1. Attosecond Flashes of Light – Illuminating electronic quantum dynamics – XXIII rd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research Group MPI – Kernphysik, Heidelberg

2. Contents Yesterday Attosecond Pulses Classical and quantum mechanics of electrons - Classical Motion of Electrons definition of important quantities - Quantum Mechanics · Electron dynamics in (intense) laser fields · Ionization - High-harmonic generation: quantum mechanical view

3. Contents Basics of short pulses and general concepts Attosecond pulse generation Mechanics of Electrons single electrons in strong laser fields Attosecond Experiments with isolated Atoms Multi-Particle Systems Molecules multi-electron dynamics (correlation) Attosecond experiments with molecules / multiple electrons Ultrafast Quantum Control of electrons, atoms, molecules Novel Directions/Applications Technology

4.  High Harmonics Quantum Mechanical M. Lewenstein et al. Phys. Rev. Lett. 49, 2117 (1994)

5. high-harmonic generation intense laser field acting on single atom probability distribution p(x,y)=|  (x,y)| 2 for the electronic wavefunction laser polarization

6. Wavepacket spreading

7. Split-Step Operator Technique

8. Streak field spectroscopy quantum mechanically, with interference Goulielmakis et al. (Krausz group), Science 305, 1267 (2004)

9. Streak-field spectroscopy Drescher et al., Nature 419, 803 (2002)

10. Auger decay in Kr Drescher et al. (Krausz group), Nature 419, 803 (2002)

11. Tunneling Spectroscopy Uiberacker et al. (Krausz group), Nature 446, 627 (2007)

12. Tunneling Spectroscopy Uiberacker et al. (Krausz group), Nature 446, 627 (2007)

13. Strong-Field Physics Experiments Blaga et al. (Paulus, Agostini, DiMauro), Nat. Physics 5, 335 (2009)

14. Strong-Field Physics Experiments Quan et al. Phys. Rev. Lett. 103, 093001 (2009)

15. Contents Basics of short pulses and general concepts Attosecond pulse generation Mechanics of Electrons single electrons in strong laser fields Attosecond Experiments with isolated Atoms Multi-Particle Systems Molecules multi-electron dynamics (correlation) Attosecond experiments with molecules / multiple electrons Ultrafast Quantum Control of electrons, atoms, molecules Novel Directions/Applications Technology

16. Contents Multi-Particle Systems (Molecules, many electrons) Attosecond experiments with molecules / multiple electrons - Molecules and molecular orbitals - Multi-electron Correlation: basics - Born-Oppenheimer and beyond - Recollision physics - Experiments with Molecules

17. Chemical Bonds http://ibchem.com/IB/ibfiles/bonding/bon_img/cov2.gif, http://en.wikipedia.org/wiki/Nitrogen http://www.unige.ch/sciences/Actualites/2007/MaximumMultiplicity/ W2_Mutiplicity.png

18. Linear Combination of Atomic Orbitals (LCAO) http://www.uweb.ucsb.edu/~jodea/chem1c.htm, http://tannerm.com/images/diatomic7.gif

19. Molecular electronic structure http://en.wikipedia.org/wiki/File:Benzene_Representations.svg

20. Complex Molecules http://dwb4.unl.edu/Chem/CHEM869K/CHEM869KLinks/www.ccp14.ac.uk /ccp/web-mirrors/llnlrupp/Xray/tutorial/pdb/helix_bonds.gif http://images.absoluteastronomy.com/images/encyclopediaimages/h/he/he xokinase_ball_and_stick_model,_with_substrates_to_scale_copy.png

21. and H igh H armonic G eneration ~100 as <1  J >1 nm Ultrashort x-ray/XUV Pulses ~200 m pulse energy pulse duration F ree E lectron L asers ~20 fs 1 fs (proj.) ~1 mJ wavelength ~1.5 Å ~1 mm fully coherent

22. Complex Molecules Neutze et al., Nature 406, 752 (2000) every molecule is different! single shot! -2 fs2 fs5 fs 10 fs 20 fs 50 fs pulse energy pulse duration F ree E lectron L asers ~20 fs 1 fs (proj.) ~1 mJ wavelength ~1.5 Å

23. DNA http://www.chemicalgraphics.com/paul/images/DNA/BallAndStick.jpg

24. macromopecular dynamics Pictures from: http://www.nfcr.org/Portals/0/Images/3d_blue_green_molecule.jpg, http://hasylab.desy.de/e77/e106/e122/e35842/e35862/Fig1_Hasylab-ultrafast_eng.jpg e.g. detach functional group (signaling protein) from enzyme receptor

25. Some theory of the chemical bond Valence bond theoryMolecular orbital theory become equivalent if extended localized electrons between two atoms delocalized electrons within entire molecule Born-Oppenheimer always inherently assumed www.jonathanpmiller.com/ http://www.york.ac.uk/che mistry/staff/academic/h- n/pkaradakov/

