Identifying the contributions of multiple-returning recollision orbits in strong-field above-threshold ionization

  • Jia Tan
  • Yang Li
  • Yueming Zhou
  • Mingrui He
  • Yinbo Chen
  • Min Li
  • Peixiang Lu
Article

Abstract

We calculate the photoelectron momentum distributions (PMDs) from strong-field above-threshold ionization of Ar in the co-linearly polarized two-color laser fields consisting a strong fundamental component and a much weaker second harmonic by solving the time-dependent Schrödinger equation. Utilizing the recently introduced phase-of-the-phase (PP) spectroscopy, we analyze the relative phase dependence of the PMDs of the recollision electrons and the jumps in the PP spectroscopy are observed. With the semi-classical model, we demonstrate that the phase jumps originate from the competition between the orbits where recollision occurs at different returnings. Thus, the relative contribution of the multiple-returning recollision orbits is unambiguously identified with the PP spectroscopy. Additionally, we show that the relative contribution of the multiple-returning recollision orbits depends on the laser wavelength and ellipticity. In elliptically polarized laser field, the yield of the high-energy photoelectrons favors the contribution of the second-returning recollision orbits. In 1600-nm laser field, the PP spectroscopy indicates that the relative contribution of multiple-returning recollision orbits is strongly sensitive to the electron energy.

Keywords

Above-threshold ionization Strong laser field Photoionization of atoms and ions 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NNSFC) under Grant Nos. 11604108, 11234004, and 11622431. Numerical simulations presented in this paper were carried out using the High Performance Computing Center experimental testbed in SCTS/CGCL.

