1. Attosecond dynamics of intense-laser induced atomic processes W. Becker Max-Born Institut, Berlin, Germany D. B. Milosevic University of Sarajevo, Bosnia and Hercegovina 395th Wilhelm und Else Heraeus Seminar „Time-dependent Phenomena in Quantum Mechanics“ Blaubeuren, Sept.12 – 16, 2007 supported in part by VolkswagenStiftung

2. Collaborators G. G. Paulus, Texas A & M, U. Jena E. Hasovic, M. Busuladzic, A. Gazibegovic-Busuladzic, U. Sarajevo, Bosnia and Hervegovina M. Kleber, T. U. Munich C. Figueira de Morisson Faria, University College, London X. Liu, Chinese Academy of Sciences, Wuhan

3. Above-threshold ionization the effects observed are single-atom effects (no collective effects) but low counts electrons have attosecond time structure just like HHG

4. Rescattering: „ears“ or „lobes“ and the plateau Yang, Schafer, Walker, Kulander, Agostini, and DiMauro, PRL 71, 3770 (1993) Paulus, Nicklich, Xu, Lambropoulos, and Walther, PRL 72, 2851 (1994)

5. Few-cycle pulses E(t) = E 0 (t) cos(  t +  )  = carrier-envelope relative phase A few-cycle pulse breaks the back-forward (left-right) symmetry of effects caused by a long pulse

6. Tunneling ionization atomic binding potential V(r) interaction erE(t) with the laser field combined effective potential V+erE(t) ground-state energy v(t 0 )=0 at the exit of the tunnel rate of tunneling ~ is highly nonlinear in the field E(t) Tunneling is a valid picture if N.B.: Tunneling takes place at some specific time t 0

7. Kinematics in a laser field velocity in a time-dependent laser field (long-wavelength approximation) p = drift momentum The electron tunnels out at t = t 0 with v(t 0 ) = 0 p = eA(t 0 ) The drift momentum is given by the vector potential at the time of ionization. Conversely, the time of ionization can be determined from the drift momentum observed. mv(t) = p – eA(t) t = 0 At the end of the laser pulse, A(t) = 0 p = drift momentum = momentum at the detector

8. The laser field provides a clock T = 2.7 fs for a Ti:Sa laser with  = 1.55 eV Electron motion in the laser field takes place on the scale of T Streaking principle: p = eA(t 0 ) + p 0

9. which can be started, e.g., by an additional xuv pulse Electron motion in the laser field takes place on the scale of T Streaking principle: p = eA(t 0 ) + p 0

10. which can be started, e.g., by an additional xuv pulse Electron motion in the laser field takes place on the scale of T Streaking principle: p = eA(t 0 ) + p 0

11. which can be started, e.g., by an additional xuv pulse Electron motion in the laser field takes place on the scale of T Streaking principle: p = eA(t 0 ) + p 0

12. Reconstruction of the electric field with the help of an attosecond xuv pulse measure the momentum of an electron ionized by the attosecond pulse at time t 0 : p = mv o + eA(t 0 ) E. Goulielmakis et al., Science 305, 1267 (2004) (mv 0 2 /2 =  – I P )

13. An old experiment redone

14. The classical electron double-slit experiment C. Jönsson, Zs. Phys. 161, 454 (1961) „The most beautiful experiment in physics“ according to a poll of the readers of Physics World (Sept. 2002) 55

15. We mention that you should NOT attempt actually to set up this experiment (unlike those we discussed earlier). The experiment has never been done this way. The problem is that the apparatus to be built would have to be impossibly small in order to display the effect of interest to us. We are doing a „thought experiment“, which we designed so that it would be easy to discuss. (Feynman 1965)

16. From slits in space to windows in time: the attosecond double slit one and the same atom can realize the single slit and the double slit at the same time

17. Single slit vs. double slit by variation of the carrier-envelope phase  A(t) = A 0 e x cos 2 (  t/nT) sin(  t -  )  = 0 „cosine“ pulse  „sine“ pulse one window in either direction one window in the positive direction, two windows in the negative direction A(t) t p=eA(t) t

18. Theory vs. experiment: solution of the TDSE including the Coulomb field „simple-man“ model ignoring the Coulomb field The Coulomb field IS important F. Lindner et al. PRL 95, 040401 (2005)

19. Quantum-mechanical description: The Strong-Field Approximation (KFR) Keldysh (1964), Faisal (1973), Reiss (1980) neglects, in brief, the Coulomb interaction in the final (continuum) state the interaction with the laser field in the initial (bound) state

21. V p0 = cont. next page

23. eA(t) p nth cycle (n+1)st cycle(n+2)nd cycle The discreteness of the spectrum is generated by the superposition of all cycles The envelope is generated by the super- position of the two solutions within one cycle One cycle vs many cycles energy

24. One member of a pair of orbits experiences the Coulomb potential more than the other Two solutions per cycle for given p

25. Interference of the two solutions from within one cycle Data: I. Yu Kiyan, H. Helm, PRL 90, 183001 (2003) 1.1 x 10 13 Wcm -2 Theory: D.B. Milosevic et al., PRA (2003) 1.3 x 10 13 Wcm -2 F-F- = 1500 nm

26. High-energy electrons through re(back-)scattering Data: I. Yu Kiyan, H. Helm, PRL 90, 183001 (2003) 1.1 x 10 13 Wcm -2 Theory: D.B. Milosevic et al., PRA (2003) 1.3 x 10 13 Wcm -2 F-F- = 1500 nm rescattering

27. Recollisions

28. Recollision: one additional interaction with the atomic potential responsible for high-order harmonic generation, nonsequential double and multiple ionization high-order above-threshold ionization (HATI)....

