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  • Letter
  • Open Access

Electronic-vibrational dynamics and coherence in x-ray transient absorption of N2+ induced by strong-field ionization

Jing Zhao1,*, Guangru Bai1, Qian Zhang1, Bin Zhang1, Wenkai Tao1, Qianyu Qiu1, Hongbin Lei1, Yue Lang1, Jinlei Liu1 et al.

Xiaowei Wang1 and Zengxiu Zhao1,2,†

  • *Contact author: jzhao@nudt.edu.cn
  • †Contact author: zhaozengxiu@nudt.edu.cn
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Phys. Rev. Research 7, L012070 – Published 14 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012070

Abstract

Attosecond transient absorption spectroscopy (ATAS) is becoming an indispensable and powerful tool in the emerging field of attochemistry, while the interpretation of measurements often requires full considerations of the coupling among various freedoms of motion. Here we develop the ionization-coupling model to incorporate the transient absorption and explore the coupled electronic-vibrational dynamics of nitrogen ions induced by strong-field ionization. It is found the coherent vibrational wave packet on the involved electronic state is created with a broad distribution of vibrational levels, which leads to the spectral overlap on the K-edge absorption. By identifying the contributions of each electronic state, the study reveals the significant role of the excited state A2Πu, differing from previous work by K-edge absorption measurements [Phys. Rev. Lett. 129, 123002 (2022)]. We uncover features of absorption from forbidden transitions within the laser pulse duration and confirm the vibronic coherence-induced quantum beating of absorption. A scheme is proposed to avoid the spectral overlap and determine the population distribution among the states, which is crucial to resolve the debate on nitrogen air lasing. This work lays down the framework to research the ionic coherence in ATAS and offers valuable insights into the intricate interplay between electronic and vibrational dynamics.

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References (52)

