obtained by tracing out the radiation field.
    Standard Born-Markov open-quantum-system modeling for Mössbauer ensembles, cited to [47,63-65]. This is the starting point of the derivation.
  • ad hoc to paper First-order cumulant factorization Eq. (6): expectation values of two-atom operators factorize, <A_n B_m> ≈ <A_n><B_m> for n≠m.
    This closes the hierarchy at lowest order. The paper gives no error bound; validity is only qualitatively checked against CDWTA. It is the central approximation of the work.
  • domain assumption Infinite translationally invariant 1D lattice with plane-wave excitation, so coherences differ only by fixed initial phases.
    Needed to reduce the N equations to three and make K time-independent. The appendix analyzes finite chains, but the main quantitative results use the infinite-chain limit.
  • domain assumption Free-space dipole-dipole couplings evaluated as polylogarithm sums, Eq. (16), using 57Fe parameters and alpha-Fe nearest-neighbor spacing.
    Assumes an ideal 1D chain in free space. Real bulk or structured environments would modify K, as the discussion acknowledges.
  • ad hoc to paper Approximate population evolution in Eq. (15): <sigma_ee>(t) ≈ sin^2(A/2) exp(-Gamma t), neglecting K_R in Eq. (13).
    Used to produce the closed-form phase formula. K_R is argued to be small compared to Gamma, but no rigorous bound is provided.
  • domain assumption Initial impulsive excitation state: <sigma_ee>(0)=sin^2(A/2) and <sigma_-bar>(0)=sin(A/2)cos(A/2).
    Standard two-level Rabi solution for a short pulse, cited to [66]. It sets initial conditions but does not by itself determine the decay dynamics.

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read the original abstract

Recent progress in accelerator-based x-ray sources brings higher excitation of ensembles of M\"ossbauer nuclei closer to experimental feasibility. Yet, a theoretical modeling of the decay dynamics of the interacting nuclear ensemble after the impulsive excitation is still an open challenge. Here, we derive a set of nonlinear equations which is capable of efficiently modeling large nuclear ensembles for arbitrary degrees of excitation. As key signature for higher excitation, we identify a non-linear time-evolution of the nuclear dipole phase, which can be tuned via the scattering geometry, and interferometrically be measured. Furthermore, we identify interesting finite-size effects in the nuclear dynamics of small ensembles. Our results provide important guidance for future experiments aiming at the non-linear excitation of nuclei. We further envision the exploration of finite size-effects in M\"ossbauer spectroscopy with highest spatial resolution, i.e., small sample volumes.

Figures

Figures reproduced from arXiv: 2510.00970 by J\"org Evers, Miriam Gerharz.

Figure 1
Figure 1. Figure 1: FIG. 1. Coupling parameter [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Nuclear dipole phase evolution as function of inci [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time-dependent intensity of the x-ray scattered by [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of the phase evolution computed with a [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Phase evolution of the central nucleus in a chain of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

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Works this paper leans on

71 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [1]

    R¨ ohlsberger, K

    R. R¨ ohlsberger, K. Schlage, B. Sahoo, S. Couet, and R. R¨ uffer, Collective lamb shift in single-photon superra- diance, Science328, 1248 (2010)

    2010

  2. [2]

    R¨ ohlsberger, H.-C

    R. R¨ ohlsberger, H.-C. Wille, K. Schlage, and B. Sahoo, Electromagnetically induced transparency with resonant nuclei in a cavity, Nature482, 199–203 (2012)

    2012

  3. [3]

    K. P. Heeg, H.-C. Wille, K. Schlage, T. Guryeva, D. Schumacher, I. Uschmann, K. S. Schulze, B. Marx, T. K¨ ampfer, G. G. Paulus, R. R¨ ohlsberger, and J. Evers, Vacuum-assisted generation and control of atomic coher- ences at x-ray energies, Phys. Rev. Lett.111, 073601 (2013)

    2013

  4. [4]

    K. P. Heeg, C. Ott, D. Schumacher, H.-C. Wille, R. R¨ ohlsberger, T. Pfeifer, and J. Evers, Interferomet- ric phase detection at x-ray energies via Fano resonance control, Phys. Rev. Lett.114, 207401 (2015)

    2015

  5. [5]

    K. P. Heeg, J. Haber, D. Schumacher, L. Bocklage, H.-C. Wille, K. S. Schulze, R. Loetzsch, I. Uschmann, G. G. Paulus, R. R¨ uffer, R. R¨ ohlsberger, and J. Evers, Tunable subluminal propagation of narrow-band x-ray pulses, Phys. Rev. Lett.114, 203601 (2015)

