typical kHz experiment amp tdc TOF/MS TMP UHV time -metal faraday photodiode disc

[o  int(t)](t)  iħ(t)  high sensitivity results HHG electrons photoelectron total rate [o  int(t)](t)  iħ(t)  TDSE-SAE 10 20 30 TW/cm2 20 15 10 TW/cm2 xenon, 1m, 30ps

plat du jour: helium & the rebirth of the classical picture helium: kHz experiment 0.8 m 1 PW/cm2 simpleman plat du jour: helium & the rebirth of the classical picture

strong-field atomic physics II Louis DiMauro log(electrons) electrons 1 PW/cm2 time-of-flight (s) ions +7 +5 +3 +1 argon charge states Lompre et al. (Saclay) He 800 nm 1.6 eV wavelength (nm) 16 14 10 12 8 log(photons) H51 H79 photons High harmonic generation L’Huillier et al. (Lund) Non-linear Non-resonant Non-perturbative

why helium? largest binding energy (Ip = 24.5 eV) of all neutral atoms total rate B. Walker et al., PRL 73, 1227 (1994) theory: He  He+ + e ADK TDSE-SAE OTB over-the-barrier (OTB) ionization: Eo = Ip2/4q3Z helium: Eo = 0.2 au (1.4 PW/cm2) R  I3/2 measurements: Is = 0.8 PW/cm2 (Eo = 0.15 au) Keldysh:  = (Ip/2Up)1/2 = 0.49 Up = 50 eV @ 0.8 m  = 50 au (25Å)  ao ~ 1Å

the simpleman’s picture of ionization quasi-classical description o electric field E = Eo sint Field amplitude  2 Time  velocity v(t) = Eo/[cost - coso] + vo quiver drift for tunneling, vo=0 Two Step Approach  Excitation  Field Motion (Continuum)

classical model: rescattering x(t) = Eo/2 (sint - sino + (o - t) cos o) Optical Cycles electron-core interaction ~ ½ cycle electron gains field energy Position collision 2 1 3 phases  collision trajectories Optical Cycle simple symmetry argument~ ½  contribute Position Time 3 5  Position Time 3 5  Position Time Re-examine the trajectories for collisions ½ return to the core!!

classical model: rescattering Schafer, Yang, DiMauro & Kulander PRL 70, 1599 (1993) P. Corkum PRL 71, 1994 (1993) excitation t=0 propagation ¼-cycle rescattering ½-cycle time  Invoke a Wave Packet View at the End. 3-step view of quasi-classical rescattering.

classical model: high harmonic connection HIGH HARMONIC RADIATION Helium, 800 nm Cutoff ~ 3Up + IP  3Up gas jet gas filled capillary Murnane & Kapteyn 800 nm 25 fs 1015 W/cm2 HHG log (number of photons) helium 16 14 12 10 8 wavelength (nm) H79 H51 table-top source of coherent short wavelength light. potential for generating attosecond (10-18 s) light pulses.

classical model: rescattering PHYSICAL CONSEQUENCE: electron capture results in odd harmonic photons. harmonic cutoff: (3Up + IP) rule !! elastic scattering yields energetic (10Up) electrons. inelastic e-2e scattering  multiple electron ejection. excitation t=0 propagation ¼-cycle rescattering ½-cycle time  3.17 Up cutoff return energy: T(t = tr) = 2Up (cos2 r + cos2 o - 2cos o cos r ) Cutoff rule: 3.17Up + Ip

quantum model: TDSE-SAE elastic rescattering tunnel (vo=0) v(t) = Eo/[cost - coso] backscatter ( = ) set: v(r) = -v(r) v(t > tr) = Eo/[(cost - cosr) – (cosr - coso)] initial bs velocity normal drift new elastic cutoff: T = 10Up quantum model: TDSE-SAE K. Schafer et al. PRL 70, 1599 (1993) Describe curves and highlight double rate Prompted work by many theory groups Emphasizes the power of kilohertz