  1. Z. Yin, Y.-P. Chang, T. Balčiūnas, Y. Shakya, A. Djorović, G. Gaulier, G. Fazio, R. Santra, L. Inhester, J.-P. Wolf, and H. J. Wörner, Femtosecond proton transfer in urea solutions probed by x-ray spectroscopy, Nature (London) 619, 749 (2023).
  2. E. Ridente, D. Hait, E. A. Haugen, A. D. Ross, D. M. Neumark, M. Head-Gordon, and S. R. Leone, Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy, Science 380, 713 (2023).
  3. D. T. Matselyukh, V. Despré, N. V. Golubev, A. I. Kuleff, and H. J. Wörner, Decoherence and revival in attosecond charge migration driven by non-adiabatic dynamics, Nat. Phys. 18, 1206 (2022).
  4. K. S. Zinchenko, F. Ardana-Lamas, I. Seidu, S. P. Neville, J. van der Veen, V. U. Lanfaloni, M. S. Schuurman, and H. J. Wörner, Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge, Science 371, 489 (2021).
  5. Y. Kobayashi, K. F. Chang, T. Zeng, D. M. Neumark, and S. R. Leone, Direct mapping of curve-crossing dynamics in IBr by attosecond transient absorption spectroscopy, Science 365, 79 (2019).
  6. M. Han, J. Fedyk, J.-B. Ji, V. Despré, A. I. Kuleff, and H. J. Wörner, Observation of nuclear wave-packet interference in ultrafast interatomic energy transfer, Phys. Rev. Lett. 130, 253202 (2023).
  7. A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, High-gain backward lasing in air, Science 331, 442 (2011).
  8. J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, High-brightness switchable multiwavelength remote laser in air, Phys. Rev. A 84, 051802(R) (2011).
  9. H. Lei, J. Yao, J. Zhao, H. Xie, F. Zhang, H. Zhang, N. Zhang, G. Li, Q. Zhang, X. Wang, Y. Yang, L. Yuan, Y. Cheng, and Z. Zhao, Ultraviolet supercontinuum generation driven by ionic coherence in a strong laser field, Nat. Commun. 13, 4080 (2022).
  10. E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, Real-time observation of valence electron motion, Nature (London) 466, 739 (2010).
  11. M. Sabbar, H. Timmers, Y.-J. Chen, A. K. Pymer, Z.-H. Loh, S. G. Sayres, S. Pabst, R. Santra, and S. R. Leone, State-resolved attosecond reversible and irreversible dynamics in strong optical fields, Nat. Phys. 13, 472 (2017).
  12. N. Saito, H. Sannohe, N. Ishii, T. Kanai, N. Kosugi, Y. Wu, A. Chew, S. Han, Z. Chang, and J. Itatani, Real-time observation of electronic, vibrational, and rotational dynamics in nitric oxide with attosecond soft x-ray pulses at 400 eV, Optica 6, 1542 (2019).
  13. O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, and M. Y. Ivanov, Strong-field control and spectroscopy of attosecond electron-hole dynamics in molecules, Proc. Natl. Acad. Sci. USA 106, 16556 (2009).
  14. N. Rohringer and R. Santra, Multichannel coherence in strong-field ionization, Phys. Rev. A 79, 053402 (2009).
  15. S. Pabst, A. Sytcheva, A. Moulet, A. Wirth, E. Goulielmakis, and R. Santra, Theory of attosecond transient-absorption spectroscopy of krypton for overlapping pump and probe pulses, Phys. Rev. A 86, 063411 (2012).
  16. Q. Zhang, H. Xie, G. Li, X. Wang, H. Lei, J. Zhao, Z. Chen, J. Yao, Y. Cheng, and Z. Zhao, Sub-cycle coherent control of ionic dynamics via transient ionization injection, Commun. Phys. 3, 50 (2020).
  17. L. Wang, G. Bai, X. Wang, J. Zhao, C. Gao, J. Wang, F. Xiao, W. Tao, P. Song, Q. Qiu, J. Liu, and Z. Zhao, Raman time-delay in attosecond transient absorption of strong-field created krypton vacancy, Nat. Commun. 15, 2705 (2024).
  18. J. Yao, S. Jiang, W. Chu, B. Zeng, C. Wu, R. Lu, Z. Li, H. Xie, G. Li, C. Yu, Z. Wang, H. Jiang, Q. Gong, and Y. Cheng, Population redistribution among multiple electronic states of molecular nitrogen ions in strong laser fields, Phys. Rev. Lett. 116, 143007 (2016).
