1. PHYSICAL CONSEQUENCE:  electron capture results in odd harmonic photons. harmonic cutoff: (3U p + IP) rule !!  elastic scattering yields energetic (10U p ) electrons.  inelastic e-2e scattering  multiple electron ejection. excitation t=0 propagation ¼-cycle rescattering ½-cycle time  strong-field atomic physics III: 2e, scaling & speculation semi-classical rescattering

2. elastic rescattering initial bs velocitynormal drift new elastic cutoff: T = 10U p quantum model: TDSE-SAE K. Schafer et al. PRL 70, 1599 (1993) tunnel (v o =0) v(t) = E o /  [cos  t - cos  o ] backscatter (  =  ) set: v(  r ) = -v(  r ) v(t > t r ) = E o /  [(cos  t - cos  r ) – (cos  r - cos  o )]

3. elastic rescattering: SFA approximation Semi-classical solution of generalized SFA Lewenstein et al., PRA 51, 1495 (1995) backscattering results in production of high energy electrons

4. the short-range physics is important. quantum diffusion reduces the effective rescattering. the recollision occurs in less than an optical cycle. elastic rescattering: experiment & theory helium, 0.8  m, 0.8 PW/cm 2

5. elastic rescattering: intensity dependence % Remember, U p  Intensity !! PW/cm 2 helium, 0.8  m in scaled energy, distributions look similar!

6. e-2e rescattering picture of multiple ionization U p  ip 2

7. two mechanisms result in the formation of He 2+ !! He  He + + e He +  He 2+ + e some insights into double ionization:  NS linked to depletion of the neutral ground state.  first electron tunnels into the continuum.  the NS yield is strongly polarization dependent as compared to the sequential processes. helium double ionization: total rate

8. 3 He 4 He Experiment performed at two intensities. 0.8 PW/cm 2 1/500 0.4 PW/cm 2 1/1000 3 He is used for coincidence measurement. helium double ionization: high sensitivity

9. 1800 “background” electrons 2 “signal” electrons The Needle in the Haystack

10. helium double ionization: e-ion coincidence interaction region e spec mass spec mechanical referencing design common interaction volume pulsed mode operation dual MCP detection UHV environment (10 -10 t)

11. mass spectrometer electron spectrometer helium double ionization: e-ion coincidence

12. e-ion coincidence apparatus: test  an 8:1 Xe:Kr gas mix test was used to test the coincidence apparatus. T:F ~ 3:1 it really, really works!

13. He + He 2+ double ionization results in “hotter” distribution than single ionization. distribution consistent with e-2e rescattering. 4×10 14 W/cm 2 8×10 14 W/cm 2 205M shots 45M He hits 1058 He 2+ coin helium double ionization: electron distributions

14. e-2e Corkum (1993) release first electron at phase  i if return energy is sufficient to excite second electron to first excited state (40 eV), then proceed. all excess energy goes to first electron (forward or backward). second electron is then field ionized with zero initial kinetic energy. 8×10 14 W/cm 2 helium double ionization: classical interpretation electron energy (U p ) counts (arb units) 100 1.001 123540 backscattered forward

15. helium double ionization: S-matrix calculation shake-off correlated energy sharing

16. e-2e classically forbidden NS The double-to-single ionization ratio is equal for 800 nm & 400 nm excitation. is everything perfect in the world? helium, 0.4  m reduce ponderomotive energy by 4 since U p  2

17. is the Keldysh picture relevant for multiple ionization?    xenon at 10 14 W/cm 2 h “photon description” helium at 10 15 W/cm 2 “dc-tunneling picture”   

18. non-sequential ionization (800 nm) xenon argon ratio double-to-single ionization non-sequential ionization exists for all inert gases in the near-ir.

19. evolution of non-sequential ionization (800 nm) normalized electron counts electron momentum (atomic units) Argon Xenon  1.2  1.6  0.8  1.2    Chaloupka et al. PRL 90, 33002-1 (2003).

20.  rescattering model captures the essential physics single electron approximation quasi-static limit tunneling regime  experimental test of the model has been limited  starting to understand many-body effects  little or no experiments: relativistic regime long wavelength regime strong-field short wavelength limit summary: strong field atomic physics

21. wavelength scaling in strong fields SF wavelength scaling parameters: Keldysh adiabaticity parameter:  -1 ponderomotive energy: U p  2 wave packet spread:  scaling laws suggest that wavelength is important parameter for altering the intense laser-atom interaction. the scaling of the physics is virtually untested. may provide a new paradigm in the physics.

