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

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Presentation on theme: "Attosecond Flashes of Light – Illuminating electronic quantum dynamics – XXIII rd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research."— Presentation transcript:

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

2 Fourier Transform

3 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

4 Mathematics of Ultrashort pulses spectral phase Taylor expansion dispersion

5 absolute (carrier-envelope) phase

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

7 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

8 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

9 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

10 Supercontinuum generation

11 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)

12 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

13 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

14 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)

15 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

16 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)

17 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

18 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

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

20 High-harmonic generation (HHG)

21 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

22 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)

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

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

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

26 Attosecond Beamline at Berkeley

27 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

28 Mo/Si multilayer mirror

29 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

30 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

31 linear (no crystal) nonlinear (with crystal) Autocorrelation

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

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

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

35 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)

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

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

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

39 Time-dependent quantum mechanics

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

41 Wave packets

42 Coherence Also for Quantum wavepackets

43 Quantum Motion

44 Wave packets

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

46 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

47 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

48 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:

49 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

50 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

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

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

53 High Harmonics Quantum Mechanical

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

55 Wavepacket spreading


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