Attosecond Flashes of Light – Illuminating electronic quantum dynamics – XXIIIrd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research Group MPI – Kernphysik, Heidelberg

Fourier Transform

Contents Basics of short pulses and general concepts Attosecond pulse generation Mechanics of Electrons single electrons in strong laser fields Attosecond Experiments with isolated Atoms Multi-Particle Systems Molecules multi-electron dynamics (correlation) Attosecond experiments with molecules / multiple electrons Ultrafast Quantum Control of electrons, atoms, molecules Novel Directions/Applications Technology

Mathematics of Ultrashort pulses spectral phase Taylor expansion dispersion

absolute (carrier-envelope) phase

Windowed Fourier Transform ‘Gabor Transform’ frequency [arb. u.] frequency [arb. u.]

Contents Basics of short pulses and general concepts Attosecond pulse generation Mechanics of Electrons single electrons in strong laser fields Attosecond Experiments with isolated Atoms Multi-Particle Systems Molecules multi-electron dynamics (correlation) Attosecond experiments with molecules / multiple electrons Ultrafast Quantum Control of electrons, atoms, molecules Novel Directions/Applications Technology

Ultrashort Pulses 1 fs = 10-15 s 1000000000000000 work power = time Observation of fast processes concentration of energy in time and space Ref: Ulrich Weichmann, Department of Physics, Wuerzburg University

Short Pulses Intense Laser Fields Power = Energy Time 100 J 5 fs = = 20 GW e.g. THz, IR, vis., UV, X-ray e- e- Light conversion X+ X+ X+ X+ X+ e- e- e- Plasma e.g. attosecond pulses femtosecond laser pulse 20 GW (100 m)2 = 2  1016 W cm2 relativistic effects above 1018W/cm2

Supercontinuum generation

Attosecond pulse generation also known as: High-Order Harmonic Generation mechanism based on: sub-optical-cycle electron acceleration (laboratory-scale table-top) attosecond x-ray pulse atomic medium detector/ experiment femtosecond laser pulse laser intensity: >1014 W/cm2

High-(order) harmonic generation first signs intensity: 1015-1016 W/cm2 wavelength: 248 nm pulse duration: 1 ps McPherson et al. J. Opt. Soc. Am. B 21, 595 (1987)

High-(order) harmonic generation first signs M. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988) intensity: ~1013 W/cm2 wavelength: 1064 nm pulse duration: 1 ps

High-harmonic generation (HHG) 80 fs 800 nm 5·1014 W/cm2 1 kHz Zr + Parylene-N filter in Neon (Ne) in Xenon (Xe) H3 80 fs 800 nm 3·1014 W/cm2 1 kHz H11 H9 H7 H5 H13 H15

Contents Today Attosecond Pulses Classical and quantum mechanics of electrons and experiments with isolated atoms - Classical Motion of Electrons definition of important quantities - Quantum Mechanics · Electron dynamics in (intense) laser fields · Ionization - High-harmonic generation: quantum mechanical view - Experiments with attosecond Pulses - Quantum state interferometry

Forces on Electrons in Atoms E(t) Intensity I ~ 1015 W/cm2 Force F = 14 nN Mass me= 9.1∙10-31 kg acc. a = 1.5∙1022 m/s2 e- F 2000 as velocity v = 3 ∙106 m/s = 1% c (speed of light) “assumed constant acceleration from rest for 200 attoseconds” Grundzustandswellenfunktionen aus \\HHG\Fortran\03_03_10 E(t) optical light wave 1 attosecond (1 as = 10-18 s) compares to 1 second as 1 second compares to more than the age of the universe (~15 Billion years)

Electron in Laser Field E(t)=E0cos(wt) linearly polarized along x axis a(t)= -eE0cos(wt) acceleration v(t)= - sin(wt) eE0 w velocity (dt a) x(t)= cos(wt) eE0 w2 position (dt v) Up=Ekin,av= e2E02 4mw2 eV ponderomotive potential = Il29.33 mm21014 W/cm2 ap= x0 = eE0 w2 ponderomotive radius

High-(order) harmonic generation first signs M. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988) intensity: ~1013 W/cm2 wavelength: 1064 nm pulse duration: 1 ps

Three-step model P. Corkum, Phys. Rev. Lett. 71, 1994 (1993) Kulander et al. Proc. SILAP, 95 (1993)

High-harmonic generation (HHG)

High-(order) harmonic generation first signs M. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988) intensity: ~1013 W/cm2 wavelength: 1064 nm pulse duration: 1 ps

High-harmonic generation Hentschel et al. (Krausz group) Nature 414, 509 (2001) P. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

Isolated Attosecond-pulse production (the conventional method) Hentschel et al. (Krausz group) Nature 414, 509 (2001) high- pass filter “cos pulse” “sin pulse”

Attosecond pulse generation Hentschel et al. Nature 414, 509 (2001)

Absolute Phase (CEP) effects CEP j CEP j+p/2 Baltuška et al. Nature 421, 611 (2003) ~ 6 femtosecond CEP (Absolute phase) stabilized laser pulse

