1. Imaginary time method and nonlinear ionization by powerful free electron lasers S.V. Popruzhenko Moscow Engineering Physics Institute, Moscow EMMI workshop “Particle dynamics under extreme matter conditions” Speyer, September 26-29, 2010

2. Outline I. Imaginary time method for time dependent QM problems ITM for time-independent tunneling generalization to the time-dependent problem Coulomb correction to the rate of ionization II. Nonlinear ionization at short wavelengths modern free electron lasers experiments on nonlinear ionization at short wavelengths nonlinear ionization rate for arbitrary frequencies can we explain the data?

3. Time-independent tunneling For a short-range well

4. Time-independent tunneling For a short-range well Can we generalize this description on the time-dependent case?

5. Time-dependent tunneling + initial conditions the initial time is complex

6. Time-dependent tunneling: imaginary time method Popov, Kuznetsov, Perelomov, 1967 The trajectory has to be found from Newton equation with the initial conditions

7. Imaginary time method nonlinear (multiphoton) ionization and excitation by intense electromagnetic fields strong field QED processes in the semiclassical domain laser-assisted decay of quasienergy states …

8. Imaginary time method ITM gives the solution in terms of classical complex trajectories. This provides a particularly convenient way to account for perturbations which cannot be considered within the conventional PT nonlinear (multiphoton) ionization and excitation by intense electromagnetic fields strong field QED processes in the semiclassical domain laser-assisted decay of quasienergy states …

9. Strong Field Approximation Coulomb correction to the SFA L.V. Keldysh, 1964 F.H.M. Faisal, 1973 H.R. Reiss, 1980

10. CCSFA: A.M. Perelomov, V.S. Popov, 1967 S.V. Popruzhenko, V.D. Mur, V.S. Popov, D. Bauer, 2008 Coulomb correction to the SFA

11. Strong field ionization rates Short-range well, static field Coulomb well, static field Hydrogen, ground state, 10 14 W/cm 2 : Perelomov, Popov,1967

12. II. Nonlinear ionization at short wavelengths modern free electron lasers experiments on nonlinear ionization at short wavelengths nonlinear ionization rate for arbitrary frequencies can we explain the data?

13. FLASH – Free electron LASer in Hamburg 2002: photon energy 12.7eV (100nm), intensity up to 10 13 W/cm 2, pulse duration 100fs; 2007: photon energy 92.8eV (13nm), intensity up to 10 16 W/cm 2, pulse duration 10fs; Currently: photon energy 200eV (6nm) is approached (6нм); its fifths harmonic is already in the KeV domain SPring-8 based SASE Source in Japan Currently: 50-62nm (photon energy around 20eV), intensity up to (1-3)*10 14 W/cm 2 LINAC Coherent Light Source in Stanford Modern free electron lasers

14. New regime of laser-matter interaction Optical and infrared lasers Intense XUV lasers

15. Nonlinear ionization at short wavelengths Nonlinear ionization at short wavelengths

16. A.A. Sorokin et al., 2007 Ionization of Xe by 10fs 13nm (93eV) pulses with intensity up to 10 16 W/cm 2 ions up to Xe 21+ were recorded 7 photons for ionization of Xe 20+ and >57 photons in total Nonlinear ionization at short wavelengths Nonlinear ionization at short wavelengths K. Motomura et al., 2009 Ionization of Ar by 100fs 62nm (20eV) pulses with intensity up to 2*10 14 W/cm 2 ions up to Xe 6+ were recorded

17. Nonlinear ionization at short wavelengths Nonlinear ionization at short wavelengths 1.Do we understand the mechanism? 2.If yes, can we provide a quantitative description?

18. Rate Static Low-frequency Arbitrary (high) frequency Nonlinear sequential ionization rates Nonlinear sequential ionization rates

19. Nonlinear ionization rates: intense XUV fields Nonlinear ionization rates: intense XUV fields W(Xe 10+ )=10 -24 !

20. Nonlinear ionization rates Nonlinear ionization rates A.M. Perelomov, V.S. Popov, 1967 S.V. Popruzhenko, V.D. Mur, V.S. Popov, D. Bauer, 2008

21. Ionization rate for arbitrary frequencies Ionization rate for arbitrary frequencies Rate Static Low- frequency Arbitrary (high) frequency

22. Comparisons with numerical results Ionization rate of Xe 17+ in the field of an XUV laser with the photon energy 93eV (13nm); 4p 0 state with I=434эВ; 5-photon ionization. The rate calculated from the TDSE numerical solution is shown by triangles.

23. Comparisons with the data The data of K. Motomura et al.: Ar at 62nm and Kr at 51nm

24. Ion stateIon. potential, eV Min. number of photons Probability, Theory 1 Probability, Theory 2 Ar + 27.621010 2 Ar 2+ 40.730.1520 Ar 3+ 59.73510 -2 10 Ar 4+ 75.14110 -3 0.3 Ar 5+ 91.05410 -6 10 -3 Ar 6+ 124.37210 -12 10 -9 Ar at 62nm, 210 14 W/cm 2, ions up to Ar 6+ have been observed Comparisons with the data

25. Ion stateIon. potential, eV Min. number of photons Probability, Theory 1 Probability, Theory 2 Kr 2+ 36.9220410 3 Kr 3+ 52.530.130 Kr 4+ 64.730.3110 2 Kr 5+ 78.54110 -3 0.5 Kr 6+ 111.05410 -7 310 -4 Kr 7+ 1266110 -9 710 -7 Kr at 50nm, 210 14 W/cm 2, ions up to Kr 7+ have been observed Comparisons with the data

26. Concluding remarks 1.Imaginary Time Method can be used for solving strong field problems difficult to approach by other methods: strong field sequential ionization rate of atoms and ions is a proper example when ITM works efficiently. 2.The nonlinear rate of ionization we derived provides much better qualitative agreement with the data obtained with intense XUV lasers than previously known rates. 3.However, it remains unclear if our rate is sufficient for quantitative description or the phenomenon. 4.Incorporation of Rydberg states may essentially improve the theory. 5.If with the Rydberg states accounted for we are still unable to reproduce the data this gives a strong support to the idea that electron-electron correlations are also important at short wavelengths.

27. Where to learn more? Theory: SVP and D. Bauer, Journal of Modern Optics 55, 2573 (2008) Applications: SVP, G.G. Paulus and D. Bauer, PRA 77, 053409 (2008) SVP, V.D. Mur, V.S. Popov and D. Bauer, PRL 101, 193003 (2008); JETP 108, 947 (2009) JETP 108, 947 (2009) Tian-Min Yan, SVP, M.J.J. Vrakking and D. Bauer, http://www.arxiv.org

28. Collaboration D. Bauer, Tian-Min Yan University of Rostock, Germany V.D. Mur Moscow Engineering Physics Institute, Russia A.Palffy, H.M.C. Cortes Max Planck Institute for Nuclear Physics, Heidelberg, Germany V.S. Popov Institute for Theoretical and Experimental Physics, Moscow, Russia M.J.J. Vrakking Max Born Institute, Berlin, Germany