    2015

  6. [6]

    Haber, K

    J. Haber, K. S. Schulze, K. Schlage, R. Loetzsch, L. Bock- lage, T. Gurieva, H. Bernhardt, H.-C. Wille, R. R¨ uffer, I. Uschmann, G. G. Paulus, and R. R¨ ohlsberger, Col- lective strong coupling of x-rays and nuclei in a nuclear optical lattice, Nature Photonics10, 445–449 (2016)

    2016

  7. [7]

    Haber, X

    J. Haber, X. Kong, C. Strohm, S. Willing, J. Gollwitzer, L. Bocklage, R. R¨ uffer, A. P´ alffy, and R. R¨ ohlsberger, Rabi oscillations of x-ray radiation between two nuclear ensembles, Nature Photonics11, 720–725 (2017)

    2017

  8. [8]

    Zhang, W.-T

    X. Zhang, W.-T. Liao, A. Kalachev, R. Shakhmura- tov, M. Scully, and O. Kocharovskaya, Nuclear quantum memory and time sequencing of a singleγphoton, Phys. Rev. Lett.123, 250504 (2019)

    2019

  9. [9]

    K. P. Heeg, A. Kaldun, C. Strohm, C. Ott, R. Subrama- nian, D. Lentrodt, J. Haber, H.-C. Wille, S. Goerttler, R. R¨ uffer, C. H. Keitel, R. R¨ ohlsberger, T. Pfeifer, and J. Evers, Coherent x-ray-optical control of nuclear exci- tons, Nature590, 401–404 (2021)

    2021

  10. [10]

    Velten, L

    S. Velten, L. Bocklage, X. Zhang, K. Schlage, A. Panch- wanee, S. Sadashivaiah, I. Sergeev, O. Leupold, A. I. Chumakov, O. Kocharovskaya, and R. R¨ ohlsberger, Nu- clear quantum memory for hard x-ray photon wave pack- ets, Science Advances10, eadn9825 (2024)

    2024

  11. [11]

    Y. V. Shvyd’ko, T. Hertrich, U. van B¨ urck, E. Gerdau, O. Leupold, J. Metge, H. D. R¨ uter, S. Schwendy, G. V. Smirnov, W. Potzel, and P. Schindelmann, Storage of nuclear excitation energy through magnetic switching, Phys. Rev. Lett.77, 3232 (1996)

    1996

  12. [12]

    Helist¨ o, I

    P. Helist¨ o, I. Tittonen, M. Lippmaa, and T. Katila, Gamma echo, Phys. Rev. Lett.66, 2037 (1991)

    2037

  13. [13]

    R¨ ohlsberger and J

    R. R¨ ohlsberger and J. Evers, Quantum Optical Phe- nomena in Nuclear Resonant Scattering, inModern M¨ ossbauer Spectroscopy, Vol. 137, edited by Y. Yoshida and G. Langouche (Springer Singapore, Singapore, 2021) pp. 105–171, series Title: Topics in Applied Physics

    2021

  14. [14]

    Gerharz, D

    M. Gerharz, D. Lentrodt, L. Bocklage, K. Schulze, C. Ott, R. Steinbr¨ ugge, O. Leupold, I. Sergeev, G. G. Paulus, C. H. Keitel, R. R¨ ohlsberger, T. Pfeifer, and J. Evers, Dark-fringe interferometer with dynamic phase control for M¨ ossbauer science (2025), arXiv:2509.24658 8 [quant-ph]

    arXiv 2025

  15. [15]

    Schindelmann, U

    P. Schindelmann, U. van B¨ urck, W. Potzel, G. V. Smirnov, S. L. Popov, E. Gerdau, Y. V. Shvyd’ko, J. J¨ aschke, H. D. R¨ uter, A. I. Chumakov, and R. R¨ uffer, Radiative decoupling and coupling of nuclear oscilla- tors by stepwise doppler-energy shifts, Phys. Rev. A65, 023804 (2002)

    2002

  16. [16]

    Vagizov, V

    F. Vagizov, V. Antonov, Y. V. Radeonychev, R. N. Shakhmuratov, and O. Kocharovskaya, Coherent control of the waveforms of recoillessγ-ray photons, Nature508, 80–83 (2014)

    2014

  17. [17]

