Abstract
By numerically solving the time-dependent Schrödinger equation, we theoretically investigate the holographic structure of the multiple-returning rescattering recorded in the photoelectron momentum distribution. In the orthogonally polarized two-color fields, we show that the interference patterns periodically oscillate with the relative phase. Tracing the relative phase where the oscillation minimizes, we find that the dependences of the phase on the parallel momentum for the first-returning and the second-returning rescattering holographic interferences are different. With the quantum-orbit model, we demonstrated that the difference is related to the ionization and rescattering times of the electron. Moreover, we show that the influence of the Coulomb interaction on the oscillation of both the first-returning rescattering and the second-returning rescattering holographic interferences can be ignored. This suggests us that the temporal characteristics of the electron can be resolved by analyzing the relative phase’s dependence of the multiple-returning holographic interference.
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References
Agueny, H., Hansen, J.: High-order photoelectron holography in the midinfrared-wavelength regime. Phys. Rev. A 98, 023414 (2018)
Arbó, D., Persson, E., Burgdörfer, J.: Time double-slit interferences in strong-field tunneling ionization. Phys. Rev. A 74, 063407 (2006)
Arbó, D., et al.: Interference of electron wave packets in atomic ionization by subcycle sculpted laser pulses. Phys. Rev. A 89, 043414 (2014)
Arbó, D., et al.: Ionization of argon by two-color laser pulses with coherent phase control. Phys. Rev. A 92, 023402 (2015)
Becker, W., Grabon, F., Kopold, R., Milošević, D., Paulus, G., Walther, H.: Above-threshold ionization: from classical features to quantum effect. Adv. At. Mol. Opt. Phys. 48, 35 (2002)
Bian, X., et al.: Subcycle interference dynamics of time-resolved photoelectron holography with midinfrared laser pulses. Phys. Rev. A 84, 043420 (2011)
Blaga, C., Catoire, F., Colosimo, P., Paulus, G., Muller, H., Agostini, P., DiMauro, L.: Strong-field photoionization revisited. Nat. Phys. 5, 335–338 (2009)
Corkum, P.: Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994 (1993)
Du, H., Wu, H., Wang, H., Yue, S., Hu, B.: Theoretical scheme for simultaneously observing forward-backward photoelectron holography. Opt. Lett. 41, 697–700 (2016)
Faisal, F.: Strong-field physics: ionization surprise. Nat. Phys. 5, 319–320 (2009)
Feit, M., Fleck, J., Steiger, A.: Solution of the schrödinger equation by a spectral method. J. Comput. Phys. 47, 412 (1982)
Ferray, M., et al.: Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B At. Mol. Opt. Phys. 21, L31 (1988)
Gaarde, M., Schafer, K.: Quantum path distributions for high-order harmonics in rare gas atoms. Phys. Rev. A 65, 031406 (2002)
Gabor, D.: A new microscopic principle. Nature 161, 777 (1948)
He, Y., He, L., Lan, P., Wang, B., Li, L., Zhu, X., Cao, W., Lu, P.: Molecular rotation movie filmed with high-harmonic generation. arXiv:1902.05662 [physics.optics] (2019)
He, L., Lan, P., Le, A., Wang, B., Wang, B., Zhu, X., Lu, P., Lin, C.: Real-time observation of molecular spinning with angular high-harmonic spectroscopy. Phys. Rev. Lett. 121, 163201 (2018a)
He, M., Li, Y., Zhou, Y., Li, M., Cao, W., Lu, P.: Direct visualization of valence electron motion using strong-field photoelectron holography. Phys. Rev. Lett. 120, 133204 (2018b)
Hickstein, D., et al.: Direct visualization of laser-driven electron multiple scattering and tunneling distance in strong-field ionization. Phys. Rev. Lett. 109, 073004 (2012)
Huismans, Y., et al.: Time-resolved holography with photoelectrons. Science 331, 61 (2011)
Huismans, Y., et al.: Scaling Laws for Photoelectron Holography in the midinfrared wavelength regime. Phys. Rev. Lett. 109, 013002 (2012)
Kang, H., et al.: Structure effects in angle-resolved high-order above-threshold ionization of molecules. Phys. Rev. Lett. 104, 203001 (2010)
Krause, J., Schafer, K., Kulander, K.: High-order harmonic generation from atoms and ions in the high intensity regime. Phys. Rev. Lett. 68, 3535 (1992)
Krausz, F., Ivanov, M.: Attosecond physics. Rev. Mod. Phys. 81, 163 (2009)
Lein, M.: Atomic physics: electrons get real. Nature 485, 313 (2012)
Li, X., Liu, W., Song, Y., Zhang, C., Long, H., Wang, K., Wang, B., Lu, P.: Enhancement of the Second Harmonic Generation from WS Monolayers by Cooperating with Dielectric Microspheres. Advanced Optical Materials 7, 1801270 (2018)
Li, M., Xie, H., Cao, W., Luo, S., Tan, J., Feng, Y., Du, B., Zhang, W., Li, Y., Zhang, Q., Lan, P., Zhou, Y., Lu P.: Photoelectron holographic interferometry to probe the longitudinal momentum offset at the tunnel exit. Phys. Rev. Lett. (accepted)
Li, L., Lan, P., Zhu, X., Huang, T., Zhang, Q., Lein, M., Lu, P.: Reciprocal-space-trajectory perspective on high harmonic generation in solids. arXiv:1809.08109 [physics.optics] (2019a)
