Imaginary time method and nonlinear ionization by powerful

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

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?

• Time-independent tunneling For a short-range well

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

• Time-dependent tunneling + initial conditions the initial time is complex

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

• 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 • …

• 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 • … 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

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

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

• Strong field ionization rates Short-range well, static field Coulomb well, static field Perelomov, Popov, 1967 Hydrogen, ground state, 1014 W/cm 2:

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?

• Modern free electron lasers FLASH – Free electron LASer in Hamburg 2002: photon energy 12. 7 e. V (100 nm), intensity up to 1013 W/cm 2, pulse duration 100 fs; 2007: photon energy 92. 8 e. V (13 nm), intensity up to 1016 W/cm 2, pulse duration 10 fs; Currently: photon energy 200 e. V (6 nm) is approached (6 нм); its fifths harmonic is already in the Ke. V domain SPring-8 based SASE Source in Japan Currently: 50 -62 nm (photon energy around 20 e. V), intensity up to (1 -3)*1014 W/cm 2 LINAC Coherent Light Source in Stanford

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

• Nonlinear ionization at short wavelengths

• Nonlinear ionization at short wavelengths A. A. Sorokin et al. , 2007 Ionization of Xe by 10 fs 13 nm (93 e. V) pulses with intensity up to 1016 W/cm 2 ions up to Xe 21+ were recorded 7 photons for ionization of Xe 20+ and >57 photons in total K. Motomura et al. , 2009 Ionization of Ar by 100 fs 62 nm (20 e. V) pulses with intensity up to 2*1014 W/cm 2 ions up to Xe 6+ were recorded

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

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

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

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

• Ionization rate for arbitrary frequencies Rate Static Lowfrequency Arbitrary (high) frequency

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

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

• Comparisons with the data Ar at 62 nm, 2 • 1014 W/cm 2, ions up to Ar 6+ have been observed Ion state Ion. potential, e. V Min. number of photons Probability, Theory 1 Probability, Theory 2 Ar+ 27. 6 2 10 102 Ar 2+ 40. 7 3 0. 15 20 Ar 3+ 59. 7 3 5 • 10 -2 10 Ar 4+ 75. 1 4 1 • 10 -3 0. 3 Ar 5+ 91. 0 5 4 • 10 -6 10 -3 Ar 6+ 124. 3 7 2 • 10 -12 10 -9

• Comparisons with the data Kr at 50 nm, 2 • 1014 W/cm 2, ions up to Kr 7+ have been observed Ion state Ion. potential, e. V Min. number of photons Probability, Theory 1 Probability, Theory 2 Kr 2+ 36. 9 2 20 4 • 103 Kr 3+ 52. 5 3 0. 1 30 Kr 4+ 64. 7 3 0. 3 1 • 102 Kr 5+ 78. 5 4 1 • 10 -3 0. 5 Kr 6+ 111. 0 5 4 • 10 -7 3 • 10 -4 Kr 7+ 126 6 1 • 10 -9 7 • 10 -7

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 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.

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) Tian-Min Yan, SVP, M. J. J. Vrakking and D. Bauer, http: //www. arxiv. org

Collaboration D. Bauer, Tian-Min Yan University of Rostock, Germany V. D. Mur Moscow Engineering Physics Institute, Russia 1. A. Palffy, H. M. C. Cortes 2. 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