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Attosecond photoelectron interferometry of resonant structures between the Ar spin-orbit-split thresholds

J. K. Wood1, C. Marante2, D. Biswas3, L. Argenti2,*, and A. Sandhu4,†

  • *Contact author: luca.argenti@ucf.edu
  • †Contact author: asandhu6@asu.edu
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Phys. Rev. Research 8, 033290 – Published 8 September, 2026

DOI: https://doi.org/10.1103/hz3c-jn2g

Abstract

Resolving the ultrafast decay of metastable electronic states into channels associated with spin-orbit-split ionization thresholds is a long-standing goal of attosecond photoelectron spectroscopy. Here, we use a variant of the rainbow reconstruction of attosecond beating by interference of two-photon transitions technique to study, experimentally and theoretically, the ultrafast dynamics, resolved in photoelectron energy and emission angle, of the autoionizing states comprised in the narrow 177 meV energy gap between the 3p−1 P3/2o2 and P1/2o2 thresholds in argon. The scheme employs three pulses: an XUV attosecond pulse train (pump), generated as odd harmonics of a fundamental IR frequency ω; a weak replica of the IR field (driver) that copropagates phase-locked with the pump; and a second IR pulse (probe) with controllable delay τ with respect to the pump. Two harmonics excite bound states below the P3/2o2 threshold and the continuum above the P1/2o2 threshold, and their overlapping sideband populates even-parity resonant states between the two thresholds, giving rise to resonant signals beating at both ω and 2ω. From the photoemission cross section and the β2 and β4 asymmetry parameters, we resolve both the nf and the np resonant series. In both theory and experiment, the relative weight of the ω and 2ω beatings changes significantly across the interthreshold gap, an evolution that we trace back to higher-order probe-photon processes. The resonant photoelectron emission is found to be strongly localized in small spots within the (β2,β4) region admissible for two-photon transitions.

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References (58)