    F. G. Vagizov, E. K. Sadykov, and O. A. Kocharovskaya, Modulation of M¨ ossbauer radiation by pulsed laser exci- tation, JETP Letters96, 812 (2013)

    2013

  18. [18]

    Sakshath, K

    S. Sakshath, K. Jenni, L. Scherthan, P. W¨ urtz, M. Herlitschke, I. Sergeev, C. Strohm, H.-C. Wille, R. R¨ ohlsberger, J. A. Wolny, and V. Sch¨ unemann, Op- tical pump - nuclear resonance probe experiments on spin crossover complexes, Hyperfine Interactions238, 89 (2017)

    2017

  19. [19]

    Kuznetsova, X

    E. Kuznetsova, X. Zhang, Y. Shvyd’ko, M. O. Scully, and O. Kocharovskaya, Spectral flux enhancement of x rays for addressing ultranarrow nuclear transitions, Phys. Rev. Lett.133, 193401 (2024)

    2024

  20. [20]

    Nazeeri, C

    A. Nazeeri, C. Brandenstein, C. Jia, L. Magrini, and G. Gratta, Coupling of a nuclear transition to a surface acoustic wave (2025), arXiv:2509.02750 [quant-ph]

    arXiv 2025

  21. [21]

    Yamashita, S

    H. Yamashita, S. Kitao, Y. Kobayashi, and M. Seto, The correlation of the gamma ray waveform with the vibra- tion phase of the resonant absorber, Interactions245, 10.1007/s10751-024-02214-3 (2024)

    work page doi:10.1007/s10751-024-02214-3 2024

  22. [22]

    L. M. Lohse, A. Negi, M. Osterhoff, P. Meyer, S. Yaroslavtsev, A. I. Chumakov, L. Bocklage, R. R¨ ohlsberger, and T. Salditt, Interferometric measure- ment of nuclear resonant phase shift with a nanoscale young double waveguide (2025), arXiv:2506.05823 [physics.optics]

    Pith/arXiv arXiv 2025

  23. [23]

    Stejskal, V

    A. Stejskal, V. Vrba, and V. Proch´ azka, Toward flexi- ble intensity control of resonantly scatteredγ-rays us- ing multi-frequency vibrating resonant absorber, Applied Physics Letters126, 084102 (2025)

    2025

  24. [24]

    Fujiwara, T

    K. Fujiwara, T. Mitsui, Y. Aoyagi, Y. Yoda, and N. Ikeda, Quantum interference of totally reflected m¨ ossbauerγ-rays from a 57fe monolayer embedded in a thin film, Journal of the Physical Society of Japan90, 084705 (2021)

    2021

  25. [25]

    P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bost- edt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Cof- fee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messer- schmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. S...

    2010

  26. [26]

    Barletta, J

    W. Barletta, J. Bisognano, J. Corlett, P. Emma, Z. Huang, K.-J. Kim, R. Lindberg, J. Murphy, G. Neil, D. Nguyen, C. Pellegrini, R. Rimmer, F. Sannibale, G. Stupakov, R. Walker, and A. Zholents, Free electron lasers: Present status and future challenges, Nuclear In- struments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors...

    2010

  27. [27]

    Ishikawa, H

    T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hat- sui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, ...

    2012

  28. [28]

    Decking, S

    W. Decking, S. Abeghyan, P. Abramian, A. Abramsky, A. Aguirre, C. Albrecht, P. Alou, M. Altarelli, P. Alt- mann, K. Amyan,et al., A MHz-repetition-rate hard x- ray free-electron laser driven by a superconducting linear accelerator, Nature photonics14, 391 (2020)

    2020

  29. [29]

    Amann, W

    J. Amann, W. Berg, V. Blank, F.-J. Decker, Y. Ding, P. Emma, Y. Feng, J. Frisch, D. Fritz, J. Hastings, et al., Demonstration of self-seeding in a hard-x-ray free- electron laser, Nature photonics6, 693 (2012)

    2012

  30. [30]

    Inoue, T

    I. Inoue, T. Osaka, T. Hara, T. Tanaka, T. Inagaki, T. Fukui, S. Goto, Y. Inubushi, H. Kimura, R. Kinjo, H. Ohashi, K. Togawa, K. Tono, M. Yamaga, H. Tanaka, T. Ishikawa, and M. Yabashi, Generation of narrow-band x-ray free-electron laser via reflection self-seeding, Nature photonics13, 319 (2019)

    2019

  31. [31]

    S. Liu, C. Grech, M. Guetg, S. Karabekyan, V. Kocharyan, N. Kujala, C. Lechner, T. Long, N. Mirian, W. Qin, S. Serkez, S. Tomin, J. Yan, S. Abeghyan, J. Anton, V. Blank, U. Boesenberg, F. Brinker, Y. Chen, W. Decking, X. Dong, S. Kear- ney, D. La Civita, A. Madsen, T. Maltezopoulos, A. Rodriguez-Fernandez, E. Saldin, L. Samoylova, M. Scholz, H. Sinn, V. S...

