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**Attosecond Flashes of Light**

– Illuminating electronic quantum dynamics – XXIIIrd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research Group MPI – Kernphysik, Heidelberg

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

/mpi/en/pfeifer

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**InterAtto Setup Phase I**

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**InterAtto Setup Phase II**

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**InterAtto Setup Phase III**

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**InterAtto Setup Phase IV**

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**InterAtto Setup Phase IVb**

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CEP Control

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Laser Pulses: 6 fs

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Fun with the laser

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**Attosecond Flashes of Light**

– Illuminating electronic quantum dynamics – XXIIIrd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research Group MPI – Kernphysik, Heidelberg

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

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**Quantum World Length Scales**

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**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

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**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

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**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

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**Why use ultrashort laser pulses?**

1877, EadweardMuybridge, Leland Stanford Ref: Physics Department, University of Wuerzburg

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**Molecular Dynamics Absorption of Light Vibration Dissociation**

Ref: Physics Department, University of Wuerzburg

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**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

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**Estimation of Quantum Time Scales**

ħ 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 = =

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**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

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**femtosecond laser pulses**

5 fs 300 meV e.g. vibrational, rotational states

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**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

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**Quantum World Time Scales**

300 nm optical cycle Short pulses can be used to monitor and control relative atomic motion and electronic motion

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**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 …

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**“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

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**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

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**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

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**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

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**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

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**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

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**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)

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**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

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**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

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**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.

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**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

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**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.

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**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:

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**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:

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**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:

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**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:

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**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

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**Coherence Dj=? latin: cohærere "cohere,“**

from com- "together" + hærere "to stick“ (etymonline.com) Dj=?

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**Spatial and Temporal Coherence**

Space/Wavevector(momentum) Domain Time/Frequency Domain intensity time intensity frequency Ref:

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**How to create coherence?**

space, r frequency, w time

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**LASERs (Light Amplification by Stimulated Emission of Radiation)**

gain medium spontaneous and stimulated emission + resonator imprint spatial and temporal pulse shape “coherence” = LASER

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**Stimulated emission ...and pumping**

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**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)

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**resonator modes Laguerre Gaussian modes (cylindrical coordinates)**

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**LASERs (Light Amplification by Stimulated Emission of Radiation)**

gain medium spontaneous and stimulated emission + resonator imprint spatial and temporal pulse shape “coherence” = LASER

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

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**Maxwell’s Equations Resulting wave equations ... and their solution**

for the case of a temporally and spatially invariant medium

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Fourier Transform

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**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

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**Mathematics of Ultrashort pulses**

spectral phase Taylor expansion dispersion

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**absolute (carrier-envelope) phase**

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**Windowed Fourier Transform**

‘Gabor Transform’ frequency [arb. u.] frequency [arb. u.]

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