1. photoelectron energy distribution for 1.6 eV photons xenon at 10 14 W/cm 2 h “photon description” helium at 10 15 W/cm 2 “dc-tunneling picture” strong-field atomic physics I Louis DiMauro OSU 2005

2. understand the limit where H int  H o probe on a time-scale where t < t o guide dynamics by tailoring H int (t) time-dependent Schrődinger equation [  o   int (t)]  (t)  iħ  (t)  strong-field atomic physics I Louis DiMauro OSU 2005

3. photoelectric effect electron energy E e = h - ip transition probability: P =  F  where   cm 2, F   /cm 2 s,   s consider cw-light:  = (1A) 2 = 10 -16 cm 2 for P  1: F ~ 10 16  /cm 2 s or intensity I ~ 10 -3 W/cm 2 100 fs (10 -13 s) light pulse: for P  1: F ~ 10 29  /cm 2 s or intensity I ~ 10 10 W/cm 2 h ip 0 EeEe Einstein (1905)

4. multi-photon photoelectric effect transition probability: P =  a F   b F  or P =  2 F 2  where  2   a   b = cm 4 s ip 0 EeEe h h electron energy E e = 2h - ip b b a a 2-photon case (h  ip) 0 EeEe electron energy E e = nh - ip  h ~ 0 ip transition probability: P =  n F n  where  n  cm 2n s n-1 n-photon case (h  ip)

5. Tunnel Rate  1/E e E +-+- xx xx VV + = coulomb -1/x DC field xE Stark -1/x + xE xx -+-+ xx = dc field -xE stark -1/x - xE xx dc-tunnel ionization

6. ac-tunnel ionization electron current E-field electrons are emitted as burst every ½-cycle.

7.  << 1tunneling low frequency and/or high intensity “dc-tunneling picture” “photon description”  >> 1multiphotonhigh frequency and/or low intensity optical frequency tunneling frequency    Keldysh (1964) theory of ionization

8. + - r=5  10 -9 cm Coulomb Law E= q/r 2 ~ 5  10 9 V/cm  1au What laser intensity gives an equivalent field strength? hydrogen atom

9. 1.06  m, 4  10 13 W/cm 2 0.53  m, 8  10 12 W/cm 2 S=0 S=1 Xe: I p =12.1 eV E e = Nh - I p 0.53  m, N=6, E N =1.9 eV 1.06  m, N=11, E N =0.77 eV ATI:  N+S = (N+S)h - I p 0.53  m, S=1, E 7 =4.2 eV above-threshold ionization (ATI) à la Agostini

10. think in ponderomotive units !!!  ponderomotive or quiver energy: U p  2  /4  displacement:   2    For 800 nm (red) laser at 10 15 W/cm 2 U p  60 eV  50 au (25 A) motion of the free electron

11. xenon long pulse, 30 ps 1  m, 30 TW/cm 2 XeXe + ionization energy h Xe Xe + ionization energy +U p (I)  N+S (  ) = (N+S)h - I p – U p (  ) intensity-dependent energy ATI & ponderomotive threshold shift perturbation theory f(  )=  2n P 2n (cos  )

12. @electrons are repelled from regions of high intensity. @long pulse (adiabatic) quiver E  translational y x ponderomotive acceleration  N+S (r,  ) = (N+S)h - I p – U p (r,  ) + U p (r,  ) intensity-independent energy

13. Freeman et al. PRL 59, 1092 (1987) @ Xenon, 100 fs, 800 nm, 70 TW/cm 2 short pulse “resonant” ATI for short pulse the ponderomotive gradient is negligible.

14. 0 electron energy E 0 E 0 E E 0 I  E 0 electron energy @Experiment is a spatial and temporal average of intensity I(r,t). role of resonance

15. Field amplitude  22 Time  electric field E = E o sin  t oo velocity v(t) = E o /  [cos  t - cos  o ] + v o quiver drift for tunneling, v o =0 the simpleman’s picture of ionization quasi-classical description: Gallagher, PRL 61, 2304 (1988) Van Linden van den Heuvell & Muller, in Multiphoton Processes (1988) Corkum, Burnett & Brunel, PRL 62, 1259 (1989)

16. v(t) = E o /  [cos  t - cos  o ] Quiver Drift VV xx VV xx @ Maximum drift energy = 2U p. predictions of the simpleman Tunnel Rate  1/E e E  in the experiment, we detect the drift energy not quiver !! T = mv 2 /2 = 2U p cos 2  o

17. simpleman comparison to experiment 1 xenon 30 TW/cm 2 U p = 3 eV bad news! helium 1 PW/cm 2 U p = 50 eV good news!       remember U p   !!!

