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  • Open Access

Intensity-dependent interferences in strong-field Rydberg-state excitation

Xiaopeng Yi1, Changtong Liang1, Li Guo2,*, Wilhelm Becker3,†, and Jing Chen4,5,‡

  • *Contact author: guoli@shnu.edu.cn
  • †Contact author: wbecker@mbi-berlin.de
  • ‡Contact author: chenjing@ustc.edu.cn
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Phys. Rev. Research 8, 013090 – Published 27 January, 2026

DOI: https://doi.org/10.1103/4d6p-55n1

Abstract

We conduct a systematic investigation of the oscillations of the Rydberg-state populations as a function of intensity arising from strong-field multiphoton excitation of Rydberg atoms. By numerically solving the time-dependent Schrödinger equation and by constructing a quantum model based on Freeman resonances, we elucidate the underlying physical mechanisms governing the intensity-dependent oscillatory behavior of the Rydberg-state population dynamics. Our analysis shows that these oscillations originate from the synergistic interplay of three distinct quantum-interference mechanisms: (1) interference between excitation pathways at the rising and falling edges of the laser pulse (long-time interference), (2) interference between different optical cycles within the same side of the laser pulse (short-time interference), and (3) interference within individual optical cycles (intracycle interference). Additionally, we find that ground-state depletion has varying degrees of influence on the oscillation patterns formed by the three interference mechanisms under different laser-intensity conditions.

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References (40)