    2023

  32. [32]

    Nam, C.-K

    I. Nam, C.-K. Min, B. Oh, G. Kim, D. Na, Y. J. Suh, H. Yang, M. H. Cho, C. Kim, M.-J. Kim, C. H. Shim, J. H. Ko, H. Heo, J. Park, J. Kim, S. Park, G. Park, S. Kim, S. H. Chun, H. Hyun, J. H. Lee, K. S. Kim, I. Eom, S. Rah, D. Shu, K.-J. Kim, S. Terentyev, V. Blank, Y. Shvyd’ko, S. J. Lee, and H.-S. Kang, High- brightness self-seeded x-ray free-electron la...

    2021

  33. [33]

    S. Liu, G. Geloni, T. Long, W. Qin, V. Kocharyan, J. Yan, L. Cao, N. Kujala, M. Guetg, M. Scholz, and W. Decking, Updates on the hard x-ray self-seeding at the european xfel, Synchrotron Radiation News38, 11 (2025)

    2025

  34. [34]

    Shenoy, Dreams with synchrotron radiation, inThe Rudolf M¨ ossbauer Story: His Scientific Work and Its Im- pact on Science and History, edited by G

    G. Shenoy, Dreams with synchrotron radiation, inThe Rudolf M¨ ossbauer Story: His Scientific Work and Its Im- pact on Science and History, edited by G. Kalvius and 9 P. Kienle (Springer, Berlin, Heidelberg, 2012)

    2012

  35. [35]

    A. I. Chumakov, A. Q. Baron, I. Sergueev, C. Strohm, O. Leupold, Y. Shvyd’ko, G. V. Smirnov, R. R¨ uffer, Y. Inubushi, M. Yabashi, K. Tono, T. Kudo, and T. Ishikawa, Superradiance of an ensemble of nuclei ex- cited by a free electron laser, Nature physics14, 261 (2018)

    2018

  36. [36]

    Shvyd’ko, R

    Y. Shvyd’ko, R. R¨ ohlsberger, O. Kocharovskaya, J. Ev- ers, G. A. Geloni, P. Liu, D. Shu, A. Miceli, B. Stone, W. Hippler, B. Marx-Glowna, I. Uschmann, R. Loet- zsch, O. Leupold, H.-C. Wille, I. Sergeev, M. Gerharz, X. Zhang, C. Grech, M. Guetg, V. Kocharyan, N. Kujala, S. Liu, W. Qin, A. Zozulya, J. Hallmann, U. Boesenberg, W. Jo, J. M¨ oller, A. Rodrig...

    2023

  37. [37]

    P. Liu, M. Gerharz, B. Marx-Glowna, W. Hippler, J.- E. Pudell, A. Zozulya, B. Stone, D. Shu, R. Loet- zsch, S. Sadashivaiah, L. Bocklage, C. Boemer, S. Liu, V. Kocharyan, D. Krebs, T. Long, W. Qin, M. Scholz, K. Schlage, I. Sergeev, H.-C. Wille, U. Boesenberg, G. A. Geloni, J. Hallmann, W. Jo, N. Kujala, A. Mad- sen, A. Rodriguez-Fernandez, R. Rysov, K. T...

    Pith/arXiv arXiv 2025

  38. [38]

    Gerharz, W

    M. Gerharz, W. Hippler, B. Marx-Glowna, S. Sadashiva- iah, K. S. Schulze, I. Uschmann, R. L¨ otzsch, K. Schlage, S. Velten, D. Lentrodt, L. Wolff, O. Leupold, I. Sergeev, H.-C. Wille, C. Strohm, M. Guetg, S. Liu, G. A. Geloni, U. Boesenberg, J. Hallmann, A. Zozulya, J.-E. Pudell, A. Rodriguez-Fernandez, M. Youssef, A. Mad- sen, L. Bocklage, G. G. Paulus, ...

    arXiv 2025

  39. [39]