  1. A. Plunkett, M. A. Alarcón, J. K. Wood, C. H. Greene, and A. Sandhu, Raman interferometry between autoionizing states to probe ultrafast wave-packet dynamics with high spectral resolution, Phys. Rev. Lett. 128, 083001 (2022).
  2. R. Forbes, V. Makhija, J. G. Underwood, A. Stolow, I. Wilkinson, P. Hockett, and R. Lausten, Quantum-beat photoelectron-imaging spectroscopy of Xe in the VUV, Phys. Rev. A 97, 063417 (2018).
  3. D. M. Villeneuve, P. Hockett, M. J. J. Vrakking, and H. Niikura, Coherent imaging of an attosecond electron wave packet, Science 356, 1150 (2017).
  4. L. D. Noordam and R. R. Jones, Probing Rydberg electron dynamics, J. Mod. Opt. 44, 2515 (1997).
  5. D. Hammerland, T. Berglitsch, P. Zhang, T. T. Luu, K. Ueda, R. R. Lucchese, and H. J. Wörner, Bond-length dependence of attosecond ionization delays in O2 arising from electron correlation to a shape resonance, Sci. Adv. 10, eadl3810 (2024).
  6. T. Okino, Y. Furukawa, Y. Nabekawa, S. Miyabe, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, Direct observation of an attosecond electron wave packet in a nitrogen molecule, Sci. Adv. 1, e1500356 (2015).
  7. A. González-Castrillo, F. Martín, and A. Palacios, Quantum state holography to reconstruct the molecular wave packet using an attosecond XUV-XUV pump-probe technique, Sci. Rep. 10, 12981 (2020).
  8. T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, Attosecond electron wave packet interferometry, Nat. Phys. 2, 323 (2006).
  9. K. Klünder, P. Johnsson, M. Swoboda, A. L’Huillier, G. Sansone, M. Nisoli, M. J. J. Vrakking, K. J. Schafer, and J. Mauritsson, Reconstruction of attosecond electron wave packets using quantum state holography, Phys. Rev. A 88, 033404 (2013).
  10. M. A. Alarcón, A. Plunkett, J. K. Wood, D. Biswas, C. H. Greene, and A. Sandhu, Quantum beats in two-color photoionization to the spin-orbit split continuum of Ar, Phys. Rev. A 108, 033107 (2023).
  11. N. Shivaram, H. Timmers, X.-M. Tong, and A. Sandhu, Attosecond-resolved evolution of a laser-dressed helium atom: Interfering excitation paths and quantum phases, Phys. Rev. Lett. 108, 193002 (2012).
  12. D. Busto, L. Barreau, M. Isinger, M. Turconi, C. Alexandridi, A. Harth, S. Zhong, R. J. Squibb, D. Kroon, S. Plogmaker, M. Miranda, Á. Jiménez-Galán, L. Argenti, C. L. Arnold, R. Feifel, F. Martín, M. Gisselbrecht, A. L’Huillier, and P. Salières, Time–frequency representation of autoionization dynamics in helium, J. Phys. B: At. Mol. Opt. Phys. 51, 044002 (2018).
  13. E. P. Månsson, D. Guénot, C. L. Arnold, D. Kroon, S. Kasper, J. M. Dahlström, E. Lindroth, A. S. Kheifets, A. L’Huillier, S. L. Sorensen, and M. Gisselbrecht, Double ionization probed on the attosecond timescale, Nat. Phys. 10, 207 (2014).
  14. J. Feist, S. Nagele, C. Ticknor, B. I. Schneider, L. A. Collins, and J. Burgdörfer, Attosecond two-photon interferometry for doubly excited states of helium, Phys. Rev. Lett. 107, 093005 (2011).
  15. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Observation of a train of attosecond pulses from high harmonic generation, Science 292, 1689 (2001).
  16. Á. Jiménez-Galán, L. Argenti, and F. Martín, Modulation of attosecond beating in resonant two-photon ionization, Phys. Rev. Lett. 113, 263001 (2014).
  17. A. Kheifets, Revealing the target electronic structure with under-threshold RABBITT, Atoms 9, 66 (2021).
  18. M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, Phase measurement of resonant two-photon ionization in helium, Phys. Rev. Lett. 104, 103003 (2010).
  19. A. S. Kheifets, Strongly resonant reconstruction of attosecond beating by interference of two-photon transitions on lithium, Phys. Rev. A 104, L021103 (2021).
  20. V. V. Serov and A. S. Kheifets, Continuous rainbow RABBITT investigation of resonant states in He and H2, J. Phys. B: At. Mol. Opt. Phys. 59, 105601 (2026).