Attosecond Beamline at Berkeley

Attosecond Beamline at Berkeley Time-of-Flight Detection of electrons Velocity-Map imaging of electrons or ions Piezo- controlled split mirror MCP piezo High-harmonic generation Filter on pellicle Split mirror 6-fs IR pulse CEP stabilized Iris Metal filter XUV grating X-ray CCD CCD

Mo/Si multilayer mirror

Attosecond Beamline at Berkeley Time-of-Flight Detection of electrons Velocity-Map imaging of electrons or ions Piezo- controlled split mirror MCP piezo High-harmonic generation Filter on pellicle Split mirror 6-fs IR pulse CEP stabilized Iris Metal filter XUV grating X-ray CCD CCD

Short pulse measurement “to measure a fast event, you need an at least equally fast probe” - Autocorrelation ‘Auto...’ -> self... - Frequency-Resolved Optical Gating FROG, building upon Autocorrelation - Temporal Analysis by Dispersing a Pair Of Light Electric Fields TADPOLE - Spectral Interferometry for Direct Electric Field Reconstruction SPIDER, building upon TADPOLE

Autocorrelation linear (no crystal) nonlinear (with crystal)

Attosecond autocorrelation measurements Tzallas et al.(Witte, Tsakiris) Nature 426, 267 (2003)

Attosecond autocorrelation measurements isolated pulses Sekikawa et al.(Watanabe) Nature 432, 605 (2004)

Attosecond autocorrelation measurements pulse trains Tzallas et al.(Witte, Tsakiris) Nature 426, 267 (2003)

FROG idea analysis by iterative algorithm measure spectrum as D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993) measure spectrum as a function of time delay 2-dim. data sets: ‘FROG-trace’ analysis by iterative algorithm Ref: http://www.physics.gatech.edu/frog/

Goulielmakis et al. (Krausz group), Science 305, 1267 (2004) Streaking Goulielmakis et al. (Krausz group), Science 305, 1267 (2004)

FROG-CRAB Y. Mairesse and F. Quéré, Science 71, 011401 (2005)

high-harmonic generation intense laser field acting on single atom probability distribution p(x,y)=|Y(x,y)|2 for the electronic wavefunction laser polarization Film zusammengestellt aus \\HHG\Fortran\03_03_11 Wellenfunktion gegen py aus \\HHG\Fortran\03_03_11\Evaluate corrected

Time-dependent quantum mechanics

Time-dependent quantum mechanics position and momentum space representation ~

Wave packets

Coherence Also for Quantum wavepackets Dj=?

Quantum “Motion”

Wave packets

Ionization Photoelectric effect (direct transition) Strong electric field (Tunneling) |1> U: barrier height |0> w: barrier width 1st order perturbation theory tunneling rate

Electron in Laser Field E(t)=E0cos(wt) linearly polarized along x axis a(t)= -eE0cos(wt) acceleration v(t)= - sin(wt) eE0 w velocity (dt a) x(t)= cos(wt) eE0 w2 position (dt v) Up=Ekin,av= e2E02 4mw2 eV ponderomotive potential = Il29.33 mm21014 W/cm2 ap= x0 = eE0 w2 ponderomotive radius

Electron in Laser Field E(t)=E0cos(wt) linearly polarized along x axis a(t)= -eE0cos(wt) acceleration v(t)= - sin(wt) eE0 w velocity (dt a) A(t)= -e dt’ E(t’) = v(t) - t Vector potential (Coulomb gauge) momentum/velocity gauge Schrödinger equation: (dipole approximation) length gauge

Electron in Laser Field E(t)=E0cos(wt) linearly polarized along x axis a(t)= -eE0cos(wt) acceleration v(t)= - sin(wt) eE0 w velocity (dt a) A(t)= -e dt’ E(t’) = v(t) - t Vector potential (Coulomb gauge,  A=0) Schrödinger equation: (dipole approximation) momentum/velocity gauge [H,p]=0  p conserved, solution:

Keldysh formalism Photoelectric effect (direct transition) 1st order perturbation theory |1> |0> Strong electric field (Tunneling) tunneling rate w: barrier width U: barrier height

ADK formula Ammosov, Delone, and Krainov, Sov. Phys. JETP 64, 1191 (1986) Ionization rate (in a.u.): Strong electric field (Tunneling) tunneling rate w: barrier width U: barrier height Experimental checks: Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)

Keldysh formalism Strong electric field (Tunneling) U: barrier height tunneling rate Strong electric field (Tunneling) w: barrier width U: barrier height

Strong-Field Approximation Strong electric field V(t)=rE(t) V r e-

High Harmonics Quantum Mechanical

high-harmonic generation intense laser field acting on single atom probability distribution p(x,y)=|Y(x,y)|2 for the electronic wavefunction laser polarization Film zusammengestellt aus \\HHG\Fortran\03_03_11 Wellenfunktion gegen py aus \\HHG\Fortran\03_03_11\Evaluate corrected

Wavepacket spreading