22. scaling for a  interaction optical frequency tunneling frequency    = (I p /2U p ) 1/2  -1 wavelength scaling in strong fields 5p 6 5p 5 inert gas (n-1)p 6 ns np 6 Can we devise an equivalent interaction? alkali atom

23. potassium (4.2 eV) 3.6  m, 1.2 TW/cm 2 h 4s 4p 3p 6  = 1.2 5p 6 5p 5 6 s 5p 5 h xenon (12.1 eV) 0.8  m, 70 TW/cm 2 UpUp electron distributions: scaled interaction

24. CCD Spectrometer 3-4  m HHG 1 ps alkali oven Cesium, 3.4  m H9H7 H5 H13 H11 high harmonics: scaled interaction you can really see these harmonics!

25. low frequency limit:  1  Large ponderomotive energy U p   2  Access tunnel ionization in more atoms  atom  Paradigm for laser-atom interaction test scaling laws accessible to control schemes simplify metrology heading towards extremes

26. ponderomotive or quiver energy: U p = 2  /4 displacement:  = 2 E neutral atoms in large ponderomotive potentials TDSE-SAE calculation (Kulander) x-ray FEL produce unprecedented electron (10U p ) and photon (3U p ) energies.

27. high frequency limit:  atom ;  >> 1 SF limit:  o  1 au heading towards extremes 4 th generation: HHG x-ray lasers x-ray fel synchrotrons x-ray FEL GW of x-rays!

28. “Resonance”  w  -2 (1+K 2 ) Lab framee - frame For  = 10 3  10 nm  e - N S S N S N S N S N N S N S N S N S N S S N S N S N Wiggler B-field w ~ cm  = (1 – v 2 /c 2 ) -1/2 fel physics: the basics

29. fel physics: configurations fel oscillators are well established facilities. operate from the far-IR — visible. high average power performance. limited by optics. high peak power (GW). short wavelength operation (1A). SASE 1 st observed in 1998 (LANL, UCLA, BNL). 109 nm light in March 2000 (TESLA, Hamburg). poor temporal “coherence”. excellent temporal “coherence”. superior & energy stability wavelength limited by availability of seed. excellent temporal “coherence”. short wavelength operation (x-rays). 1 st demonstration Dec 1999 (BNL).

30. SLAC project Linac Coherent Light Source (LCLS) 1.5-15 A, 10 12 /pulse, 200 fs, 120 Hz commissioning 2007-08 shorter means bigger: SASE x-fel projects

31. atomic physics thrust

32. science with x-fel Five experiments slated for first operations see 2000 BESAC report “LCLS: The first experiments” at www.er.doe.gov/production/bes/BESAC/pubs.html. target studies: atomic physics femotchemistry nanoscale dynamics in condensed phase plasma & warm dense matter structural studies on single biomolecules Real answer: No one knows?

33. xenon at 10 14 W/cm 2 h double ionization in NS MP limit xenon at 770 nm and 790 nm total rate double ionization 5 ng 764f ng 764f photoelectron 770 nm Xe + Xe 2+ Rudati et al. PRL 92, 203001-1 (2004).

34. isolated core excitation Isolated Core Excitation Gallagher & Cooke (1978) Xe Xe + 5s 2 5p 5 5s 1 5p 6 Xe +* 5s 2 5p 5 Rydberg doubly excited ICE Rydberg state is a spectator, while the core electron is excited. used for studying doubly excited states in alkaline-earth atoms. 2e gnd state Rydberg blue light Rydberg core transition red light

35. Rydberg time FREEMAN 5s 2 5p 6 1 S 5s 2 5p 5 2 P 5s 2 5p 5 nf,ng Xe Xe + Xe ++ 5s 2 5p 4 3 P doubly excited FIRE 5s5p 6 nf,ng Xe +* 5s5p 6 2 S field independent resonant enhancement 5 ng 764f ng 764f photoelectron 770 nm Xe + Xe 2+ transient Rydberg population is shelved, while the core electron is excited. the differential shift between Rydberg & doubly excited states is near zero. unlike ICE, the Rydberg electron is not a simple spectator in FIRE. scheme of Charalambidis et al. holds at low intensity, U p   E PRA 50, R2822 (1994).