1. Attosecond Flashes of Light
– Illuminating electronic quantum dynamics –
XXIIIrd 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
‘Gabor Transform’
frequency [arb. u.]
frequency [arb. u.]

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 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

9. 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

10. Supercontinuum generation

11. 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

12. 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)

13. 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

14. 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

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(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)

17. 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

18. 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

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

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

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

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

25. 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

26. Attosecond Beamline at Berkeley

27. 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

28. Mo/Si multilayer mirror

29. 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

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

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 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:

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

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

38. 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
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Wellenfunktion gegen py aus \\HHG\Fortran\03_03_11\Evaluate corrected

39. Time-dependent quantum mechanics

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

41. Wave packets

42. Coherence
Also for Quantum wavepackets
Dj=?

43. Quantum “Motion”

44. Wave packets

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

46. 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

47. 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

48. 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:

49. Keldysh formalism Photoelectric effect (direct transition)
1st 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)
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)

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

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

53. High Harmonics Quantum Mechanical

54. 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

55. Wavepacket spreading