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

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/mpi/en/pfeifer InterAtto – where we are from...

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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 – XXIII rd Heidelberg Graduate Days Lecture Series Thomas Pfeifer InterAtto Research Group MPI – Kernphysik, Heidelberg

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Quantum World

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Quantum World Length Scales

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Scientific Time Scales Age of Universe1 second shortest light pulse 80 as human time scale molecular time scale electronic time scale geological/astronomical time scale nuclear time scale

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

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

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Molecular Dynamics Ref: Physics Department, University of Wuerzburg Absorption of LightVibrationDissociation

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Measurement of molecular dynamics (internuclear wavepackets) Control of some chemical reactions moving towards: Measurement and Control of electron dynamics Evolution of Ultrafast Science Ref: Physics Department, University of Wuerzburg

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Estimation of Quantum Time Scales LILI = ħ m p a 0 2 Molecular rotation frequency Molecular vibration frequency DmpDmp Electron vibration frequency DmeDme LILI = ħ m e a 0 2 Electron rotation frequency T r =300 fs T v =7 fs T e =150 as

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Quantum Level Spacings Separation: Electronic, Vibrational, Rotational Energy Internuclear Distance 0 5 e,2 e,1 e,0 total el,n vib,m rot,l v,n rot,l

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

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attosecond pulses 50 as 30 eV as electronic states 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 1 as = s light travels: 0.3 nm (3 Ångstrom)

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

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

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...for their studies of extremely fast chemical reactions, effected by disturbing the equlibrium by means of very short pulses of energy. Manfred Eigen George Porter Ronald Norrish...for his studies of the transition states of chemical reactions using 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.

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attosecond pulse production detector/ experiment atomic medium femtosecond laser pulse also known as: High-Order Harmonic Generation laser intensity: >10 14 W/cm 2 attosecond x-ray pulse(s) mechanism based on: sub-optical-cycle electron acceleration (laboratory-scale table-top)

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and H igh H armonic G eneration ~100 as <1 J >1 nm Ultrashort x-ray/XUV Pulses ~200 m pulse energy pulse duration F ree E lectron L asers ~20 fs 1 fs (proj.) ~1 mJ wavelength ~1.5 Å ~1 mm fully coherent

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... in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him. Wilhelm C. Röntgen 1901, Physics Röntgen-X-Rays 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 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 high spatial resolution comes withhigh temporal resolution speed of light c = T (optical cycle) (wavelength) FEL

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

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Fundamental Question(s) of Attosecond/Ultrafast Science - 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 observe understand control Quantum Motion (Dynamics) of Electrons

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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) - Maxwells 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 1678Christian HuygensLight is wave-like 1704Sir Isaac NewtonLight is particle-like (travel in straight lines and reflect from surfaces), aetheral medium for refraction 1740'sLeonhard EulerLight is wave-like, Huygens approach became prevailing theory afterwards 1788Joseph 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. 1803Thomas YoungDouble-slit experiment supports the wave theory of light and demonstrates the effect of interference. 1807John DaltonPublished his Atomic Theory of Matter. 1811Amedeo 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. 1833William 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 (contd) some selected milestones 1839Alexandre Edmond Becquerel Observed the photoelectric effect via an electrode in a conductive solution exposed to light. 1873James 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. 1877Ludwig BoltzmannSuggested that the energy states of a physical system could be discrete. 1885Johann BalmerDiscovered that the four visible lines of the hydrogen spectrum could be assigned integers in a series 1888Johannes RydbergModified the Balmer formula to include the other series of lines, producing the Rydberg formula 1896Henri BecquerelDiscovered 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). 1897J. J. ThomsonShowed 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 (contd) some selected milestones 1900Max PlanckTo 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. 1905Albert EinsteinDetermines the equivalence of matter and energy 1905Albert EinsteinFirst 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. 1905Albert EinsteinTo explain the photoelectric effect (1839), he postulated, as based on Plancks quantum hypothesis (1900), that light itself consists of individual quantum particles (photons) [1911 pub.] Ernest Rutherfordalpha 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 (contd) some selected milestones 1909Geoffrey 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 and 1916 Albert EinsteinShowed 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. 1913Robert 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. 1913Niels BohrTo 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 (contd) some selected milestones 1918Ernest RutherfordDiscovers the proton 1922Otto 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. 1923Louis De BrogliePostulated that electrons in motion are associated with waves the lengths of which are given by Plancks constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p. 1924Satyendra Nath BoseHis work on quantum mechanics provides the foundation for Bose-Einstein statistics, the theory of the Bose-Einstein condensate, and the discovery of the boson. 1925Werner HeisenbergDeveloped the matrix mechanics formulation of QM 1925Wolfgang PauliOutlined the Pauli exclusion principle which states that no two identical fermions may occupy the same quantum state simultaneously. 1926Gilbert LewisCoined the term photon, which he derived from the Greek word for light, φως (transliterated phôs). Ref:

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Quantum History (contd) some selected milestones 1926Erwin Schrödinger Used De Broglies electron wave postulate (1924) to develop a wave equation, gave the correct values for spectral lines of the hydrogen atom. 1927Clinton Davisson and Lester Germer demonstrate the wave nature of the electron in the Electron diffraction experiment 1927Walter HeitlerUsed Schrödingers wave equation (1926) to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond. 1928Linus PaulingOutlined the nature of the chemical bond in which he used Heitlers quantum mechanical covalent bond model (1927) to outline the quantum mechanical basis. 1929John Lennard- Jones Introduced the linear combination of atomic orbitals approximation for the calculation of molecular orbitals. 1932Werner 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 (contd) some selected milestones 1948Richard FeynmanStated the path integral formulation of quantum mechanics. 1949Freeman DysonDetermined 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 today Theodore Maiman many more people demonstration of the first Laser some active fields of research: - quantum information/computing - macroscopic quantum systems (building Schrödingers 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 latin: cohærere "cohere, from com- "together" + hærere "to stick (etymonline.com)

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

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How to create coherence? (r)=0 frequency, ( )=0 space, r 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 pumping

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resonator solve Maxwells 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) 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

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Maxwells 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 frequency [arb. u.] Gabor Transform

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