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

2. InterAtto – where we are from... http://www.mpi-hd.mpg.de
/mpi/en/pfeifer

3. InterAtto Setup Phase I

4. InterAtto Setup Phase II

5. InterAtto Setup Phase III

6. InterAtto Setup Phase IV

7. InterAtto Setup Phase IVb

8. CEP Control

9. Laser Pulses: 6 fs

10. Fun with the laser

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

12. Quantum World http://www.almaden.ibm.com/vis/stm/images/stm15.jpg

13. Quantum World Length Scales

14. Scientific Time Scales
shortest light pulse 80 as
1 second
Age of Universe
“human” time scale
molecular time scale
geological/astronomical time scale
electronic time scale
nuclear time scale

15. How “long” is a femtosecond?
earth
moon
Our laser pulses:
5 fs
wavelength of blue light
A laser pulse of
5 fs duration (time) is 1.5 m long (space)
Ref: Physics Department, University of Wuerzburg

16. Snapshots of Fast Processes
exposure time too large:
blurred image insufficient temporal resolution
exposure time short enough: sharp image
sufficient temporal resolution
Ref: Physics Department, University of Wuerzburg

17. Why use ultrashort laser pulses?
1877, EadweardMuybridge, Leland Stanford
Ref: Physics Department, University of Wuerzburg

18. Molecular Dynamics Absorption of Light Vibration Dissociation
Ref: Physics Department, University of Wuerzburg

19. Evolution of Ultrafast Science
Measurement of molecular dynamics (internuclear wavepackets)
Control of some chemical reactions
Grundzustandswellenfunktionen aus \\HHG\Fortran\03_03_10
moving towards: Measurement and Control of electron dynamics
Ref: Physics Department, University of Wuerzburg

20. Estimation of Quantum Time Scalesħ
mpa02 1
2000
Molecular rotation frequency
=  
Tr=300 fs D mp 1
2000 1 50  
Molecular vibration frequency
  
Tv=7 fs D me  1
Electron vibration frequency
 
Grundzustandswellenfunktionen aus \\HHG\Fortran\03_03_10
Te=150 as 1 L I ħ
mea02
Electron rotation frequency
=  =

21. Quantum Level Spacings
Separation: Electronic, Vibrational, Rotational
Ytotal=yel,nFvib,mfrot,l
Energy
Ye,2
Ye,1 5
Ye,0
frot,l
Fv,n
Internuclear Distance

22. femtosecond laser pulses
5 fs
300 meV
e.g. vibrational, rotational states

23. attosecond pulses as 1 as = 10-18 s light travels: 0.3 nm (3 Ångstrom)
30 eV as
Classical e- orbit period, Hydrogen: 152 as
1s-2s/p wavefunction period
- Hydrogen: ~ 400 as
- H-like Uranium ~ 0.05 as
Auger (core-hole) lifetimes: ~100 as-~10 fs
electronic states

24. Quantum World Time Scales
300 nm optical cycle
Short pulses can be used to monitor and control relative atomic motion
and electronic motion

25. ultrafast quantum motion
femtosecond
pulsed lasers
(IR, Vis., UV)
example:
diatomic molecule
internuclear distance d ~ Å
vibrational period
T > 5 fs (5∙10-15 s)
spectroscopic & quantum control
techniques
d [Å]
|molecule|2
Courtesy: M. Erdmann, V. Engel
Na2
vibrations, relative atomic motion
pump–probe
CARS,
pump–dump,
STIRAP …

26. “fast” Nobel prizes 1967, Chemistry 1999, Chemistry
100 nanosec.
1967, Chemistry
“...for their studies of extremely fast chemical
reactions, effected by disturbing the equlibrium
by means of very short pulses of energy.“
1 picosec.
Manfred Eigen George Porter Ronald Norrish
1999, Chemistry
“...for his studies of the transition states of chemical reactions
using femtosecond spectroscopy.“
Ahmed Zewail
2005, Physics (1/2)
10 femtosec.
“...for their contributions to the development of
laser-based precision spectroscopy,
including the optical frequency comb technique.“
Theodor Hänsch John Hall

