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

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


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


1877, EadweardMuybridge, Leland Stanford

Molecular Dynamics


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


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



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.



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


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


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.



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









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








Mathematics of Ultrashort pulsesspectral phaseTaylor expansiondispersion

absolute (carrier-envelope) phase

Windowed Fourier Transform

freq

uenc

y [a

rb. u

.]

frequency [arb. u.]

‘Gabor Transform’

Documents

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