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

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Fourier Transform

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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

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Mathematics of Ultrashort pulses spectral phase Taylor expansion dispersion

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absolute (carrier-envelope) phase

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

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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

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

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Short Pulses Intense Laser Fields femtosecond laser pulse Plasma e-e- e-e- e-e- e-e- X+X+ e-e- X+X+ X+X+ X+X+ X+X+ Power = Energy Time 100 J 5 fs = = 20 GW 20 GW (100 m) 2 = 2 10 16 W cm 2 relativistic effects above 10 18 W/cm 2

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Supercontinuum generation

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Attosecond pulse generation detector/ experiment atomic medium femtosecond laser pulse also known as: High-Order Harmonic Generation laser intensity: >10 14 W/cm 2 attosecond x-ray pulse mechanism based on: sub-optical-cycle electron acceleration (laboratory-scale table-top)

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High-(order) harmonic generation first signs McPherson et al. J. Opt. Soc. Am. B 21, 595 (1987) intensity: 10 15 -10 16 W/cm 2 wavelength: 248 nm pulse duration: 1 ps

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High-(order) harmonic generation first signs M. Ferray, A. LHuillier et al. J. Phys. B 21, L31 (1988) intensity: ~10 13 W/cm 2 wavelength: 1064 nm pulse duration: 1 ps

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in Xenon (Xe) H3 H5H7H9H11 H15 H13 80 fs 800 nm 5·10 14 W/cm 2 1 kHz Zr + Parylene-N filter in Neon (Ne) 80 fs 800 nm 3·10 14 W/cm 2 1 kHz High-harmonic generation (HHG)

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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

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Forces on Electrons in Atoms e-e- F E(t)E(t) Intensity I ~ 10 15 W/cm 2 Force F = 14 nN Mass m e = 9.110 -31 kg acc. a = 1.510 22 m/s 2 velocity v = 3 10 6 m/s = 1% c (speed of light) assumed constant acceleration from rest for 200 attoseconds 2000 as optical light wave E(t)E(t) 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)

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Electron in Laser Field E(t)=E 0 cos( t) a(t)= -eE 0 cos( t) v(t)= - sin( t) eE 0 x(t)= cos( t) eE 0 linearly polarized along x axis acceleration velocity ( dt a) position ( dt v) ponderomotive potential ponderomotive radius U p =E kin,av = e2E02e2E02 4m a p = x 0 = eE 0 = I 2 9.33 eV m 10 14 W/cm 2

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High-(order) harmonic generation first signs M. Ferray, A. LHuillier et al. J. Phys. B 21, L31 (1988) intensity: ~10 13 W/cm 2 wavelength: 1064 nm pulse duration: 1 ps

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

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High-harmonic generation (HHG)

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High-(order) harmonic generation first signs M. Ferray, A. LHuillier et al. J. Phys. B 21, L31 (1988) intensity: ~10 13 W/cm 2 wavelength: 1064 nm pulse duration: 1 ps

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H3 H5 H7 H9 H11 H15 H13 High-harmonic generation P. Corkum, Phys. Rev. Lett. 71, 1994 (1993) Hentschel et al. (Krausz group) Nature 414, 509 (2001)

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

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

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

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Attosecond Beamline at Berkeley

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

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Mo/Si multilayer mirror

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

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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

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linear (no crystal) nonlinear (with crystal) Autocorrelation

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

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

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

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

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

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

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high-harmonic generation intense laser field acting on single atom probability distribution p(x,y)=| (x,y)| 2 for the electronic wavefunction laser polarization

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Time-dependent quantum mechanics

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Time-dependent quantum mechanics position and momentum space representation ~ ~ ~

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Wave packets

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Coherence Also for Quantum wavepackets

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Quantum Motion

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Wave packets

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

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Electron in Laser Field E(t)=E 0 cos( t) a(t)= -eE 0 cos( t) v(t)= - sin( t) eE 0 x(t)= cos( t) eE 0 linearly polarized along x axis acceleration velocity ( dt a) position ( dt v) ponderomotive potential ponderomotive radius U p =E kin,av = e2E02e2E02 4m a p = x 0 = eE 0 = I 2 9.33 eV m 10 14 W/cm 2

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Electron in Laser Field E(t)=E 0 cos( t) a(t)= -eE 0 cos( t) v(t)= - sin( t) eE 0 linearly polarized along x axis acceleration velocity ( dt a) Vector potential (Coulomb gauge) A(t)= -e dt E(t) = v(t) - t Schrödinger equation: (dipole approximation) length gauge momentum/velocity gauge

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Electron in Laser Field E(t)=E 0 cos( t) a(t)= -eE 0 cos( t) v(t)= - sin( t) eE 0 linearly polarized along x axis acceleration velocity ( dt a) Vector potential (Coulomb gauge, A=0) A(t)= -e dt E(t) = v(t) - t Schrödinger equation: (dipole approximation) momentum/velocity gauge [H,p]=0 p conserved, solution:

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

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

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

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

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High Harmonics Quantum Mechanical

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high-harmonic generation intense laser field acting on single atom probability distribution p(x,y)=| (x,y)| 2 for the electronic wavefunction laser polarization

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Wavepacket spreading

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