References

  1. Almajid, M.A., Zabel, M., Skruszewicz, S., Tiggesbäumker, J., Bauer, D.: Two-color phase-of-the-phase spectroscopy in the multiphoton regime. J. Phys. B 50, 194001 (2017)ADSCrossRefGoogle Scholar
  2. Ammosov, M. V., Delone, N. B., Kraǐnov, V. P.: Tunneling ionization of complex atoms and of atomic ions in an alternating electromagnetic field. Z. Eksp. T. Fiz. 91, 2008 (1986) [Sov. Phys. JETP 64, 1191–1194 (1986)] Google Scholar
  3. Bandrauk, A.D., Chelkowski, S.: LIED: laser induced electron diffraction by intense lasermolecule interactionan exact non-bornoppenheimer simulation of the one-electron system: H\(_2^+\). J. Mol. Struct. (Theochem) 591, 199–205 (2002)CrossRefGoogle Scholar
  4. Becker, W., Grasbon, F., Kopold, R., Milošević, D.B., Paulus, G.G., Walther, H.: Above-threshold ionization: from classical features to quantum effects. Adv. At. Mol. Opt. Phys. 48, 35–98 (2002)ADSCrossRefGoogle Scholar
  5. Blaga, C.I., Xu, J., DiChiara, A.D., Sistrunk, E., Zhang, K., Agostini, P., Miller, T.A., DiMauro, L.F., Lin, C.D.: Imaging ultrafast molecular dynamics with laser-induced electron diffraction. Nature 483, 194–197 (2012)ADSCrossRefGoogle Scholar
  6. Bondar, D.I., Yudin, G.L., Liu, W.K., Ivanov, M.Y., Bandrauk, A.D.: Nonsequential double ionization below laser-intensity threshold: anticorrelation of electrons without excitation of parent ion. Phys. Rev. A 83, 013420 (2011)ADSCrossRefGoogle Scholar
  7. Chelkowski, S., Foisy, C., Bandrauk, A.D.: Electron-nuclear dynamics of multiphoton H\(_2^{+}\) dissociative ionization in intense laser fields. Phys. Rev. A 57, 1176–1185 (1998)ADSCrossRefGoogle Scholar
  8. Delone, N.B., Krainov, V.P.: Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation. J. Opt. Soc. Am. B 8, 1207–1211 (1991)ADSCrossRefGoogle Scholar
  9. Dudovich, N., Smirnova, O., Levesque, J., Mairesse, Y., Ivanov, M.Y., Villeneuve, D.M., Corkum, P.B.: Measuring and controlling the birth of attosecond XUV pulses. Nat. Phys. 2, 781–786 (2006)CrossRefGoogle Scholar
  10. Feit, M.D., Fleck, J.A., Steiger, A., Comput, J.: Solution of the Schrödinger equation by a spectral method. Physics 47, 412–433 (1982)MathSciNetMATHGoogle Scholar
  11. Ferray, M., L’Huillier, A., Li, X.F., Lompré, L.A., Mainfray, G., Manus, C.: Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31–L35 (1988)ADSCrossRefGoogle Scholar
  12. He, P., Takemoto, N., He, F.: Photoelectron momentum distributions of atomic and molecular systems in strong circularly or elliptically polarized laser fields. Phys. Rev. A 91, 063413 (2015)ADSCrossRefGoogle Scholar
  13. He, M., Li, Y., Zhou, Y., Li, M., Lu, P.: Temporal and spatial manipulation of the recolliding wave packet in strong-field photoelectron holography. Phys. Rev. A 93, 033406 (2016)ADSCrossRefGoogle Scholar
  14. He, M., Zhou, Y., Li, Y., Li, M., Lu, P.: Revealing the target structure information encoded in strong-field photoelectron hologram. Opt. Quant. Electron. 49, 232 (2017)CrossRefGoogle Scholar
  15. Hernández-García, C., et al.: Zeptosecond high harmonic keV X-ray waveforms driven by midinfrared laser pulses. Phys. Rev. Lett. 111, 033002 (2013)ADSCrossRefGoogle Scholar
  16. Hickstein, D.D., et al.: Direct visualization of laser-driven electron multiple scattering and tunneling distance in strong-field ionization. Phys. Rev. Lett. 109, 073004 (2012)ADSCrossRefGoogle Scholar
  17. Huismans, Y., et al.: Time-resolved holography with photoelectrons. Science 331, 61–64 (2011)ADSCrossRefGoogle Scholar
  18. Huismans, Y., et al.: Scaling laws for photoelectron holography in the midinfrared wavelength regime. Phys. Rev. Lett. 109, 013002 (2012)ADSCrossRefGoogle Scholar
  19. Itatani, J., Levesque, J., Zeidler, D., Niikura, H., Pépin, H., Kieffer, J.C., Corkum, P.B., Villeneuve, D.M.: Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004)ADSCrossRefGoogle Scholar
  20. Kang, H., et al.: Structure effects in angle-resolved high-order above-threshold ionization of molecules. Phys. Rev. Lett. 104, 203001 (2010)ADSCrossRefGoogle Scholar