Li, J., Zhang, Q., Li, L., Zhu, X., Huang, T., Lan, P., Lu, P.: Orientation dependence of high-order harmonic generation in nanowire. Phys. Rev. A 99, 033421 (2019b)
Lindner, F., et al.: Attosecond double-slit experiment. Phys. Rev. Lett. 95, 040401 (2005)
Liu, C., Hatsagortsyan, K.: Origin of unexpected low energy structure in photoelectron spectra induced by midinfrared strong laser fields. Phys. Rev. Lett. 105, 113003 (2010)
Liu, K., Luo, S., Li, M., Li, Y., Feng, Y., Du, B., Zhou, Y., Lu, P., Barth, I.: Detecting and characterizing the nonadiabaticity of laser-induced quantum tunneling. Phys. Rev. Lett. 122, 053202 (2019)
Ma, X., Zhou, Y., Li, N., Li, M., Lu, P.: Attosecond control of correlated electron dynamics in strong-field nonsequential double ionization by parallel two-color pulses. Opt. Laser Technol. 108, 235–240 (2018)
Ma, X., Zhou, Y., Chen, Y., Li, M., Li, Y., Zhang, Q., Lu, P.: Timing the release of the correlated electrons in strong-field nonsequential double ionization by circularly polarized two-color laser fields. Opt. Express 27(3), 1825–1837 (2019)
Marchenko, T., Huismans, Y., Schafer, K., Vrakking, M.: Criteria for the observation of strong-field photoelectron holography. Phys. Rev. A 84, 053427 (2011)
Meckel, M., Staudte, A., Patchkovskii, S., Villeneuve, D., Corkum, P., DÖrner, R., Spanner, M.: Signatures of the continuum electron phase in molecular strong-field photoelectron holography. Nat. Phys. 10, 594 (2014)
Paulus, G., Nicklich, W., Xu, H., Lambropoulos, P., Walther, H.: Plateau in above threshold ionization spectra. Phys. Rev. Lett. 72, 2851 (1994)
Qin, Y., Li, M., Li, Y., He, M., Luo, S., Liu, Y., Zhou, Y., Lu, P.: Asymmetry of the photoelectron momentum distribution from molecular ionization in elliptically polarized laser pulses. Phys. Rev. A 99, 013431 (2019)
Quan, W., et al.: Classical aspects in above-threshold ionization with a midinfrared strong laser field. Phys. Rev. Lett. 103, 093001 (2009)
Salières, P., et al.: Feynman’s path-integral approach for intense-laser-atom interactions. Science 292, 902–905 (2001)
Shar, D., Soifer, H., Bruner, B., Dagan, M., Mairesse, Y., Patchkovskii, S., Ivanov, M., Smirnova, O., Dudovich, N.: Resolving the time when an electron exits a tunneling barrier. Nature 484, 343 (2012)
Smirnova, O., et al.: High harmonic interferometry of multi-electron dynamics in molecules. Nature 460, 972–977 (2009)
Tan, J., Zhou, Y., He, M., Chen, Y., Ke, Q., Liang, J., Zhu, X., Li, M., Lu, P.: Determination of the ionization time using attosecond photoelectron interferometry. Phys. Rev. Lett. 121, 253203 (2018a)
Tan, J., Zhou, Y., Li, M., He, M., Liu, Y., Lu, P.: Accurate measurement of laser intensity using photoelectron interference in strong-field tunneling. Opt. Express 26, 020063 (2018b)
Tan, J., Zhou, Y., He, M., Ke, Q., Liang, J., Li, Y., Li, M., Lu, P.: Time-resolving tunneling ionization via strong-fieldphotoelectron holography. Phys. Rev. A 99, 033402 (2019)
Tong, A., Li, Q., Ma, X., Zhou, Y., Lu, P.: Internal collision induced strong-field nonsequential double ionization in molecules. Optics Express 27, 6415 (2019)
Walker, B., Sheehy, B., DiMauro, L., Agostini, P., Schafer, K., Kulander, K.: Precision measurement of strong field double ionization of helium. Phys. Rev. Lett. 73, 1227 (1994)
Wang, R., Zhang, Q., Li, D., Xu, S., Cao, P., Zhou, Y., Cao, W., Lu, P.: Identification of tunneling and multiphoton ionization in intermediate Keldysh parameterregime. Opt. Express 27, 6471–6482 (2019)
Xie, X., et al.: Attosecond probe of vlence-electron wave packets by subcycle sculpted laser fields. Phys. Rev. Lett. 108, 193004 (2012)
Xie, H., Li, M., Li, Y., Zhou, Y., Lu, P.: Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields. Opt. Express 24, 027726 (2016)
Yan, T., Popruzhenko, S., Vrakking, M., Bauer, D.: Low-energy structures in strong field ionization revealed by quantum orbits. Phys. Rev. Lett. 105, 253002 (2010)
Zhai, C., Zhang, Y., Zhang, Q.: Characterizing the ellipticity of an isolated attosecond pulse. Opt. Commun. 437, 104–109 (2019)
Zhang, X., Zhu, X., Wang, D., Li, L., Liu, X., Liao, Q., Lan, P., Lu, P.: Ultrafast oscillating-magnetic-field generation based on electronic-current dynamics. Phys. Rev. A 99, 013414 (2019)
Zhou, Y., Huang, C., Lu, P.: Coulomb-tail effect of electron–electron interaction on nonsequential double ionization. Phys. Rev. A 84, 023405 (2011a)
Zhou, Y., Huang, C., Tong, A., Liao, Q., Lu, P.: Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses. Opt. Express 19, 2301–2308 (2011b)
Zhou, Y., Tolstikhin, O., 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)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (11874163, 11622431, 61475055,11604108, 11627809) and Program for HUST Academic Frontier Youth Team.
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Liu, Y., Tan, J., He, M. et al. Photoelectron holographic interferences from multiple returning in strong-field tunneling ionization. Opt Quant Electron 51, 145 (2019). https://doi.org/10.1007/s11082-019-1868-y
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DOI: https://doi.org/10.1007/s11082-019-1868-y