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

28. Ultrashort x-ray/XUV Pulses
FreeElectronLasers
and HighHarmonicGeneration
~100 as
<1 J
>1 nm
wavelength
~1.5 Å
pulse energy
~1 mJ
pulse duration
~1 mm
~20 fs
1 fs (proj.)
~200 m
fully coherent

29. Röntgen-“X“-Rays 1901, Physics high spatial
“... in recognition of the extraordinary services
he has rendered by the discovery of
the remarkable rays subsequently named after him.“
Wilhelm C. Röntgen
1914, Physics
M. von Laue
1915, Physics
W.H.Bragg, W.L.Bragg
1917, Physics C. G. Barkla
1924, Physics M. Siegbahn
1927, Physics
A. H. Compton
1936, Chemistry
P. Debye
1962, Chemistry
M. F. Perutz, J. C. Kendrew
1962, Medicine
F. Crick, J. Watson, M. Wilkins
1964, Chemistry
D. Crowfoot Hodgkin
1976, Chemistry
W. N. Lipscomb
l (wavelength)
1979, Medicine
A. M. Cormack, G. N. Hounsfield
1981, Physics
M. Siegbahn
1985, Chemistry
H. A. Hauptman, J. Karle
1988, Chemistry
J. Deisenhofer, R. Huber, H. Michel
2002, Physics
Riccardo Giacconi
speed of light c =
T (optical cycle)
high spatial
resolution comes with high temporal resolution
FEL

30. ultrafast quantum motion
attosecond
pulsed source
(soft x-ray)
example:
diatomic molecule
example:
electrons in atoms
internuclear distance d ~ Å
orbital size ~ Å e-
vibrational period
T < 5 fs
orbital period
T < (<<) 1 fs
attosecond = s ?
attosecond
spectroscopy/
quantum control methods ?
|molecule|2 x y
E-field polarization
5 nm
|electron|2
H-atom ionizing

31. Fundamental Question(s) of Attosecond/Ultrafast Science
observe
understand
control
Quantum Motion (Dynamics) of Electrons
- Coherence among electronic states
- Correlations (Entanglement) in 2-or-more-electron systems
observation on very short time scales
molecular bonding dynamics
(beyond Born-Oppenheimer phenomena?)
- Quantum Control (steer electrons in atoms and molecules)
- Dynamics in Strong Laser Fields

32. Methods of Attosecond Physics
Experimental
Theoretical
- Laser pulses (Femtosecond duration)
- Carrier-envelope phase (CEP) stabilization (reproducability of electric field)
- Frequency conversion
(Laser to XUV)
- Vacuum system (due to absorption of XUV light) - X-ray optics (refocusing of attosecond pulses - Precision control of time delay
(motion control of nm accuracy) - X-ray spectroscopy (attosecond pulse spectra) - Photoelectron/-ion spectroscopy (measurement of photoproducts)
- Fourier Techniques (Laser Pulses and Data Analysis)
- Maxwell’s equations (Propagation of light)
- Schrödinger equation (Propagation of quantum states) - Newton equation (Propagation of classical states)
-Multi-particle wavefunctions (electron-ion or electron-electron)
- Split-step operator methods
(solution of time-dependent equations)
-Density matrices (to treat decoherence)

33. 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

34. Contents Today Basics of short pulses and general concepts
Attosecond pulse generation
- History of Quantum Physics
- Coherence and Lasers
- Short Pulse Concepts and Mathematics
- High-harmonic generation (HHG) - Attosecond Pulse generation
- Measurement of short pulses/events

35. Quantum History some selected milestones
1678
Christian Huygens
Light is wave-like
1704
Sir Isaac Newton
Light is particle-like (travel in straight lines and reflect from surfaces), “aetheral medium” for refraction
1740's
Leonhard Euler
Light is wave-like, Huygens approach became prevailing theory afterwards
1788
Joseph Louis Lagrange
Stated a re-formulation of classical mechanics that would be critical to the later development of a quantum mechanical theory of matter and energy.
1803
Thomas Young
Double-slit experiment supports the wave theory of light and demonstrates the effect of interference.
1807
John Dalton
Published his Atomic Theory of Matter.
1811
Amedeo Avogadro
proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules, Atomic Theory of Matter.
1833
William Rowan Hamilton
Stated a reformulation of classical mechanics that arose from Lagrangian mechanics; later: connection to quantum mechanics as understood through Hamiltonian mechanics.

