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**Attosecond Flashes of Light**

– Illuminating electronic quantum dynamics – XXIIIrd 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**

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

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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 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

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**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

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**Supercontinuum generation**

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**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

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**High-(order) harmonic generation**

first signs intensity: W/cm2 wavelength: nm pulse duration: 1 ps McPherson et al. J. Opt. Soc. Am. B 21, 595 (1987)

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**High-(order) harmonic generation**

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

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**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

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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(t) Intensity I ~ W/cm2 Force F = 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 = 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)=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 = Il29.33 mm21014 W/cm2 ap= x0 = eE0 w2 ponderomotive radius

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**High-(order) harmonic generation**

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

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**High-harmonic generation**

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

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**Isolated Attosecond-pulse production**

(the conventional method) Hentschel et al. (Krausz group) Nature 414, 509 (2001) high- pass filter “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 j CEP j+p/2 Baltuška et al. Nature 421, 611 (2003) ~ 6 femtosecond CEP (Absolute phase) stabilized laser pulse

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**Attosecond Beamline at Berkeley**

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**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

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**Mo/Si multilayer mirror**

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**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

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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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Autocorrelation linear (no crystal) nonlinear (with crystal)

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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 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:

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

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

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

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**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

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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 Dj=?

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Quantum “Motion”

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Wave packets

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**Ionization Photoelectric effect (direct transition)**

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

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**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 = Il29.33 mm21014 W/cm2 ap= x0 = eE0 w2 ponderomotive radius

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**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

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**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:

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**Keldysh formalism Photoelectric effect (direct transition)**

1st 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) 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)

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**Keldysh formalism Strong electric field (Tunneling) U: barrier height**

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

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**Strong-Field Approximation**

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

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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)=|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

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Wavepacket spreading

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