  21. Ke, S., Wang, B., Long, H., Wang, K., Lu, P.: Topological mode switching in a graphene doublet with exceptional points. Opt. Quant. Electron. 49, 224 (2017)Google Scholar
  22. Kopold, R., Milošević, D.B., Becker, W.: Rescattering processes for elliptical polarization: a quantum trajectory analysis. Phys. Rev. Lett. 84, 3831–3834 (2000)ADSCrossRefGoogle Scholar
  23. Krausz, F., Ivanov, M.: Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009)ADSCrossRefGoogle Scholar
  24. Lai, X., Wang, C., Chen, Y., Hu, Z., Quan, W., Liu, X., Chen, J., Cheng, Y., Xu, Z., Becker, W.: Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases. Phys. Rev. Lett. 110, 043002 (2013)ADSCrossRefGoogle Scholar
  25. Li, Y., Zhu, X., Lan, P., Zhang, Q., Qin, M., Lu, P.: Molecular-orbital tomography beyond the plane-wave approximation. Phys. Rev. A 89, 045401 (2014)ADSCrossRefGoogle Scholar
  26. Li, Y., Li, M., Zhou, Y., Ma, X., Xie, H., Lan, P., Lu, P.: Carrier-envelope phase dependent photoelectron energy spectra in low intensity regime. Opt. Express 25, 11233–11243 (2017)Google Scholar
  27. Liu, X., Zhu, X., Li, L., Li, Y., Zhang, Q., Lan, P., Lu, P.: Selection rules of high-order-harmonic generation: symmetries of molecules and laser fields. Phys. Rev. A 94, 033410 (2016)ADSCrossRefGoogle Scholar
  28. Liu, X., Zhu, X., Lan, P., Zhang, X., Wang, D., Zhang, Q., Lu, P.: Time-dependent population imaging for high-order-harmonic generation in solids. Phys. Rev. A 95, 063419 (2017)Google Scholar
  29. Ma, X., Zhou, Y., Lu, P.: Multiple recollisions in strong-field nonsequential double ionization. Phys. Rev. A 93, 013425 (2016)ADSCrossRefGoogle Scholar
  30. Ma, X., Li, M., Zhou, Y., Lu, P.: Nonsequential double ionization of Xe by mid-infrared laser pulses. Opt. Quant. Electron. 49, 170 (2017)CrossRefGoogle Scholar
  31. Mauger, F., Chandre, C., Uzer, T.: Recollisions and correlated double ionization with circularly polarized light. Phys. Rev. Lett. 105, 083002 (2010)ADSCrossRefGoogle Scholar
  32. Meckel, M., et al.: Laser-induced electron tunneling and diffraction. Science 320, 1478–1482 (2008)ADSCrossRefGoogle Scholar
  33. Meckel, M., Staudte, A., Patchkovskii, S., Villeneuve, D.M., Corkum, P.B., Dörner, R., Spanner, M.: Signatures of the continuum electron phase in molecular strong-field photoelectron holography. Nat. Phys. 10, 594–600 (2014)CrossRefGoogle Scholar
  34. Mercer, I., Mevel, E., Zerne, R., L’Huillier, A., Antoine, P., Wahlström, C.G.: Spatial mode control of high-order harmonics. Phys. Rev. Lett. 77, 1731–1734 (1996)ADSCrossRefGoogle Scholar
  35. Milošević, D.B., Paulus, G.G., Bauer, D., Becker, W.: Above-threshold ionization by few-cycle pulses. J. Phys. B 39, R203 (2006)CrossRefGoogle Scholar
  36. Möller, M., Meyer, F., Sayler, A.M., Paulus, G.G., Kling, M.F., Schmidt, B.E., Becker, W., Milošević, D.B.: Off-axis low-energy structures in above-threshold ionization. Phys. Rev. A 90, 023412 (2014)ADSCrossRefGoogle Scholar
  37. Okunishi, M., Morishita, T., Prümper, G., Shimada, K., Lin, C.D., Watanabe, S., Ueda, K.: Experimental retrieval of target structure information from laser-induced rescattered photoelectron momentum distributions. Phys. Rev. Lett. 110, 143001 (2008)ADSCrossRefGoogle Scholar
  38. Paulus, G.G., Nicklich, W., Xu, H., Lambropoulos, P., Walther, H.: Plateau in above threshold ionization spectra. Phys. Rev. Lett. 72, 2851 (1994)ADSCrossRefGoogle Scholar
  39. Protopapas, M., Keitel, C.H., Knight, P.L.: Atomic physics with super-high intensity lasers. Rep. Prog. Phys. 60, 389–486 (1997)ADSCrossRefGoogle Scholar
  40. Ray, D., et al.: Large-angle electron diffraction structure in laser-induced rescattering from rare gases. Phys. Rev. Lett. 100, 143002 (2008)ADSCrossRefGoogle Scholar
  41. Rezvani, S. A., Hong, Z., Pang, X., Wu, S., Zhang, Q., Lu, P.: Ultrabroadband tunable OPA design using a spectrally broadened pump source. Opt. lett. 42, 3367–3370 (2017)Google Scholar
  42. Salières, P., et al.: Feynman’s path-integral approach for intense-laser-atom interactions. Science 292, 902–905 (2001)ADSCrossRefGoogle Scholar