    Lentrodt, C

    D. Lentrodt, C. H. Keitel, and J. Evers, Toward nonlinear optics with M¨ ossbauer nuclei using x-ray cavities, Phys. Rev. Lett.135, 033801 (2025)

    2025

  40. [40]

    K.-J. Kim, Y. Shvyd’ko, and S. Reiche, A proposal for an x-ray free-electron laser oscillator with an energy- recovery linac, Phys. Rev. Lett.100, 244802 (2008)

    2008

  41. [41]

    Margraf, R

    R. Margraf, R. Robles, A. Halavanau, J. Kryzywinski, K. Li, J. MacArthur, T. Osaka, A. Sakdinawat, T. Sato, Y. Sun, K. Tamasaku, Z. Huang, G. Marcus, and D. Zhu, Low-loss stable storage of 1.2 ˚A x-ray pulses in a 14 m bragg cavity, Nature Photonics17, 878–882 (2023)

    2023

  42. [42]

    Rauer, I

    P. Rauer, I. Bahns, B. Friedrich, S. Casalbuoni, M. D. Felice, M. Dommach, I. F. Martin, W. Fre- und, J. Gr¨ unert, M. Guetg, I. Karpics, S. Karabekyan, A. Koch, N. Kujala, D. L. Civita, J. Liu, T. Mal- tezopoulos, M. Makita, F. Mayet, L. M¨ uller, B. Rio, L. Samoylova, S. Schmidtchen, M. Scholz, A. Silenzi, V. Strauch, D. Thoden, T. Wohlenberg, M. Vannon...

    work page doi:10.21203/rs.3.rs-7274597/v1 2025

  43. [43]

    Adams, G

    B. Adams, G. Aeppli, T. Allison, A. Q. R. Baron, P. Bucksbaum, A. I. Chumakov, C. Corder, S. P. Cramer, S. DeBeer, Y. Ding, J. Evers, J. Frisch, M. Fuchs, G. Gr¨ ubel, J. B. Hastings, C. M. Heyl, L. Hol- berg, Z. Huang, T. Ishikawa, A. Kaldun, K.-J. Kim, T. Kolodziej, J. Krzywinski, Z. Li, W.-T. Liao, R. Lind- berg, A. Madsen, T. Maxwell, G. Monaco, K. Ne...

    Pith/arXiv arXiv 2019

  44. [44]

    C. D. Mink and M. Fleischhauer, Collective radiative in- teractions in the discrete truncated Wigner approxima- tion, SciPost Phys.15, 233 (2023)

    2023

  45. [45]

    Kagan, A

    Y. Kagan, A. M. Afanas’ev, and V. G. Kohn, On excita- tion of isomeric nuclear states in a crystal by synchrotron radiation, Journal of Physics C: Solid State Physics12, 615–631 (1979)

    1979

  46. [46]

    J. P. Hannon and G. T. Trammell, Coherentγ-ray optics, Hyperfine Interactions123, 127 (1999)

    1999

  47. [47]

    K. P. Heeg and J. Evers, X-ray quantum optics with M¨ ossbauer nuclei embedded in thin-film cavities, Phys. Rev. A88, 043828 (2013)

    2013

  48. [48]

    Lentrodt, K

    D. Lentrodt, K. P. Heeg, C. H. Keitel, and J. Evers, Ab initio quantum models for thin-film x-ray cavity qed, Phys. Rev. Res.2, 023396 (2020)

    2020

  49. [49]

    X. Kong, D. E. Chang, and A. P´ alffy, Green’s-function formalism for resonant interaction of x rays with nuclei in structured media, Phys. Rev. A102, 033710 (2020)

    2020

  50. [50]

    Lentrodt, C

    D. Lentrodt, C. H. Keitel, and J. Evers, Excitation of narrow x-ray transitions in thin-film cavities by focused pulses (2025)

    2025

  51. [51]

    Wolff and J

    L. Wolff and J. Evers, Characterization and detection method for x-ray excitation of M¨ ossbauer nuclei beyond the low-excitation regime, Phys. Rev. A108, 043714 (2023)

    2023

  52. [52]

    K. P. Heeg, C. H. Keitel, and J. Evers, Inducing and detecting collective population inversions of M¨ ossbauer nuclei (2016), arXiv:1607.04116 [quant-ph]

    Pith/arXiv arXiv 2016

  53. [53]

    R¨ ohlsberger,Nuclear Condensed Matter Physics with Synchrotron Radiation: Basic Principles, Methodology and Applications(Springer, Berlin, Heidelberg, 2004)