26. Complexity of Wavefunctions everything else: numerics necessary for example: store wavefunctions on a grid 10 points (double precision, 8 B(Bytes)) in each dimension Ground states (and ignoring nuclear core wavefunctions and most nuclear spin states): Hydrogen atom: 16 kB Helium atom: 32 MB Hydrogen molecule:64 GB Oxygen atom: 2  10 18 GB Methane (16 daltons, [Da]):6.5  10 34 GB Biomolecule: (kDa-MDa): ~10 1,000 - 10 1,000,000 GB (10 3(N-1)  2 (N-1) )  8 B - a few ZB (ZettaBytes), 10 12 GB is the estimated total data stored digitally estimate by IDC (International Data Corporation) - 50 PB (PetaBytes), 10 6 GB is estimated information written by mankind in known history Hydrogen atom (1 electron, 1 nucleus) can be found analytically

27. Some theory of the chemical bond Density Functional Theory (DFT) Hartree-Fock Theory (HF) (single Slater determinant) problems with ground states energetically close to excited states or in bond-breaking situations Quantum chemistry methods - Configuration interaction (CI) - Multi-configurational self-consistent field (MCSCF) combination between configuration interaction (where the molecular orbitals are not varied but the expansion of the wave function) and Hartree-Fock (where there is only one determinant but the molecular orbitals are varied). - Semi-empirical quantum chemistry methods for large molecules where other methods fail improvements: http://upload.wikimedia.org/wikipedia/en/7/7e/Electron_correlation.png

28. Hybridization http://www.grandinetti.org/Teaching/Chem121/Lectures/Hybridization/ sp 2

29. Hybridization http://www.grandinetti.org/Teaching/Chem121/Lectures/Hybridization/ sp

30. Hybridization http://www.grandinetti.org/Teaching/Chem121/Lectures/Hybridization/ sp 3

31. Correlated lectron dynamics location 1 location 2 e-e- e-e- e-e- e-e- Scientific Goal of AttoPhysics  ( 1, 2 ) ≠ Ψ( 1 ) ×Ψ ( 2 ) interaction (Coulomb) symmetry (Fermions) Correlation e-e- e-e- e-e- e-e- interacting non-interacting (Entanglement) 0 1 e-e-

32. location 1 e-e- location 2 e-e- fundamental role in radiation damage (ionization+excitation) importance in life sciences Lanzara group, UC Berkeley Scientific Goal of AttoPhysics Sept. 2007 Giant MagnetoresistanceHigh T c superconductivity Correlated lectron dynamics e-e- e-e- e-e-  ( 1, 2 ) ≠ Ψ( 1 ) ×Ψ ( 2 ) interaction (Coulomb) symmetry (Fermions) Correlation e-e- e-e- e-e- e-e- interacting non-interacting any bonding orbital in matter typically occupied by 2 electrons e-e- e-e-

33. Two-electron dynamics Pisharody and Jones Science 303, 813 (2004) – Rydberg electrons – Barium atoms

34. Quantum Level Spacings in a molecule Separation: Electronic, Vibrational, Rotational Energy Internuclear Distance 0 5  e,2  e,1  e,0  total  el,n  vib,m  rot,l  v,n  rot,l

35. Born-Oppenheimer Approximation Full Hamiltonian Reduced Hamiltonian (internuclear only) http://www.nat.vu.nl/~wimu/MolPhys.html Product Wavefunction:

36. Estimation of Quantum Time Scales LILI  =    ħ m p a 0 2 Molecular rotation frequency Molecular vibration frequency DmpDmp      Electron vibration frequency  DmeDme LILI  =  = ħ m e a 0 2 Electron rotation frequency 1 2000 1 2000  1 50 1 T r =300 fs T v =7 fs T e =150 as

37. Recollision Physics e-e- Paul Corkum, NRC Canada Strong laser field ħ  HHG elastic scattering  ATI spectroscopy parameters: - alignment angle - laser intensity / ellipticity / wavelength / CEP,... - multicolor excitation -... e-e- e-e- inelastic scattering  NSDI, excitation, fragmentation

38. Three-step model P. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

39. Molecular recollision

40. HHG ellipticity dependence A. Flettner et al. (Gerber group) EPJ D (2002) ellipticity normalized harmonic yield molecule atom linear elliptic

41. Argon and Nitrogen static polarizability

42. Ellipticity experiment setup

43. Example measurement: H13 in Ar

44. Experiment and Model: Ar

45. Nitrogen vs. Argon

46. HHG-Simulation

47. Earlier Results

48. simulation results Ar vs. N 2 ellipticity

49. Electron-Wavepacket - Shaping ionization propagationrecombination 1 Å3 Å4 Å different degrees of delocalization

50. momentum p y [a.u.] |  (p y )| 2 y coordinate [a.u.] |  (y)| 2 Temporal evolution in laser field 10 Å 4 Å 3 Å 1 Å x y H-Atom

51. internuclear-distance dependence atom molecular ground state 

52.  driver pulsepump pulse Pump–Drive Scheme T.P. et al. Phys. Rev. A 70, 013805 (2004)

53. Molecular Tomography Itatani et al.(Corkum, Villeneuve) Nature 432, 867 (2004)