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

rescattering: numerical method (Kulander) divide optical cycle into a large number of equally spaced time intervals and calculate a tunneling rate. at each phase of the field, launch a gaussian wave packet at the outer turning point of the suppressed effective potential with zero velocity. initial conditions are determined from SAE results. propagate in the combined field until it escapes or returns to the plane of the nucleus. returning trajectories are assumed to spread freely. allow for only one return of the wave packet. calculate the differential elastic cross-section using partial wave analysis. electron spectrum is determined by summing all time intervals. double ionization is calculated using field-free e-2e inelastic cross-section. spatial and temporal averaging is included for comparison to measurement.

elastic rescattering: experiment & theory helium, 0.8 m, 0.8 PW/cm2 the short-range physics is important. quantum diffusion reduces the effective rescattering. the recollision occurs in less than an optical cycle. Make comparison with Helium spectrum Describe the Quantum Calculation Describe all the PES studies performed

elastic rescattering: intensity dependence helium, 0.8 m Remember, Up  Intensity !! PW/cm2 in scaled energy, distributions look similar!

elastic rescattering: intensity dependence Rutherford (coulomb) scattering  b vo  3Up  

elastic rescattering: intensity dependence Rutherford predicts a 100-fold decrease in high energy electrons over intensity range of experiment. not bad for an experimentalist.

elastic rescattering: intensity dependence helium: experiment & theory energy (eV) Up coulomb e – He+

elastic rescattering: atomic dependence rescattering is sensitive to the atomic core (cross-section). 1 PW/cm2 coulomb e – He+ e – Ne+ intensity (W/cm2)

elastic rescattering: differential cross-section  b vo initial bs velocity normal drift vx(t) = Eo/[(cost - cosr) – cos (cosr - coso)] vy(t) = -Eo/[sin (cosr - coso)] Theta=0, vy=0 Theta=pi, vx=max Correlation between scattering angle and final energy relationship between scattered, , and detected, d, angles.

elastic rescattering: differential cross-section electron cutoff energy versus detector angle 8Up 6Up 2Up

elastic rescattering: differential cross-section helium, 0.8 m, 1 PW/cm2

elastic rescattering: differential cross-section helium: experiment & theory electron counts

quantum view Ken Kulander

strong-field double ionization time   m/q “direct” ionization multiple charge states readily observed in an intense laser field. some charge states cannot be described by a “single” rate.

helium double ionization: total rate two mechanisms result in the formation of He2+ !! He  He+ + e He+  He2+ + 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. Describe curves and highlight double rate Prompted work by many theory groups Emphasizes the power of kilohertz

we ran out of steam: computationally tomorrow’s plat du jour two-electron soup á la carte experiments pioneer the future

helium double ionization: polarization dependence 0.2 (NS) and 4 (sequential) PW/cm2 In neon, polarization dependence of NS and HHG agreed with classical analysis Dietrich et al. PRA 50, R3585 (1994)

helium double ionization: high sensitivity Experiment performed at two intensities. 0.8 PW/cm2 1/500 0.4 PW/cm2 1/1000 3He is used for coincidence measurement.

helium double ionization: high sensitivity 1800 “background” electrons 2 “signal” electrons The Needle in the Haystack

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)

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

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!

helium double ionization: electron distributions 4×1014 W/cm2 205M shots 45M He hits 1058 He2+ coin He+ He2+ 8×1014 W/cm2 double ionization results in “hotter” distribution than single ionization. distribution consistent with e-2e rescattering.

helium double ionization: classical interpretation electron energy (Up) counts (arb units) 100 1 .001 2 3 5 4 backscattered forward 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. 8×1014 W/cm2 e-2e Corkum (1993)

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

double ionization experiments: other atoms Frankfurt group Ar2+ & He2+ ion recoil (COLTRIMS) Ar2+ e-ion coincidence Freiburg group Ne2+ ion recoil (COLTRIMS) Ar2+ e-COLTRIMS Crete group Xe2+ e-ion coincidence Michigan group Ar2+ e-ion coincidence BNL group Ar2+ & Xe2+ e-ion coincidence

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