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Quantum-orbit approach for an elliptically polarized laser field

Quantum-orbit approach for an elliptically polarized laser field. Wilhelm Becker. Max-Born-Institut, Berlin, Germany. Workshop „Attoscience: Exploring and Controlling Matter on its Natural Time Scale“, KITPC, Beijing, May 12, 2011. Collaborators:.

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Quantum-orbit approach for an elliptically polarized laser field

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  1. Quantum-orbit approach for an elliptically polarized laser field Wilhelm Becker Max-Born-Institut, Berlin, Germany Workshop „Attoscience: Exploring and Controlling Matter on its Natural Time Scale“, KITPC, Beijing, May 12, 2011

  2. Collaborators: C. Figueira de Morisson Faria, University College, London S. P. Goreslavski, MEPhI, Moscow R. Kopold, Siemens, Regensburg X. Liu, CAS, Wuhan D. B. Milosevic, U. Sarajevo G. G. Paulus, U. Jena S. V. Popruzhenko, MEPhI, Moscow N. I. Shvetsov- Shilovski, U. Jena

  3. Motivation NSDI knee experimentally measured for circular polarization NSDI knee observed in completely classical (CC) and semiclassical (tunneling-classical; TC) simulations for circular polarization Dependence of a process on ellipticity is indicative of the mechanism

  4. Nonsequential double ionization exists for circular polarization

  5. NSDI for a circularly polarized laser field magnesium, Ip1 = 7.6 eV, Ip2 = 15.0 eV, Ip3 = 80 eV, 120 fs, 800 nm linear circular G. D. Gillen, M. A. Walker, L. D. Van Woerkom, PRA 64, 043413 (2001)

  6. Double-ionization yield from completely classical (CC) simulations Ip = 1.3 a.u. X. Wang, J. H. Eberly, NJP 12, 093047 (2010)

  7. Electron trajectories from completely classical double-ionization simulations doubly-ionizing orbits tend to be „long orbits“ X. Wang, J. H. Eberly, NJP 12, 093047 (2010)

  8. CC simulation: escape over the Stark saddle depends on parameters helium, Ip = 2.24 a.u. a = 1 b = 1 no knee magnesium, Ip = 0.83 a.u. a = 3 b = 1 a knee F. Mauger, C. Chandre, T. Uzer, PRL 105, 083002 (2010)

  9. Elliptical polarization helps revealing the mechanism

  10. Ellipticity dependence reveals the mechanism HH 21 in argon, measured and simulated NSDI of argon, measured and simulated ellipticity P. Dietrich, N. H. Burnett, M. Yu. Ivanov, P. B. Corkum, PRA 50, R3589 (1994)

  11. An example of ellipticity as a diagnostic tool NSDI of neon as a function of wavelength for various ellipticities calculated by the tunneling-classical-trajectory model constant intensity I = 1.0 x 1015 Wcm-2 transition to the standard rescattering mechanism at about 200 nm X. Hao, G. Wang, X. Jia, W. Li, J. Liu, J. Chen, PRA 80, 023408 (2009)

  12. Recollision and elliptical (linear --> circular) polarization Simplest simple-man argument: for sufficiently large ellipticity, especially for circular polarization, an electron released with zero velocity will not return to its place of birth no recollision-induced processes However, electrons are released with nonzero distribution of transverse velocities recollision is possible for suitable transverse momentum (But, no HHG for circular polarization, QM dipole selection rule)

  13. Quantum-orbit formalism

  14. Formal description of recollision processes = „direct“ + rescattered 1st-order Born approximation HATI into a state with final (drift) momentum p: Vf = continuum scattering potential), <yf| = <ypVolkov |

  15. Formal description of recollision processes = „direct“ + rescattered Low-frequency approximation (LFA) HATI into a state with final (drift) momentum p: Vf = continuum scattering potential), <yf| = <ypVolkov |

  16. Evaluation by stationary phase (steepest descent) with respect to the integration variables t, t‘, k

  17. Saddle-point equations for high-order ATI the (complex) solutions ts‘, ts, and qs (s=1,2,...) determine electron orbits in the laser field („quantum orbits“)

  18. Saddle-point equations tunneling at constant energy return to the ion elastic rescattering

  19. Many returns: for given final state, there are many solutions of the saddle-point equations „Long orbits“

  20. Building up the ATI spectrum from quantum orbits shortest 14 orbits shortest six orbits 1 +...+ 6 shortest two orbits 1+2 Magnitude of the contributions of the various pairs of orbits Significance of longer orbits decreases due to spreading

  21. x(t=ts‘) = 0, but Re [x(Re ts‘)] = „tunnel exit“ different from 0

  22. Quantum orbits (real parts) for elliptical polarization position of the ion tunnel exit x = semimajor axis y = semiminor axis Re y (a.u.) Note: the shortest orbits require the largest transverse momenta to return semimajor polarization axis

  23. Why longer orbits require lower transverse momenta to return short orbit: transverse drift is significant

  24. Why longer orbits require lower transverse momenta to return longer orbit: transverse drift is much reduced

  25. The contribution of an orbit is weighted exponentially prop. to exp(-pdrift2/Dp2) short orbits have large pdrift and are suppressed

  26. What is the difference between the saddle points for linear and for elliptical polarization? linear pol.: for Ip = 0 and qT = 0, the solution t‘ is real simple-man model elliptical pol.: even for Ip = 0 and qT = 0, the solution t‘ is complex (cannot have both qx - eAx(t‘) = 0 and qy- eAy(t‘) = 0) can only say that q - eA(t‘) is a complex null vector