  43. Skruszewicz, S., Tiggesbäumker, J., Meiwes-Broes, K.H., Arbeiter, M., Fennel, T, Bauer, D.: Two-color strong-field photoelectron spectroscopy and the phase of the phase. Phys. Rev. Lett. 115, 043001 (2015)ADSCrossRefGoogle Scholar
  44. Spanner, M., Smirnova, O., Corkum, P.B., Ianov, M.Y.: Reading diffraction images in strong field ionization of diatomic molecules. J. Phys. B 37, L243–L250 (2004)ADSCrossRefGoogle Scholar
  45. Tong, A., Zhou, Y., Lu, P.: Bifurcation of ion momentum distributions in sequential double ionization by elliptically polarized laser pulses. Opt. Quant. Electron. 49, 77 (2017)CrossRefGoogle Scholar
  46. Tong, X., Hino, K., Toshima, N.: Phase-dependent atomic ionization in few-cycle intense laser fields. Phys. Rev. A 74, 031405 (2006)ADSCrossRefGoogle Scholar
  47. Tong, X., Watahiki, S., Hino, K., Toshima, N.: Numerical observation of the rescattering wave packet in laser-atom interactions. Phys. Rev. Lett. 99, 093001 (2007)ADSCrossRefGoogle Scholar
  48. Walker, B., Sheehy, B., DiMauro, L.F., Agostini, P., Schafer, K.J., Kulander, K.C.: Precision measurement of strong field double ionization of helium. Phys. Rev. Lett. 73, 1227–1230 (1994)ADSCrossRefGoogle Scholar
  49. Walt, S.G., et al.: Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering. Nat. Commun. 8, 15651 (2017)ADSCrossRefGoogle Scholar
  50. Wang, C., et al.: Extraction of electronion differential scattering cross sections for C\(_2\)H\(_4\) by laser-induced rescattering photoelectron spectroscopy. J. Phys. B 45, 131001 (2012)ADSCrossRefGoogle Scholar
  51. Wang, Z., Li, M., Zhou, Y., Lan, P., Lu, P.: Correlated electron-nuclear dynamics in above-threshold multiphoton ionization of asymmetric molecule. Sci. Rep. 7, 42585 (2017a)ADSCrossRefGoogle Scholar
  52. Wang, S., Wang, B., Qin, C., Wang, K., Long, H., Lu, P.: Rabi oscillations of optical modes in a waveguide with dynamic modulation. Opt. Quant. Electron. 49, 389 (2017b)Google Scholar
  53. Wörner, H.J., Niikura, H., Bertrand, J.B., Corkum, P.B., Villeneuve, D.M.: Observation of electronic structure minima in high-harmonic generation. Phys. Rev. Lett. 102, 103901 (2009)ADSCrossRefGoogle Scholar
  54. Xie, H., Li, M., Zhou, Y., Lu, P.: Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields. Opt. Express 24, 27726–27737 (2016)ADSCrossRefGoogle Scholar
  55. Yu, J., Sun, X., Shao, Y., Li, M., Gong, Q., Liu, Y.: Retrieving the ionization dynamics of high-energy photoelectrons in elliptically polarized laser fields. Phys. Rev. A 92, 043411 (2015)ADSCrossRefGoogle Scholar
  56. Zherebtsov, S., et al.: Carrierenvelope phase-tagged imaging of the controlled electron acceleration from SiO\(_2\) nanospheres in intense few-cycle laser fields. New J. Phys. 14, 075010 (2012)ADSCrossRefGoogle Scholar
  57. Zhou, Y., Huang, C., Lu, P.: Coulomb-tail effect of electron-electron interaction on nonsequential double ionization. Phys. Rev. A 84, 023405 (2011)ADSCrossRefGoogle Scholar
  58. Zhou, Y., Li, M., Li, Y., Tong, A., Li, Q., Lu, P.: Dissection of electron correlation in strong-field sequential double ionization using a classical mode. Opt. Express 25, 8450–8458 (2017)ADSCrossRefGoogle Scholar
  59. Zhou, Y., Tolstikhin, O.I., Morishita, T.: Near-forward rescattering photoelectron holography in strong-field ionization: extraction of the phase of the scattering amplitude. Phys. Rev. Lett. 116, 173001 (2016)ADSCrossRefGoogle Scholar
  60. Zuo, T., Bandrauk, A.D., Corkum, P.B.: Laser-induced electron diffraction: a new tool for probing ultrafast molecular dynamics. Chem. Phys. Lett. 259, 313–320 (1996)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jia Tan
    • 1
  • Yang Li
    • 1
  • Yueming Zhou
    • 1
  • Mingrui He
    • 1
  • Yinbo Chen
    • 1
  • Min Li
    • 1
  • Peixiang Lu
    • 1
    • 2
  1. 1.School of PhysicsHuazhong University of Science and TechnologyWuhanPeople’s Republic of China
  2. 2.Laboratory of Optical Information TechnologyWuhan Institute of TechnologyWuhanPeople’s Republic of China

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