    R. R¨ ohlsberger,Nuclear Condensed Matter Physics with Synchrotron Radiation: Basic Principles, Methodology and Applications(Springer, Berlin, Heidelberg, 2004)

    2004

  54. [54]

    Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 (2011), january 2011 Special Issue

    U. Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 (2011), january 2011 Special Issue

    2011

  55. [55]

    X. Kong, Y. Chang, L. Zhang, J. Yuan, and Y.-G. Ma, Multiphoton emission of x-rays from cooperative reso- nant nuclei, Phys. Rev. Res.7, 013030 (2025)

    2025

  56. [56]

    Kubo, Generalized cumulant expansion method, Jour- nal of the Physical Society of Japan17, 1100 (1962)

    R. Kubo, Generalized cumulant expansion method, Jour- nal of the Physical Society of Japan17, 1100 (1962)

    1962

  57. [57]

    S´ anchez-Barquilla, R

    M. S´ anchez-Barquilla, R. E. F. Silva, and J. Feist, Cu- mulant expansion for the treatment of light–matter in- teractions in arbitrary material structures, The Journal of Chemical Physics152, 034108 (2020)

    2020

  58. [58]

    Kira and S

    M. Kira and S. W. Koch, Cluster-expansion representa- tion in quantum optics, Phys. Rev. A78, 022102 (2008)

    2008

  59. [59]

    Rubies-Bigorda, S

    O. Rubies-Bigorda, S. Ostermann, and S. F. Yelin, Char- acterizing superradiant dynamics in atomic arrays via a cumulant expansion approach, Phys. Rev. Res.5, 013091 (2023)

    2023

  60. [60]

    Kirton and J

    P. Kirton and J. Keeling, Superradiant and lasing states in driven-dissipative dicke models, New Journal of Physics20, 015009 (2018)

    2018

  61. [61]

    Kr¨ amer and H

    S. Kr¨ amer and H. Ritsch, Generalized mean-field ap- proach to simulate the dynamics of large open spin 10 ensembles with long range interactions, The Euro- pean Physical Journal D69, 10.1140/epjd/e2015-60266- 5 (2015)

    work page doi:10.1140/epjd/e2015-60266- 2015

  62. [62]

    Robicheaux and D

    F. Robicheaux and D. A. Suresh, Beyond lowest order mean-field theory for light interacting with atom arrays, Phys. Rev. A104, 023702 (2021)

    2021

  63. [63]

    Asenjo-Garcia, J

    A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble, Atom-light interactions in quasi-one-dimensional nanostructures: A green’s-function perspective, Phys. Rev. A95, 033818 (2017)

    2017

  64. [64]

    Ficek and S

    Z. Ficek and S. Swain,Quantum interference and coher- ence: theory and experiments, Springer series in optical sciences (Springer, Heidelberg, 2005)

    2005

  65. [65]

    Kiffner, M

    M. Kiffner, M. Macovei, J. Evers, and C. H. Kei- tel, Vacuum-induced processes in multi-level atoms, in Progress in Optics, Vol. 55 (Elsevier Science, Burlington,

  66. [66]

    Allen and J

    L. Allen and J. Eberly,Optical resonance and two-level atoms(Dover books on physics and chemistry, 1987)

    1987

  67. [67]

    N. N. Greenwood,M¨ ossbauer spectroscopy(Springer Sci- ence & Business Media, 2012)

    2012

  68. [68]

    Diekmann, D

    O. Diekmann, D. Lentrodt, and J. Evers, Inverse design approach to x-ray quantum optics with M¨ ossbauer nuclei in thin-film cavities, Phys. Rev. A105, 013715 (2022)

    2022

  69. [69]

    Diekmann, D

    O. Diekmann, D. Lentrodt, and J. Evers, Inverse design in nuclear quantum optics: From artificial x-ray multi- level schemes to spectral observables, Phys. Rev. A106, 053701 (2022)

    2022

  70. [70]

    Longo, C

    P. Longo, C. H. Keitel, and J. Evers, Tailoring super- radiance to design artificial quantum systems, Scientific Reports6, 10.1038/srep23628 (2016)

    work page doi:10.1038/srep23628 2016

  71. [71]

    Longo and J

    P. Longo and J. Evers, Probing few-excitation eigenstates of interacting atoms on a lattice by observing their col- lective light emission in the far field, Phys. Rev. A90, 063834 (2014)

    2014