  27. Examples: HHG and HATI

  28. Above-threshold ionization by an elliptically polarized laser field x = 0.5 w = 1.59 eV I = 5 x 1014 Wcm-2 The plateau becomes a stair The shortest orbits make the smallest contributions, but with the highest cutoff R. Kopold, D. B. Milosevic, WB, PRL 84, 3831 (2000)

  29. Quantum orbits for elliptical polarization: Experiment vs. theory x = 0.36 xenon at 0.77 x 1014Wcm-2 The plateau becomes a staircase The shortest orbits are not always the dominant orbits Salieres, Carre, Le Deroff, Grasbon, Paulus, Walther, Kopold, Becker, Milosevic, Sanpera, Lewenstein, Science 292, 902 (2001)

  30. Alternative description: quasienergy formalism (zero-range potential or effective-range theory) B. Borca, M. V. Frolov, N. L. Manakov, A. F. Starace, PRL 87, 133001 (2001) N. L. Manakov, M. V. Frolov, B. Borca, A. F. Starace, JPB 36, R49 (2003) A. V. Flegel, M. V. Frolov, N. L. Manakov, A. F. Starace, JPB 38, L27 (2005)

  31. Staircase for HATI Ip = 0.9 eV w = 1.59 eV I = 5 x 1014 Wcm-2 x = 0.5 R. Kopold, D. B. Milosevic, WB, PRL 84, 3831 (2000)

  32. Staircase for HHG Ip = 0.9 eV w = 1.59 eV I = 5 x 1014 Wcm-2 x = 0.5

  33. Quantum orbits in the complex t0 and t1 plane Im wt0 Re wti orbits 1,2 orbits 3,4 orbits 5,6 HATI: * (asterisk) HHG: (diamond) x = 0.5, 780 nm, He 5 x 1014 Wcm-2 wt0 wt1

  34. HATI for various ellipticities Ip = 0.9 eV w = 1.59 eV I = 5 x 1014 Wcm-2 strong drop for e > 0.3

  35. HHG for various ellipticities Ip = 13.6 eV w = 1 eV I = 1.4 x 1014 Wcm-2 dramatic drop for e > 0.2 D. B. Milosevic, JPB 33, 2479 (2000)

  36. Cutoffs for HHG orbits 1 c1 = 3.17 c2 = 1.32 (Lewenstein, Ivanov) pair of orbits 2 c1 = 1.54 c2 = 0.88 3 c1 = 2.40 c2 = 1.10 D. B. Milosevic, JPB 33, 2479 (2000) HATI cutoff pair 1 Emax = 10.01 Up + 0.54 Ip M. Busuladzic, A. Gazibegovic-Busuladzic, D. B. Milosevic, Laser Phys. 16, 289 (2006)

  37. Interference of direct and rescattered electrons G. G. Paulus, F. Grasbon, A. Dreischuh, H. Walther, R. Kopold, WB, PRL 84, 3791 (2000)

  38. Mechanism of the second plateau theory: 5.7 x 1013 Wcm-2 „Xe (Ip = 0.436)“ x = 0.48 experiment: 7.7 x 1013 Wcm-2 Xe 800 nm x = 0.36

  39. Interference of direct and rescattered electrons rescattered direct The contributions of just the rescattered and just the direct electrons individually are only smoothly dependent on the angle, only the superposition is structured

  40. Conditions for interference between direct and rescattered electrons direct elliptical linear direct yield yield rescattered rescattered energy energy for elliptical polarization, the yields of direct and rescattered electrons are comparable over a larger energy range See, however, Huismans et al., Science (2011)

  41. Example: NSDI for elliptical polarization

  42. NSDI from a simple semiclassical model R(t) = ADK tunneling rate t = start time, t‘(t) = recollision time E(t‘) = kinetic energy of the recolliding electron (t‘ - t)-3 = effect of spreading Vp1p2 = form factor (to be ignored) d(...) = energy conservation in rescattering C. Figueira de Morisson Faria, H. Schomerus, X. Liu, WB, PRA 69, 043405 (2004)

  43. NSDI by an elliptically polarized field: the bad news x = 0 --> 0.4 8 o.o.m.! Ti:Sa neon I = 8 x 1014 Wcm-2 N. I. Shvetsov-Shilovski, S. P. Goreslavski, S. V. Popruzhenko, WB, PRA 77, 063405 (2008)

  44. NSDI for elliptical polarization: ion-momentum distribution Ti:Sa neon I=8 x1014 Wcm-2 first six returns first return only this case to be realized by a single-cycle pulse N. I. Shvetsov-Shilovski, S. P. Goreslavski, S. V. Popruzhenko, WB, PRA 77, 063405 (2008)

  45. NSDI for elliptical polarization: electron-electron-momentum correlation W(p1x,p2x|p1y>0,p2y>0) first six returns first return only single-cycle pulse case! N. I. Shvetsov-Shilovski, S. P. Goreslavski, S. V. Popruzhenko, WB, PRA 77, 063405 (2008)

  46. Asymmetry of the momentum-momentum correlation between the first and the third quadrant 8 x 1014 Wcm-2 asymmetry is strongly intensity-dependent depending upon which orbits are dominant 4 x 1014 Wcm-2 a = 10% for x = 0.1 yield is down by 3 should be measurable

  47. Try some ellipticity Coulomb focusing is desirable to increase the effects ATI spectra for elliptical polarization are coming up from X. Y. Lai and X. Liu

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