29. Formal description of rescattering

32. Mechanism of nonsequential double ionization: Recollision of a first-ionized electron with the ion On a revisit (the first or a later one), the first-ionized electron can free another bound electron (or several electrons) in an inelastic collision time position in the laser-field direction

33. Quantum orbits in space and time ionization time = t´t = recollision time

34. Few-cycle-pulse ATI spectrum: violation of backward-forward symmetry Different cutoffs Peaks vs no peaks argon, 800 nm 7-cycle duration sine square envelope cosine pulse, CEP = 0 10 14 Wcm -2 D. B. Milosevic, G. G. Paulus, WB, PRA 71, 061404 (2005)

35. Few-cycle high-energy ATI spectra as a function of the CE phase very pronounced left-right (backward-forward) asymmetry employed to determine the CE phase Paulus et al. PRL 93, 253004 (2003)

36. Nonsequential double and multiple ionization

37. Sequential vs. nonsequential ionization: the total rate the „knee“ B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander, PRL 73, 1227 (1994 ) nonsequential = not sequential first observation and identification of a nonsequential channel: A. L‘Huillier, L.A. Lompre, G. Mainfray, C. Manus, PRA 27, 2503 (1983) The mechanism is, essentially, rescattering, like for high-order ATI and HHG SAEA NB: the effect disappears for circular polarization

38. Nonsequential double ionization: the ion momentum neon R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C..D. Schröter, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, W. Sandner, PRL 84, 447 (2000) ion-momentum distribution is double-peaked laser field polarization

39. S-matrix element for nonsequential double ionization (rescattering scenario) A. Becker, F.H.M. Faisal, PRL 84, 3546 (2000); R. Kopold, W. Becker, H. Rottke, W. Sandner, PRL 85, 3781 (2000); S.V. Popruzhenko, S. P Goreslavski, JPB 34, L230 (2001); C. Faria, H. Schomerus, X. Liu, W. Becker, PRA 69, 043405 (2004) time V 12 V(r,r‘) = V 12 = electron-electron interaction V(r‘‘) = binding potential of the first electron = Volkov state

40. S-matrix element for nonsequential double ionization (rescattering scenario) A. Becker, F.H.M. Faisal, PRL 84, 3546 (2000); R. Kopold, W. Becker, H. Rottke, W. Sandner, PRL 85, 3781 (2000); S.V. Popruzhenko, S. P Goreslavski, JPB 34, L230 (2001); C. Faria, H. Schomerus, X. Liu, W. Becker, PRA 69, 043405 (2004) time V 12 V(r,r‘) = V 12 = (effective) electron-electron interaction

41. A classical model Injection of the electron into the continuum at time t‘ at the rate R(t‘) The rest is classical: The electron returns at time t=t(t‘) with energy E ret (t) Energy conservation in the ensuing recollision |V pk | 2 R(t‘) = |E(t‘)| -1 exp[-4(2m|E 01 | 3 ) 1/2 /(3e|E(t‘)|)] highly nonlinear in the field E(t‘)

42. A classical model Injection of the electron into the continuum at time t‘ at the rate R(t‘) The rest is classical: The electron returns at time t=t(t‘) with energy E ret (t) Energy conservation in the ensuing recollision All phase space, no specific dynamics Cf. statistical models in chemistry, nuclear, and particle physics

43. Comparison: quantum vs classical model quantum classical sufficiently high above threshold, the classical model works as well as the full quantum model

44. Triple ionization Assume it takes the time  t for the electrons to thermalize time NB: one internal propagator  4 additional integrations

45. Nonsequential N-fold ionization via a thermalized N-electron ensemble Ion-momentum distribution: fully differential N-electron distribution: integrate over unobserved momentum components = mv(t+  t)  t = „thermalization time“

46. Ne 3+ Ne 4+

47. Comparison with Ne 3+ MBI—MPI-HD data experiment: 1.5 x 10 15 Wcm -2 Moshammer et al., PRL (2000) MPI-HD –- MBI collaboration classical statistical model at 1.0 x 10 15 Wcm -2  t = 0  t = 0.17T X. Liu, C. Faria, W. Becker, P.B. Corkum, JPB 39, L305 (2006)

48. Quantum effects of long quantum orbits alternatively: Wigner-Baz threshold effects (Manakov, Starace) cf. poster by D. B. Milosevic

49. Intensity-dependent enhancements of groups of ATI peaks Constructive interference of long orbits at a channel closing, I p + U p = (integer) x  experiment: Hertlein, Bucksbaum, Muller, JPB 30, L197 (1997) theory: Kopold, Becker, Kleber, Paulus, JPB 35, 217 (2002) intensity increases by ~ 5%

50. Quantummechanical energies: E p = n  – U p - I p at a channel closing, U p + I p = N  hence E p = 0 for N = n the electron can revisit the ion infinitely often „Long orbits“ or „late returns“ interference of different pathways into the same final state

51. calculated ATI spectrum No. of orbits 10 8 6 4 2 long vs. short „longer orbits“ 4 and more

52. ATI channel-closing (CC) enhancements electron energy = 199 eV, Ti:Sa laser, He, 1.04 x 10 15 Wcm -2 < I < 1.16 x 10 15 Wcm -2 number of quantum orbits included in the calculation a few orbits are sufficient to reproduce the spectrum, except near CCs

53. ATI channel-closing (CC) enhancements electron energy = 199 eV, Ti:Sa laser, He, 1.04 x 10 15 Wcm -2 < I < 1.16 x 10 15 Wcm -2 number of quantum orbits included in the calculation a few orbits are sufficient to reproduce the spectrum, except near CCs

54. Constructive interference of many long orbits

55. Conclusions

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