attosecond flashes of light – illuminating electronic quantum dynamics – thomas pfeifer...
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Attosecond Flashes of Light
– Illuminating electronic quantum dynamics –
Thomas PfeiferInterAtto Research GroupMPI – Kernphysik, Heidelberg
XXIIIrd Heidelberg Graduate DaysLecture Series
http://www.mpi-hd.mpg.de /mpi/en/pfeifer
InterAtto – where we are from...
InterAtto Setup Phase I
InterAtto Setup Phase II
InterAtto Setup Phase III
InterAtto Setup Phase IV
InterAtto Setup Phase IVb
CEP Control
Laser Pulses: 6 fs
Fun with the laser
Attosecond Flashes of Light
– Illuminating electronic quantum dynamics –
XXIIIrd Heidelberg Graduate DaysLecture Series
Thomas PfeiferInterAtto Research GroupMPI – Kernphysik, Heidelberg
Quantum World
http://startswithabang.com/?p=1795
http://www.almaden.ibm.com/vis/stm/images/stm15.jpg
Quantum World Length Scales
Scientific Time Scales
Age of Universe1 secondshortest light pulse
80 as
“human” time scale
molecular time scale
electronic time scale
geological/astronomical time scale
nuclear time scale
How “long” is a femtosecond?
Ref: Physics Department, University of Wuerzburg
5 fs
A laser pulse of5 fs duration (time)
is1.5 m long (space)
Our laser pulses:
wavelength of blue light
moonearth
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
Why use ultrashort laser pulses?Does a galloping horse, at any time,
have all legs in the air?How do atoms move within molecules?
required time resolution: milliseconds required time resolution: femtoseconds1 fs = 10-15 s
slow-motion with short exposure timeshelps to clear up fast events
extreme slow-motion with fs laser pulseshelps to illuminate ultrafast events
Ref: Physics Department, University of Wuerzburg
1877, EadweardMuybridge, Leland Stanford
Molecular Dynamics
Ref: Physics Department, University of Wuerzburg
Absorption of Light Vibration Dissociation
Measurement of moleculardynamics (internuclear wavepackets)
Control of some chemicalreactions
moving towards:Measurement and Control of
electron dynamics
Evolution of Ultrafast Science
Ref: Physics Department, University of Wuerzburg
Estimation of Quantum Time Scales
LI
=
ħmpa0
2Molecular rotation frequency
Molecular vibration frequency Dmp
Electron vibration frequency Dme
LI
= = ħmea0
2Electron rotation frequency
12000
12000 1 1
1 50
1 1
Tr=300 fs
Tv=7 fs
Te=150 as
Quantum Level SpacingsSeparation: Electronic, Vibrational, Rotational
Energy
Internuclear Distance
0
5
e,2
e,1
e,0
totalel,nvib,mrot,l
v,n
rot,l
femtosecond laser pulses
5 fs300 meV
e.g.
vib
ratio
nal,
rota
tiona
lst
ates
attosecond pulses
50 as30 eV
as
elec
tron
icst
ates
Classical e- orbit period, Hydrogen: 152 as1s-2s/p wavefunction period
- Hydrogen: ~ 400 as
- H-like Uranium~ 0.05 as
Auger (core-hole) lifetimes: ~100 as-~10 fs
1 as = 10-18 s light travels: 0.3 nm (3 Ångstrom)
Quantum World Time Scales
Short pulses can be used to monitor and control relative atomicrelative atomic motion
300 nm optical cycle
and electronicelectronic motion
d [Å]
|molecule|2
Courtesy: M. Erdmann, V. Engel
ultrafast quantum motion
vibrations,relative atomic
motion
example:diatomic moleculeinternuclear
distance d ~ Å
femtosecondpulsed lasers(IR, Vis., UV)
spectroscopic & quantum control
techniques
vibrational periodT > 5 fs (5∙10-15 s)
pump–probeCARS,
pump–dump,STIRAP
…
Na2
“...for their studies of extremely fast chemicalreactions, effected by disturbing the equlibriumby means of very short pulses of energy.“
Manfred Eigen George Porter Ronald Norrish
“...for his studies of the transition states of chemical reactionsusing femtosecond spectroscopy.“
Ahmed Zewail
“...for their contributions to the development of laser-based precision spectroscopy,including the optical frequency comb technique.“
Theodor Hänsch John Hall
1999, Chemistry
1967, Chemistry
2005, Physics (1/2)
“fast” Nobel prizes
100 nanosec.
1 picosec.
10 femtosec.
attosecond pulse production
detector/experiment
atomic medium
femtosecondlaser pulse
also known as: High-Order Harmonic Generation
laser intensity:>1014 W/cm2
attosecondx-ray pulse(s)
mechanism based on:sub-optical-cycle electron acceleration
(laboratory-scale table-top)
and HighHarmonicGeneration
~100 as
<1 J
>1 nm
Ultrashort x-ray/XUV Pulses
~200 m
pulse energy
pulse duration
FreeElectronLasers
~20 fs 1 fs (proj.)