36. Quantum History (cont’d) some selected milestones
1839
Alexandre Edmond Becquerel
Observed the photoelectric effect via an electrode in a conductive solution exposed to light.
1873
James Clerk Maxwell
Published his theory of electromagnetism in which light was determined to be an electromagnetic wave (field) that could be propogated in a vacuum.
1877
Ludwig Boltzmann
Suggested that the energy states of a physical system could be discrete.
1885
Johann Balmer
Discovered that the four visible lines of the hydrogen spectrum could be assigned integers in a series
1888
Johannes Rydberg
Modified the Balmer formula to include the other series of lines, producing the Rydberg formula
1896
Henri Becquerel
Discovered “radioactivity”, certain elements or isotopes spontaneously emit one of three types of energetic entities: alpha particles (positive charge), beta particles (negative charge), and gamma particles (neutral charge).
1897
J. J. Thomson
Showed that cathode rays (1838) bend under the influence of both an electric field and a magnetic field, negatively charged subatomic electrical particles or “corpuscles” (electrons), stripped from the atom; and in 1904 proposed the “plum pudding model“, calculated the mass-to-charge ratio of the electron

37. Quantum History (cont’d) some selected milestones
1900
Max Planck
To explain black body radiation (1862), he suggested that electromagnetic energy could only be emitted in quantized form, i.e. the energy could only be a multiple of an elementary unit E = hν, where h is Planck's constant and ν is the frequency of the radiation.
1905
Albert Einstein
Determines the equivalence of matter and energy
First to explain the effects of Brownian motion as caused by the kinetic energy (i.e., movement) of atoms, which was subsequently, experimentally verified by Jean Baptiste Perrin, thereby settling the century-long dispute about the validity of John Dalton's atomic theory.
To explain the photoelectric effect (1839), he postulated, as based on Planck’s quantum hypothesis (1900), that light itself consists of individual quantum particles (photons).
1907 [1911 pub.]
Ernest Rutherford
alpha particles at gold foil and noticed that some bounced back thus showing that atoms have a small-sized positively charged atomic nucleus at its center.

38. Quantum History (cont’d) some selected milestones
1909
Geoffrey Ingram Taylor
Demonstrated that interference patters of light were generated even when the light energy introduced consisted of only one photon: wave-particle duality of matter and energy was fundamental to the later development of quantum field theory.
1909 and 1916
Albert Einstein
Showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum p = h / λ, making them full-fledged particles.
1913
Robert Andrews Millikan
"oil drop" experiment published, determines the electric charge of the electron. Determination of the fundamental unit of electric charge made it possible to calculate the Avogadro constant (which is the number of atoms or molecules in one mole of any substance) and thereby to determine the atomic weight of the atoms of each element.
Niels Bohr
To explain the Rydberg formula (1888), Bohr hypothesized that negatively charged electrons revolve around a positively charged nucleus at certain fixed “quantum” distances, each of these “spherical orbits” has a specific energy associated with it such that electron movements between orbits requires “quantum” emissions or absorptions of energy.
Ref:

39. Quantum History (cont’d) some selected milestones
1918
Ernest Rutherford
Discovers the proton
1922
Otto Stern and Walther Gerlach
Stern-Gerlach experiment detects discrete values of angular momentum for atoms in the ground state passing through an inhomogeneous magnetic field leading to the discovery of the spin of the electron.
1923
Louis De Broglie
Postulated that electrons in motion are associated with waves the lengths of which are given by Planck’s constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p.
1924
Satyendra Nath Bose
His work on quantum mechanics provides the foundation for Bose-Einstein statistics, the theory of the Bose-Einstein condensate, and the discovery of the boson.
1925
Werner Heisenberg
Developed the matrix mechanics formulation of QM
Wolfgang Pauli
Outlined the “Pauli exclusion principle” which states that no two identical fermions may occupy the same quantum state simultaneously.
1926
Gilbert Lewis
Coined the term photon, which he derived from the Greek word for light, φως (transliterated phôs).
Ref:

