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  1. Molecules in a laser field:semiclassical & quantal treatmentE. Fiordilino*§,G. Castiglia*§, P. P. Corso*§, R. Daniele, F. Morales, G. Orlando* and F. Persico*§* CNISM and Dipartimento di Scienze Fisiche ed Astronomiche, Via Archirafi 36, 90123 Palermo, Italy.§ Consorzio COMETA - Research Line: Atoms in Strong Fields, Dipartimento di Scienze Fisiche ed Astronomiche, Via Archirafi 36, 90123 Palermo, Italy. C N I S M ISCHIA 2009

  2. High Harmonic Generation ISCHIA 2009

  3. Diffused radiation Molecule Laser Artistic spectrum ISCHIA 2009

  4. Fullerene ISCHIA 2009

  5. ISCHIA 2009

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  8. Pulse duration 64 oc ISCHIA 2009

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  16. Cutoff law at low field ISCHIA 2009

  17. Diatomic molecules in a laser field ISCHIA 2009

  18. Full hamiltonian ISCHIA 2009

  19. H2+Classical nuclei ISCHIA 2009

  20. Schroedinger equation for the electron Newton equation for the nuclei Hamiltonian electron nuclei interaction nucleus-nucleus interaction ISCHIA 2009

  21. It is evident the presence of regularly spaced sidebands around the odd harmonic peaks The satellite peak spacing is exactly given by the nuclei vibration frequency ISCHIA 2009

  22. 1D model for various molecular isotopes Different molecular isotopes are characterized by different satellite peak spacing Each satellite peak spacing is directly related to the corresponding nuclear vibration frequency ISCHIA 2009

  23. Fixed nuclei: spectrum for M=M0 No side-bands around the odd harmonic lines of HHG are present ISCHIA 2009

  24. Schroedinger equation in 3D The presence of the satellite peaks in the harmonic spectrum does not depend upon the dimensionality of the model. The harmonic lines present side peaks whose separation scales as ISCHIA 2009

  25. H2 ISCHIA 2009

  26. 1D semiclassical model for various H2 molecular isotopes ISCHIA 2009

  27. 1D full quantum calculations for H2+ ISCHIA 2009

  28. Conceptual considerations suggest the use of a full quantal calculation for the molecule. ISCHIA 2009

  29. ΔωN ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 ISCHIA 2009

  30. 1D full-quantum model for various H2+ isotopes T = 4 o.c. ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 For short pulses heavy nuclei win ISCHIA 2009

  31. 1D full-quantum model for various H2+ molecular isotopes T = 8 o.c. ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 ISCHIA 2009

  32. 1D full-quantum model for various H2+ molecular isotopes T = 16 o.c. ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 For long pulse light nuclei win ISCHIA 2009

  33. 1D full-quantum model for various H2+ molecular isotopes T = 32 o.c. ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 ISCHIA 2009

  34. 1D full-quantum model for various H2+ isotopes T = 64 o.c. ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 ISCHIA 2009

  35. 1D full quantum calculations for molecular ions oscillations of the nuclei spread of the nuclear wavefunction ____ M = M0 ____ M = 4 M0 ____ M = 16 M0 ISCHIA 2009

  36. Ionization Signal Nuclear wavefunction spread Isotopiceffect: the intensity of the harmonics decreases by increasing the mass of the nuclei Possible explanation: Nuclear wavefunction for lighter nuclei easily spreads and crosses a region of R with enhanced ionization ISCHIA 2009

  37. ISOTOPIC EFFECT SHORT LASER PULSE: The intensity of harmonics increases by decreasing nuclear mass LONG LASER PULSE: The intensity of harmonics decreases by decreasing nuclear mass The nuclear wavefunction does not reach the critical ionization region The nuclear wavefunction approaches the critical ionization region ISCHIA 2009

  38. CONCLUSIONS • Fullerene should emit harmonics: I hope experiments will • come soon. • The motion of the nuclei introduces in the HHG spectrum • satellite peaks of the odd-harmonics. The presence of the • side-peaks is a direct evidence of the nuclear vibration • motion. • A full quantum model shows an isotopic effect in the • HHG spectra. References: N. L. Wagner, A. Wüest, I. P. Christov, T. Popmintchev, X. Zhou, M. M. Murnane, H. C. Kapteyn, PNAS 103, 13279 (2006). P. P. Corso, E. Fiordilino, F. Persico, JPB 40, 1383 (2007). S. De Luca and E. Fiordilino, J. Phys. B: At. Mol. Opt. Phys. 29, 3277 (1996). ISCHIA 2009

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