  1. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, Above-threshold ionization with subpicosecond laser pulses, Phys. Rev. Lett. 59, 1092 (1987).
  2. M. V. Fedorov and A. M. Movsesian, Field-induced effects of narrowing of photoelectron spectra and stabilisation of Rydberg atoms, J. Phys. B: At. Mol. Opt. Phys. 21, L155 (1988).
  3. M. P. de Boer and H. G. Muller, Observation of large populations in excited states after short-pulse multiphoton ionization, Phys. Rev. Lett. 68, 2747 (1992).
  4. B. B. Wang, X. F. Li, P. M. Fu, J. Chen, and J. Liu, Coulomb potential recapture effect in above-barrier ionization in laser pulses, Chin. Phys. Lett. 23, 2729 (2006).
  5. T. Nubbemeyer, U. Eichmann, and W. Sandner, Excited neutral atomic fragments in the strong-field dissociation of N2 molecules, J. Phys. B: At. Mol. Opt. Phys. 42, 134010 (2009).
  6. L. V. Keldysh, Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP 47, 1307 (1964).
  7. T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, Strong-field tunneling without ionization, Phys. Rev. Lett. 101, 233001 (2008).
  8. L. Fechner, N. Camus, A. Krupp, J. Ullrich, T. Pfeifer, and R. Moshammer, Creation and survival of autoionizing states in strong laser fields, Phys. Rev. A 92, 051403(R) (2015).
  9. N. I. Shvetsov-Shilovski, S. P. Goreslavski, S. V. Popruzhenko, and W. Becker, Capture into Rydberg states and momentum distributions of ionized electrons, Laser Phys. 19, 1550 (2009).
  10. H. Yun, J. H. Mun, S. I. Hwang, S. B. Park, I. A. Ivanov, C. H. Nam, and K. T. Kim, Coherent extreme-ultraviolet emission generated through frustrated ionization, Nat. Photon. 12, 620 (2018).
  11. J. McKenna, S. Zeng, J. J. Hua, A. M. Sayler, M. Zohrabi, N. G. Johnson, B. Gaire, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, Frustrated tunneling ionization during laser-induced D2 fragmentation: Detection of excited metastable D* atoms, Phys. Rev. A 84, 043425 (2011).
  12. I. A. Ivanov, A. S. Kheifets, and K. T. Kim, Correlation analysis of frustrated tunneling ionization, Phys. Rev. A 107, 043106 (2023).
  13. H. Zimmermann, S. Patchkovskii, M. Ivanov, and U. Eichmann, Unified time and frequency picture of ultrafast atomic excitation in strong laser fields, Phys. Rev. Lett. 118, 013003 (2017).
  14. S. Hu, X. Hao, H. Lv, M. Li, S. Yu, J. Chen, X. Jia, F. Yao, J. Zhang, and B. Xu, Quantum dynamics of atomic Rydberg excitation in strong laser fields, Opt. Express 27, 31629 (2019).
  15. M. Liu, S. Xu, S. Hu, W. Becker, W. Quan, X. Liu, and J. Chen, Electron dynamics in laser-driven atoms near the continuum threshold, Optica 8, 765 (2021).
  16. P. Kruit, J. Kimman, H. G. Muller, and M. J. Van der Wiel, The AC Stark shift as an intensity probe in resonant multiphoton ionisation of xenon, J. Phys. B: At. Mol. Phys. 16, 937 (1983).
  17. W. Zhang, X. Gong, H. Li, P. Lu, F. Sun, Q. Ji, K. Lin, J. Ma, H. Li, J. Qiang, F. He, and J. Wu, Electron-nuclear correlated multiphoton-route to Rydberg fragments of molecules, Nat. Commun. 10, 757 (2019).
  18. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Sub-barrier pathways to Freeman resonances, Phys. Rev. A 102, 053105 (2020).
  19. S. P. Xu, M. Q. Liu, S. L. Hu, Z. Shu, W. Quan, Z. L. Xiao, Y. Zhou, M. Z. Wei, M. Zhao, R. P. Sun, Y. L. Wang, L. Q. Hua, C. Gong, X. Y. Lai, J. Chen, and X. J. Liu, Observation of a transition in the dynamics of strong-field atomic excitation, Phys. Rev. A 102, 043104 (2020).
  20. D. Chetty, R. D. Glover, B. A. deHarak, X. M. Tong, H. Xu, T. Pauly, N. Smith, K. R. Hamilton, K. Bartschat, J. P. Ziegel, N. Douguet, A. N. Luiten, P. S. Light, I. V. Litvinyuk, and R. T. Sang, Observation of dynamic Stark resonances in strong-field excitation, Phys. Rev. A 101, 053402 (2020).
  21. R. K. Malla, V. Y. Chernyak, C. Sun, and N. A. Sinitsyn, Carrier-envelope phase-dependent strong-field excitation, Phys. Rev. Lett. 129, 033201 (2022).
  22. U. Bengs, S. Patchkovskii, M. Ivanov, and N. Zhavoronkov, All-optical Stückelberg spectroscopy of strongly driven Rydberg states, Phys. Rev. Res. 4, 023135 (2022).
  23. E. C. G. Stückelberg, Theory of inelastic collisions between atoms, Helv. Phys. Acta 5, 369 (1932).
  24. L. D. Landau, On the theory of transfer of energy at collisions II, Phys. Z. Sowjetunion 2, 46 (1932).
  25. C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. London, Ser. A 137, 696 (1932).
  26. G. N. Gibson, R. R. Freeman, and T. J. McIlrath, Verification of the dominant role of resonant enhancement in short-pulse multiphoton ionization, Phys. Rev. Lett. 69, 1904 (1992).
  27. Y. Zhao, Y. Zhou, J. Liang, Q. Ke, Y. Liao, M. Li, and P. Lu, Dynamic interference in strong-field multiphoton excitation and ionization, Phys. Rev. A 106, 063103 (2022).
  28. P. V. Demekhin and L. S. Cederbaum, Dynamic interference of photoelectrons produced by high-frequency laser pulses, Phys. Rev. Lett. 108, 253001 (2012).
  29. M. Baghery, U. Saalmann, and J. M. Rost, Essential conditions for dynamic interference, Phys. Rev. Lett. 118, 143202 (2017).
  30. Q.-C. Ning, U. Saalmann, and J. M. Rost, Electron dynamics driven by light-pulse derivatives, Phys. Rev. Lett. 120, 033203 (2018).
  31. S. Hu, X. Yi, L. Guo, C. Bi, and J. Chen, Atomic Rydberg-state excitation in strong spatially inhomogeneous fields, Phys. Rev. A 107, 033104 (2023).
  32. H. Bachau, E. Cormier, P. Decleva, J. E. Hansen, and F. Martín, Applications of B-splines in atomic and molecular physics, Rep. Prog. Phys. 64, 1815 (2001).
  33. J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Adv. Comput. Math. 6, 207 (1996).
  34. F. J. Dyson, The radiation theories of Tomonaga, Schwinger, and Feynman, Phys. Rev. 75, 486 (1949).
  35. F. J. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75, 1736 (1949).
  36. If the field A(t) is of infinite extent, the sum of all contributions yields a δ-function spectrum with its peaks occurring when Up+En+Ip=kω with any integer k.
  37. T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, Giant Rydberg excitons in the copper oxide Cu2O, Nature (London) 514, 343 (2014).
  38. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2, Phys. Rev. Lett. 113, 076802 (2014).
  39. Q. Hu, Z. Zhan, H. Cui, Y. Zhang, F. Jin, X. Zhao, M. Zhang, Z. Wang, Q. Zhang, K. Watanabe, T. Taniguchi, X. Cao, W.-M. Liu, F. Wu, S. Yuan, and Y. Xu, Observation of Rydberg moiré excitons, Science 380, 1367 (2023).
  40. Q. Shang, K. Dini, H. Jiang, N. W. E. Seet, X. Cai, S. Ru, X. Lu, W. C. Yu, J. Zhao, Q. Xiong, T. C. H. Liew, J. Zúñiga-Pérez, and W. Gao, On-chip photonic crystal dressed Rydberg exciton polaritons with enhanced nonlinearity in monolayer WS2, Nat. Commun. 16, 10352 (2025).

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Phys. Rev. Research 8, 013090– Published 27 January, 2026
  • Received 17 November 2025
  • Accepted 8 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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