  19. H. Xu, E. Lötstedt, A. Iwasaki, and K. Yamanouchi, Sub-10-fs population inversion in N2+ in air lasing through multiple state coupling, Nat. Commun. 6, 8347 (2015).
  20. Y. Liu, P. Ding, G. Lambert, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, Recollision-induced superradiance of ionized nitrogen molecules, Phys. Rev. Lett. 115, 133203 (2015).
  21. M. Britton, P. Laferrière, D. H. Ko, Z. Li, F. Kong, G. Brown, A. Naumov, C. Zhang, L. Arissian, and P. B. Corkum, Testing the role of recollision in N2+ air lasing, Phys. Rev. Lett. 120, 133208 (2018).
  22. H. Li, E. Lötstedt, H. Li, Y. Zhou, N. Dong, L. Deng, P. Lu, T. Ando, A. Iwasaki, Y. Fu, S. Wang, J. Wu, K. Yamanouchi, and H. Xu, Giant enhancement of air lasing by complete population inversion in N2+, Phys. Rev. Lett. 125, 053201 (2020).
  23. A. Mysyrowicz, R. Danylo, A. Houard, V. Tikhonchuk, X. Zhang, Z. Fan, Q. Liang, S. Zhuang, L. Yuan, and Y. Liu, Lasing without population inversion in N2+, APL Photon. 4, 110807 (2019).
  24. L. Arissian, B. Kamer, A. Rastegari, D. M. Villeneuve, and J.-C. Diels, Transient gain from N2+ in light filaments, Phys. Rev. A 98, 053438 (2018).
  25. M. Richter, M. Lytova, F. Morales, S. Haessler, O. Smirnova, M. Spanner, and M. Ivanov, Rotational quantum beat lasing without inversion, Optica 7, 586 (2020).
  26. H. Xie, H. Lei, G. Li, Q. Zhang, X. Wang, J. Zhao, Z. Chen, J. Yao, Y. Cheng, and Z. Zhao, Role of rotational coherence in femtosecond-pulse-driven nitrogen ion lasing, Phys. Rev. Res. 2, 023329 (2020).
  27. Y. Zhang, E. Lötstedt, T. Ando, A. Iwasaki, H. Xu, and K. Yamanouchi, Rotational population transfer through the a2Πu−x2Σg+−b2Σu+ coupling in N2+ lasing, Phys. Rev. A 104, 023107 (2021).
  28. T. Ando, E. Lötstedt, A. Iwasaki, H. Li, Y. Fu, S. Wang, H. Xu, and K. Yamanouchi, Rotational, vibrational, and electronic modulations in N2+ lasing at 391 nm: Evidence of coherent b2Σu+−x2Σg+−a2Πu coupling, Phys. Rev. Lett. 123, 203201 (2019).
  29. V. T. Tikhonchuk, Y. Liu, R. Danylo, A. Houard, and A. Mysyrowicz, Theory of femtosecond strong field ion excitation and subsequent lasing in N2+, New J. Phys. 23, 023035 (2021).
  30. N. V. Golubev, J. Vaníček, and A. I. Kuleff, Core-valence attosecond transient absorption spectroscopy of polyatomic molecules, Phys. Rev. Lett. 127, 123001 (2021).
  31. A. Magunia, M. Rebholz, E. Appi, C. C. Papadopoulou, H. Lindenblatt, F. Trost, S. Meister, T. Ding, M. Straub, G. D. Borisova, J. Lee, R. Jin, A. von der Dellen, C. Kaiser, M. Braune, S. Düsterer, S. Ališauskas, T. Lang, C. Heyl, B. Manschwetus et al., Time-resolving state-specific molecular dissociation with XUV broadband absorption spectroscopy, Sci. Adv. 9, eadk1482 (2023).
  32. C. Kleine, M.-O. Winghart, Z.-Y. Zhang, M. Richter, M. Ekimova, S. Eckert, M. J. J. Vrakking, E. T. J. Nibbering, A. Rouzée, and E. R. Grant, Electronic state population dynamics upon ultrafast strong field ionization and fragmentation of molecular nitrogen, Phys. Rev. Lett. 129, 123002 (2022).
  33. F. Calegari, G. Sansone, S. Stagira, C. Vozzi, and M. Nisoli, Advances in attosecond science, J. Phys. B: At. Mol. Opt. Phys. 49, 062001 (2016).
  34. M. Nisoli, The birth of attochemistry, Opt. Photon. News 30, 32 (2019).
  35. Y. Kobayashi and S. R. Leone, Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy, J. Chem. Phys. 157, 180901 (2022).
  36. X. M. Tong, Z. X. Zhao, and C. D. Lin, Theory of molecular tunneling ionization, Phys. Rev. A 66, 033402 (2002).
