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Attosecond dynamics of intense-laser induced atomic processes

Attosecond dynamics of intense-laser induced atomic processes. W. Becker Max-Born Institut, Berlin, Germany D. B. Milosevic University of Sarajevo, Bosnia and Hercegovina. supported in part by VolkswagenStiftung. 395th Wilhelm und Else Heraeus Seminar

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Attosecond dynamics of intense-laser induced atomic processes

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  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 supported in part by VolkswagenStiftung 395th Wilhelm und Else Heraeus Seminar „Time-dependent Phenomena in Quantum Mechanics“ Blaubeuren, Sept.12 – 16, 2007

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

  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 Paulus, Nicklich, Xu, Lambropoulos, and Walther, PRL 72, 2851 (1994) Yang, Schafer, Walker, Kulander, Agostini, and DiMauro, PRL 71, 3770 (1993)

  5. Few-cycle pulses E(t) = E0(t) cos(wt + f) f = 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) ground-state energy interaction erE(t) with the laser field combined effective potential V+erE(t) v(t0)=0 at the exit of the tunnel is highly nonlinear in the field E(t) rate of tunneling ~ Tunneling is a valid picture if N.B.: Tunneling takes place at some specific time t0

  7. Kinematics in a laser field velocity in a time-dependent laser field (long-wavelength approximation) mv(t) = p – eA(t) <A(t)>t = 0 p = drift momentum The electron tunnels out at t = t0 with v(t0) = 0 p = eA(t0) 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. 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 w = 1.55 eV Electron motion in the laser field takes place on the scale of T Streaking principle: p = eA(t0) + p0

  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(t0) + p0

  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(t0) + p0

  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(t0) + p0

  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 t0: p = mvo + eA(t0) (mv02/2 = W – IP) E. Goulielmakis et al., Science 305, 1267 (2004)

  13. An old experiment redone

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

  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 f A(t) = A0 ex cos2(p t/nT) sin(wt -f) A(t) „cosine“ pulse f = 0 t one window in either direction p=eA(t) „sine“ pulse A(t) f = p /2 one window in the positive direction, two windows in the negative direction t

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

  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

  20. Vp0 = <p-eA(t)|V|0> cont. next page

  21. One cycle vs many cycles p eA(t) 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 energy

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

  23. Interference of the two solutions from within one cycle F- l = 1500 nm Data: I. Yu Kiyan, H. Helm, PRL 90, 183001 (2003) 1.1 x 1013 Wcm-2 Theory: D.B. Milosevic et al., PRA (2003) 1.3 x 1013 Wcm-2

  24. High-energy electrons through re(back-)scattering F- l = 1500 nm rescattering Data: I. Yu Kiyan, H. Helm, PRL 90, 183001 (2003) 1.1 x 1013 Wcm-2 Theory: D.B. Milosevic et al., PRA (2003) 1.3 x 1013 Wcm-2

  25. Recollisions

  26. 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) ....

  27. Formal description of rescattering

  28. Mechanism of nonsequential double ionization: Recollision of a first-ionized electron with the ion time position in the laser-field direction 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

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

  30. Few-cycle-pulse ATI spectrum: violation of backward-forward symmetry argon, 800 nm 7-cycle duration sine square envelope cosine pulse, CEP = 0 1014 Wcm-2 Different cutoffs Peaks vs no peaks D. B. Milosevic, G. G. Paulus, WB, PRA 71, 061404 (2005)

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

  32. Nonsequential double and multiple ionization

  33. Sequential vs. nonsequential ionization: the total rate the „knee“ 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) SAEA The mechanism is, essentially, rescattering, like for high-order ATI and HHG NB: the effect disappears for circular polarization B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander, PRL 73, 1227 (1994)

  34. Nonsequential double ionization: the ion momentum ion-momentum distribution is double-peaked 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) neon laser field polarization

  35. S-matrix element for nonsequential double ionization (rescattering scenario) V(r,r‘) = V12 = electron-electron interaction V12 V(r‘‘) = binding potential of the first electron = Volkov state time • 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)

  36. S-matrix element for nonsequential double ionization (rescattering scenario) V(r,r‘) = V12 = (effective) electron-electron interaction V12 time • 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)

  37. 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 Eret(t) Energy conservation in the ensuing recollision |Vpk|2 R(t‘) = |E(t‘)|-1 exp[-4(2m|E01|3)1/2/(3e|E(t‘)|)] highly nonlinear in the field E(t‘)

  38. 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 Eret(t) Energy conservation in the ensuing recollision All phase space, no specific dynamics Cf. statistical models in chemistry, nuclear, and particle physics

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

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

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

  42. Ne3+ Ne3+ Ne4+

  43. Comparison with Ne3+ MBI—MPI-HD data Dt = 0 Dt = 0.17T experiment: 1.5 x 1015 Wcm-2 classical statistical model at 1.0 x 1015 Wcm-2 Moshammer et al., PRL (2000) MPI-HD –- MBI collaboration X. Liu, C. Faria, W. Becker, P.B. Corkum, JPB 39, L305 (2006)

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

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

  46. „Long orbits“ or „late returns“ Quantummechanical energies: Ep = nw – Up - Ip at a channel closing, Up + Ip = Nw hence Ep = 0 for N = n the electron can revisit the ion infinitely often interference of different pathways into the same final state

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