  21. V. V. Serov and A. S. Kheifets, Rainbow RABBITT as a probe of coherent Rabi dynamics, arXiv:2606.10272.
  22. D. Hammerland, P. Zhang, A. Bray, C. Perry, S. Kuehn, P. Jojart, I. Seres, V. Zuba, Z. Varallyay, K. Osvay, et al., Effect of electron correlations on attosecond photoionization delays in the vicinity of the Cooper minima of argon, arXiv:1907.01219.
  23. C. Alexandridi, D. Platzer, L. Barreau, D. Busto, S. Zhong, M. Turconi, L. Neoričić, H. Laurell, C. Arnold, A. Borot, et al., Attosecond photoionization dynamics in the vicinity of the Cooper minima in argon, Phys. Rev. Res. 3, L012012 (2021).
  24. C. Cirelli, C. Marante, S. Heuser, C. Petersson, Á. J. Galán, L. Argenti, S. Zhong, D. Busto, M. Isinger, S. Nandi, et al., Anisotropic photoemission time delays close to a Fano resonance, Nat. Commun. 9, 955 (2018).
  25. S. Donsa, M. Ederer, R. Pazourek, J. Burgdörfer, and I. Březinová, Angle-resolved time delays for shake-up ionization of helium, Phys. Rev. A 102, 033112 (2020).
  26. F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
  27. A. Maquet, J. Caillat, and R. Taïeb, Attosecond delays in photoionization: Time and quantum mechanics, J. Phys. B: At. Mol. Opt. Phys. 47, 204004 (2014).
  28. L. Gallmann, I. Jordan, H. J. Wörner, L. Castiglioni, M. Hengsberger, J. Osterwalder, C. A. Arrell, M. Chergui, E. Liberatore, U. Rothlisberger, et al., Photoemission and photoionization time delays and rates, Struct. Dyn. 4, 061502 (2017).
  29. V. Gruson, L. Barreau, Á. Jiménez-Galan, F. Risoud, J. Caillat, A. Maquet, B. Carré, F. Lepetit, J.-F. Hergott, T. Ruchon, L. Argenti, R. Taïeb, F. Martín, and P. Salières, Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron, Science 354, 734 (2016).
  30. S. Luo, R. Weissenbilder, H. Laurell, R. Y. Bello, C. Marante, M. Ammitzböll, L. Neoričić, A. Ljungdahl, R. J. Squibb, R. Feifel, M. Gisselbrecht, C. L. Arnold, F. Martín, E. Lindroth, L. Argenti, D. Busto, and A. L’Huillier, Influence of final state interactions in attosecond photoelectron interferometry, Phys. Rev. Res. 6, 043271 (2024).
  31. M. Turconi, L. Barreau, D. Busto, M. Isinger, C. Alexandridi, A. Harth, R. J. Squibb, D. Kroon, C. L. Arnold, R. Feifel, M. Gisselbrecht, L. Argenti, F. Martín, A. L’Huillier, and P. Salières, Spin–orbit-resolved spectral phase measurements around a Fano resonance, J. Phys. B: At. Mol. Opt. Phys. 53, 184003 (2020).
  32. L. Neoričić, D. Busto, H. Laurell, R. Weissenbilder, M. Ammitzböll, S. Luo, J. Peschel, H. Wikmark, J. Lahl, S. Maclot, R. J. Squibb, S. Zhong, P. Eng-Johnsson, C. L. Arnold, R. Feifel, M. Gisselbrecht, E. Lindroth, and A. L’Huillier, Resonant two-photon ionization of helium atoms studied by attosecond interferometry, Front. Phys. 10, 964586 (2022).
  33. L. Drescher, T. Witting, O. Kornilov, and M. J. J. Vrakking, Phase dependence of resonant and antiresonant two-photon excitations, Phys. Rev. A 105, L011101 (2022).
  34. A. Autuori, D. Platzer, M. Lejman, G. Gallician, L. Maëder, A. Covolo, L. Bosse, M. Dalui, D. Bresteau, J.-F. Hergott, O. Tcherbakoff, H. J. B. Marroux, V. Loriot, F. Lépine, L. Poisson, R. Taïeb, J. Caillat, and P. Salières, Anisotropic dynamics of two-photon ionization: An attosecond movie of photoemission, Sci. Adv. 8, eabl7594 (2022).
  35. M. Moioli, M. M. Popova, K. R. Hamilton, D. Ertel, D. Busto, I. Makos, M. D. Kiselev, S. N. Yudin, H. Ahmadi, C. D. Schröter, T. Pfeifer, R. Moshammer, E. V. Gryzlova, A. N. Grum-Grzhimailo, K. Bartschat, and G. Sansone, Role of intermediate resonances in attosecond photoelectron interferometry in neon, Phys. Rev. Res. 7, 023034 (2025).
  36. M. Han, H. Liang, J.-B. Ji, L. C. Sum, K. Ueda, J. M. Rost, and H. J. Wörner, Interference control of Fano resonances and dynamical imaging of an electron wave packet, Ultrafast Sci. 5, 0091 (2025).