  37. B. Zhang and Z. Zhao, SLIMP: Strong laser interaction model package for atoms and molecules, Comput. Phys. Commun. 192, 330 (2015).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012070 for the details of the ionization-coupling model, potential-energy curves, XAS pulse width dependence, angle-resolved absorption spectra, and polarization scheme for probing electronic populations in pre-aligned molecules, which includes Refs. [51, 52].
  39. A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, Synthesized light transients, Science 334, 195 (2011).
  40. R. Santra, V. S. Yakovlev, T. Pfeifer, and Z.-H. Loh, Theory of attosecond transient absorption spectroscopy of strong-field-generated ions, Phys. Rev. A 83, 033405 (2011).
  41. L. O. Werme, B. Grennberg, J. Nordgren, C. Nordling, and K. Siegbahn, Fine structure in the x-ray emission spectrum of N2, compared with electron spectroscopy, Nature (London) 242, 453 (1973).
  42. M. Ehara, H. Nakatsuji, M. Matsumoto, T. Hatamoto, X.-J. Liu, T. Lischke, G. Prümper, T. Tanaka, C. Makochekanwa, M. Hoshino, H. Tanaka, J. R. Harries, Y. Tamenori, and K. Ueda, Symmetry-dependent vibrational excitation in N 1s photoionization of N2: Experiment and theory, J. Chem. Phys. 124, 124311 (2006).
  43. R. Lindblad, L. Kjellsson, R. C. Couto, M. Timm, C. Bülow, V. Zamudio-Bayer, M. Lundberg, B. von Issendorff, J. T. Lau, S. L. Sorensen, V. Carravetta, H. Ågren, and J.-E. Rubensson, X-ray absorption spectrum of the N2+ molecular ion, Phys. Rev. Lett. 124, 203001 (2020).
  44. Z. Wei, J. Li, L. Wang, S. T. See, M. H. Jhon, Y. Zhang, F. Shi, M. Yang, and Z.-H. Loh, Elucidating the origins of multimode vibrational coherences of polyatomic molecules induced by intense laser fields, Nat. Commun. 8, 735 (2017).
  45. J. Bakos, AC Stark effect and multiphoton processes in atoms, Phys. Rep. 31, 209 (1977).
  46. M. Chini, X. Wang, Y. Cheng, Y. Wu, D. Zhao, D. A. Telnov, S.-I. Chu, and Z. Chang, Sub-cycle oscillations in virtual states brought to light, Sci. Rep. 3, 1105 (2013).
  47. S. Zhou, C. Bao, B. Fan, H. Zhou, Q. Gao, H. Zhong, T. Lin, H. Liu, P. Yu, P. Tang, S. Meng, W. Duan, and S. Zhou, Pseudospin-selective Floquet band engineering in black phosphorus, Nature (London) 614, 75 (2023).
  48. F. Lépine, M. Y. Ivanov, and M. J. J. Vrakking, Attosecond molecular dynamics: Fact or fiction? Nat. Photon. 8, 195 (2014).
  49. T. Driver, M. Mountney, J. Wang, L. Ortmann, A. Al-Haddad, N. Berrah, C. Bostedt, E. G. Champenois, L. F. DiMauro, J. Duris, D. Garratt, J. M. Glownia, Z. Guo, D. Haxton, E. Isele, I. Ivanov, J. Ji, A. Kamalov, S. Li, M.-F. Lin et al., Attosecond delays in x-ray molecular ionization, Nature (London) 632, 762 (2024).
  50. H. J. B. Marroux, A. P. Fidler, A. Ghosh, Y. Kobayashi, K. Gokhberg, A. I. Kuleff, S. R. Leone, and D. M. Neumark, Attosecond spectroscopy reveals alignment dependent core-hole dynamics in the ICl molecule, Nat. Commun. 11, 5810 (2020).
  51. B. Kempgens, A. Kivimäki, M. Neeb, H. M. Köppe, A. M. Bradshaw, and J. Feldhaus, A high-resolution N 1s photoionization study of the N2 molecule in the near-threshold region, J. Phys. B: At. Mol. Opt. Phys. 29, 5389 (1996).
  52. T. Seideman, Rotational excitation and molecular alignment in intense laser fields, J. Chem. Phys. 103, 7887 (1995).

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Phys. Rev. Research 7, L012070– Published 14 March, 2025
  • Received 21 September 2023
  • Revised 28 August 2024
  • Accepted 7 February 2025
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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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