18. simpleman comparison to experiment 2 Agostini, Muller et al. 1s 2 2s 2 2p 6 3s 2 3p 6  1s 2 2s 2 2p 5 3s 2 3p 6 L-shell ionization e(200 eV) + dressing Simpleman sideband estimate: v(t) = E o /  [cos  t - cos  o ] + v o with v o  kinetic energy broadening: experiment: T o = 200 eV, U p = 20 meV  T = 6 sidebands good simpleman!

19. moving beyond the simpleman quantum model: TDSE-SAE K. Schafer et al. PRL 70, 1599 (1993) ~ 10 -4–5 helium, 0.8  m, 1 PW/cm 2 ideal case 10 Hz & 100 channel experiment: 100 e/shot or 1 e/ch*s, 10 5 range  28 hrs!

20. 1 au field adequate for atomic physics? n-photon ionization perturbation theory: P =  n F n  saturation (depletion): P    F s = (  n  ) -1/n helium (24 eV, 16-photons): F s = 10 33 p/s*cm 2 or E s ~ 0.1 au over-the-barrier ionization V(x) = -Ze 2 /x – eE o x solve for E o : E o = I p 2 /4q 3 Z helium: E o = 0.2 au answer: 1 au field is adequate for neutral atomic ionization!

21. for high sensitivity measurements baseline: 1 au field strength (3.5  10 16 W/cm 2 ) pulse: 100 fs duration & 4  m beam waist  1 mJ pulse energy typical laser produces a few Watts average power  10 3 pulses per second @kilohertz regenerative amplification (late 1980s): Mourou, Bado, Bouvier (Rochester) Saeed, Kim, DiMauro (BNL) Fayer (Stanford) … @seminal work (LLNL): Lowdermilk & Murray, J App. Phys. 51, 2436 (1980).

22. for kilohertz regenerative amplification @cw or quasi-cw pumping factors: absorption spectrum, lifetime, thermal coefficients, … @material properties damage, saturation fluence, … YLF, YAG, glass: millisecond lifetimes, broad absorption poor thermal properties, narrow emission  Ti:sapphire: microsecond lifetimes, narrow absorption good thermal properties, broad emission  @advantages of regenerative amplification: high amplification 10 6-8 excellent spatial mode good stability 1-3% rms

23. kHz regenerative amp circa MDCCCCLXXXVIII AD HR Pockels cell YLF head coupling polarizers PD1 Q-switch & trap PD1 dump out

24. extract maximum energy minimize optical damage 1000x stretcher positive GVD amplifier media ultra-fast laser oscillator * G. Mourou and Strickland (1985) Chirped Pulse Amplification (CPA) 1000x compressor negative GVD state-of-the-art systems  10 20 W/cm 2 kilohertz operation  10 16 W/cm 2 for amplifying short pulse

25. typical kHz experiment amptdc TOF/MS TMP UHV time  - metal faraday photodiode disc

26. 20 15 10 TW/cm 2 xenon, 1  m, 30ps high sensitivity results photoelectrontotal rate [  o   int (t)]  (t)  iħ  (t)  TDSE-SAE 10 20 30 TW/cm 2 HHG electrons

27. @ higher sensitivity  new insights scattering “rings” in high-order ATI xenon, 1  m, 10 13 W/cm 2

28.  1/2  “rings” appear within an energy window !  “rings” appearance is intensity dependent!  “rings” scale with ponderomotive energy Remember, U p  Intensity !! theory: Schafer & Kulander scattering “rings”: intensity dependence

29. scattering “rings”: short pulse xenon, 0.8  m, 50 fs exp1D argon, 0.8  m, 50 fs 1D: soft core potential: V(x) = -(1 + x 2 ) -1/2

30. helium: kHz experiment tomorrow’s plat du jour: helium & the rebirth of the classical picture 0.8  m 1 PW/cm 2 simpleman