  37. S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, Attosecond angle-resolved photoelectron spectroscopy, Phys. Rev. Lett. 91, 223902 (2003).
  38. J. Joseph, F. Holzmeier, D. Bresteau, C. Spezzani, T. Ruchon, J. F. Hergott, O. Tcherbakoff, P. D’Oliveira, J. C. Houver, and D. Dowek, Angle-resolved studies of XUV–IR two-photon ionization in the RABBITT scheme, J. Phys. B: At. Mol. Opt. Phys. 53, 184007 (2020).
  39. D. Biswas, J. K. Wood, N. Chakraborty, A. S. Kheifets, and A. Sandhu, Spin-orbit and angle-resolved resonant attosecond photoionization delays, Phys. Rev. Res. 8, 023058 (2026).
  40. I. Cacelli, V. Carravetta, A. Rizzo, and R. Moccia, The calculation of photoionisation cross sections of simple polyatomic molecules by L2 methods, Phys. Rep. 205, 283 (1991).
  41. D. Hammerland, P. Zhang, S. Kühn, P. Jojart, I. Seres, V. Zuba, Z. Varallyay, D. Charalambidis, K. Osvay, T. T. Luu, et al., Reconstruction of attosecond pulses in the presence of interfering dressing fields using a 100 kHz laser system at ELI-ALPS, J. Phys. B: At. Mol. Opt. Phys. 52, 23LT01 (2019).
  42. D. H. Parker and A. T. J. B. Eppink, Photoelectron and photofragment velocity map imaging of state-selected molecular oxygen dissociation/ionization dynamics, J. Chem. Phys. 107, 2357 (1997).
  43. E. Champenois, CPBASEX, GitHub commit 00ef967, 2020, https://github.com/e-champenois/CPBASEX.
  44. G. A. Garcia, L. Nahon, and I. Powis, Two-dimensional charged particle image inversion using a polar basis function expansion, Rev. Sci. Instrum. 75, 4989 (2004).
  45. T. Carette, J. M. Dahlström, L. Argenti, and E. Lindroth, Multiconfigurational Hartree-Fock close-coupling ansatz: Application to the argon photoionization cross section and delays, Phys. Rev. A 87, 023420 (2013).
  46. L. Roantree, J. Wragg, H. van der Hart, and A. Brown, Energy- and angle-resolved spectral phases via semirelativistic ab initio RABBITT simulations, Phys. Rev. A 108, 023112 (2023).
  47. C. F. Fischer, Hartree-Fock Method for Atoms. A Numerical Approach (John Wiley and Sons, Inc., New York, 1977).
  48. A. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database (ver. 5.12), [Online], https://physics.nist.gov/asd [18 December 2025], National Institute of Standards and Technology, Gaithersburg, MD, 2024.
  49. S. Mehmood, E. Lindroth, and L. Argenti, Ionic coherence in resonant above-threshold attosecond ionization spectroscopy, Phys. Rev. A 107, 033103 (2023).
  50. Y.-Y. Lee, T.-Y. Dung, R.-M. Hsieh, J.-Y. Yuh, Y.-F. Song, G. H. Ho, T.-P. Huang, W.-C. Pan, I.-C. Chen, S.-Y. Tu, A. H. Kung, and L. C. Lee, Autoionizing Rydberg series (np′,nf′) of Ar investigated by stepwise excitations with lasers and synchrotron radiation, Phys. Rev. A 78, 022509 (2008).
  51. A. Jiménez-Galán, F. Martín, and L. Argenti, Two-photon finite-pulse model for resonant transitions in attosecond experiments, Phys. Rev. A 93, 023429 (2016).
  52. U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961).
  53. M. S. Child, Limits on the asymmetry parameters for two- and three-photon photofragmentation, Phys. Chem. Chem. Phys. 10, 6169 (2008).
  54. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific Publishing Co., Teaneck, NJ, 1987).
  55. C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences, revised ed. (Springer, New York, 2001), Vol. 27.
  56. 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).
  57. J. Muga, J. Palao, B. Navarro, and I. Egusquiza, Complex absorbing potentials, Phys. Rep. 395, 357 (2004).
  58. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Dover printing, 10th GPO printing ed. (Dover, New York, 1964).

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Phys. Rev. Research 8, 033290– Published 8 September, 2026
  • Received 27 June 2026
  • Accepted 18 August 2026
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