~1 mJ
wavelength~1.5 Å
~1 mm
fullycoherent
“... in recognition of the extraordinary serviceshe has rendered by the discovery ofthe remarkable rays subsequently named after him.“
Wilhelm C. Röntgen
1901, Physics
Röntgen-“X“-Rays
1914, PhysicsM. von Laue
1915, PhysicsW.H.Bragg, W.L.Bragg
1917, PhysicsC. G. Barkla
1924, PhysicsM. Siegbahn
1927, PhysicsA. H. Compton
1936, ChemistryP. Debye
1962, ChemistryM. F. Perutz, J. C. Kendrew
1962, MedicineF. Crick, J. Watson, M. Wilkins
1964, ChemistryD. Crowfoot Hodgkin
1976, ChemistryW. N. Lipscomb
1979, MedicineA. M. Cormack, G. N. Hounsfield
1981, PhysicsM. Siegbahn
1985, ChemistryH. A. Hauptman, J. Karle
1988, ChemistryJ. Deisenhofer, R. Huber, H. Michel
2002, PhysicsRiccardo Giacconi
high spatialresolution comes with high temporal
resolution
speed of light c = T (optical cycle)
(wavelength)
xy
E-field polarization5 nm
|electron|2
ultrafast quantum motion
|molecule|2
example:diatomic moleculeinternuclear
distance d ~ Å
vibrational periodT < 5 fs
orbital periodT < (<<) 1 fs
attosecond = 10-18 s
orbital size~ Å
e-
example:electrons in atoms
attosecondpulsed source
(soft x-ray)
attosecondspectroscopy/
quantum control methods
? ?H-atom ionizing
Fundamental Question(s)of Attosecond/Ultrafast Science
- Coherence among electronic states- Correlations (Entanglement) in 2-or-more-electron systems
observation on very short time scalesmolecular bonding dynamics
(beyond Born-Oppenheimer phenomena?)
- Quantum Control (steer electrons in atoms and molecules)
- Dynamics in Strong Laser Fields
observeunderstand
controlQuantum Motion (Dynamics)
of Electrons
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)
ContentsBasics of short pulses and general conceptsAttosecond pulse generation
Mechanics of Electronssingle electronsin strong laser fields
Attosecond Experiments with isolated Atoms
Multi-Particle SystemsMoleculesmulti-electron dynamics (correlation)
Attosecond experiments with molecules / multiple electrons
Ultrafast Quantum Controlof electrons, atoms, molecules
Novel Directions/ApplicationsTechnology
Contents TodayBasics 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
Quantum Historysome 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.
http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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
http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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
1905 Albert Einstein 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.
1905 Albert Einstein 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.
http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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 momentump = 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.
1913 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: http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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
1925 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: http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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
1927 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: http://en.wikipedia.org/wiki/History_of_quantum_mechanics
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: http://en.wikipedia.org/wiki/History_of_quantum_mechanics
Contents TodayBasics 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
Coherence
latin: cohærere "cohere,“from com- "together" + hærere "to stick“ (etymonline.com)
Spatial and Temporal Coherence
Ref: http://grad.physics.sunysb.edu/~amarch/int.gif
time
frequency
intensity
intensity
Time/Frequency DomainSpace/Wavevector(momentum)Domain
How to create coherence?
(r)=0
frequency,
()=0
space, r
time
LASERs(Light Amplification by Stimulated Emission of Radiation)
=
+
gain mediumspontaneous and stimulated emission
resonatorimprint spatial and temporal pulse shape“coherence”
LASER
Stimulated emission
http://en.wikipedia.org/wiki/Stimulated_emission http://en.wikipedia.org/wiki/Population_inversion#Three-level_lasers
...and pumping
resonator
http://en.wikipedia.org/wiki/Optical_cavity
solve Maxwell’s equations withboundary conditions (mirrors) to find
stationary E(x,y,z)(compare QM ground state)
resonator modes
http://en.wikipedia.org/wiki/Transverse_mode
Laguerre Gaussian modes(cylindrical coordinates)
Laguerre Gaussian modes(cylindrical coordinates)
LASERs(Light Amplification by Stimulated Emission of Radiation)
=
+
gain mediumspontaneous and stimulated emission
resonatorimprint spatial and temporal pulse shape“coherence”
LASER
Laser System
Maxwell’s Equations
Resulting wave equations ... and their solution)(
0),( rkErE tiet
)(0),( rkBrB tiet
for the case of a temporallyand spatially invariant medium
Fourier Transform
Contents TodayBasics 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
Mathematics of Ultrashort pulsesspectral phaseTaylor expansiondispersion
absolute (carrier-envelope) phase
Windowed Fourier Transform
freq
uenc
y [a
rb. u
.]
frequency [arb. u.]
‘Gabor Transform’