40. Quantum History (cont’d) some selected milestones
1926
Erwin Schrödinger
Used De Broglie’s electron wave postulate (1924) to develop a “wave equation”, gave the correct values for spectral lines of the hydrogen atom.
1927
Clinton Davisson and Lester Germer
demonstrate the wave nature of the electron in the Electron diffraction experiment
Walter Heitler
Used Schrödinger’s wave equation (1926) to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond.
1928
Linus Pauling
Outlined the nature of the chemical bond in which he used Heitler’s quantum mechanical covalent bond model (1927) to outline the quantum mechanical basis.
1929
John Lennard-Jones
Introduced the linear combination of atomic orbitals approximation for the calculation of molecular orbitals.
1932
Werner Heisenberg
Applied perturbation theory to the two-electron problem and showed how resonance arising from electron exchange could explain exchange forces.
Ref:

41. Quantum History (cont’d) some selected milestones
1948
Richard Feynman
Stated the path integral formulation of quantum mechanics.
1949
Freeman Dyson
Determined the equivalence of the formulations of quantum electrodynamics that existed by that time — Richard Feynman's diagrammatic path integral formulation and the operator method developed by Julian Schwinger and Sin-Itiro Tomonaga. A by-product of that demonstration was the invention of the Dyson series.
1960
...
today
Theodore Maiman
many more people
demonstration of the first Laser
some active fields of research:
- quantum information/computing
- macroscopic quantum systems (“building Schrödinger’s cat”)
- correlated/entangled quantum systems (applications: giant
magnetoresistance (hard drives), superconductivity) - time-resolved quantum dynamics - coherent/quantum control
Ref:

42. Contents Today Basics of short pulses and general concepts
Attosecond pulse generation
- History of Quantum Physics
- Coherence and Lasers
- Short Pulse Concepts and Mathematics
- High-harmonic generation (HHG) - Attosecond Pulse generation
- Measurement of short pulses/events

43. Coherence Dj=? latin: cohærere "cohere,“
from com- "together" + hærere "to stick“ (etymonline.com)
Dj=?

44. Spatial and Temporal Coherence
Space/Wavevector(momentum)
Domain
Time/Frequency Domain
intensity
time
intensity
frequency
Ref:

45. How to create coherence?
space, r
frequency, w
time

46. LASERs (Light Amplification by Stimulated Emission of Radiation)
gain medium spontaneous and stimulated emission +
resonator imprint spatial and temporal pulse shape “coherence” =
LASER

47. Stimulated emission ...and pumping

48. resonator stationary E(x,y,z) (compare QM ground state)
solve Maxwell’s equations with
boundary conditions (mirrors) to find
stationary E(x,y,z)
(compare QM ground state)

49. resonator modes Laguerre Gaussian modes (cylindrical coordinates)

50. LASERs (Light Amplification by Stimulated Emission of Radiation)
gain medium spontaneous and stimulated emission +
resonator imprint spatial and temporal pulse shape “coherence” =
LASER

51. Laser System
Grundzustandswellenfunktionen aus \\HHG\Fortran\03_03_10

52. Maxwell’s Equations Resulting wave equations ... and their solution
for the case of a temporally and spatially invariant medium

53. Fourier Transform

54. Contents Today Basics of short pulses and general concepts
Attosecond pulse generation
- History of Quantum Physics
- Coherence and Lasers
- Short Pulse Concepts and Mathematics
- High-harmonic generation (HHG) - Attosecond Pulse generation
- Measurement of short pulses/events

55. Mathematics of Ultrashort pulses
spectral phase
Taylor expansion
dispersion

56. absolute (carrier-envelope) phase

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