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Advanced Atomic, Molecular and Optical Physics (Theory part) (Experimental part) Andrey Surzhykov José R. Crespo López-Urrutia, Ullrich Joachim, Thomas Stöhlker Monday 14:00-16:00 KIP HS 1 Wednesday 14:00-16:00 KIP HS 1 Tutorial (Theory or Experiment) Tuesday 14:00-16:00 Thursday 14:00-16:00 10 October 2011 Advanced Atomic Molecular and Optical Physics The course provides insight in fundamental concepts and techniques of modern atomic, molecular and optical physics, emphasizing active research areas and applications such as: (1) Ultraprecise measurements of time, frequency, energy, and mass, and applications to fundamental physics studies. Trapping and cooling of atoms, ions and molecules. (2) Fundamental quantum dynamics occurring in energetic and soft collisions of ions with photons, electrons and atoms. Interactions of ion beams with biological targets. (3) Spectroscopy of relativistic, quantum electrodynamic and parity violation effects in few-electron heavy ions. Laboratory astrophysics with ions at very high temperatures. (4) Interactions of intense, short pulse lasers and free-electron lasers with manyelectron targets. Molecular structure and dynamics explored in pump-probe experiments on femtosecond to attosecond time scales. Theory, practical implementation of calculational methods, and experiment will be discussed and compared in case studies. Advanced Atomic, Molecular and Optical Physics Andrey Surzhykov José R. Crespo López-Urrutia Joachim Ullrich Thomas Stöhlker Physikalisches Institut, Heidelberg Max-Planck-Institut für Kernphysik, Heidelberg Gesellschaft für Schwerionenforschung, Darmstadt Why atomic physics / quantum science? • Atoms are the best examples of quantum systems we have. • They can be prepared in very well defined states. • Their temporal evolution can be measured and manipulated. • Atomic physics experiments can be reproduced all over the world. • They deliver the most accurate results in any experimental science. • All interactions (electromagnetic, weak, strong, and gravitation) can be explored by means of atomic physics experiments. • Small is beautiful! Atomic physics and fundamental research A) Test of fundamental theories (QED, Gravitation ect.) by means of (ultra-)high precision experiments B) Exploring the quantum dynamics of few-particle systems Coulomb interaction precisely known, but: only the two-particle Coulomb system is analytically solvable Experiments provide tests for theoretical approximations and models or new numerical (computational) methods Time-resolved studies build the basis for the manipulation of quantum dynamics Example: Highest accuracy •Atomic clocks run „wrong“ by 5 minutes in 13 billion years. •Time (and thus frequencies) can be measured with the highest accuracy among all physical quantities. •Example: the 1S-2S transition in atomic hydrogen: 2.466.061.413.187.103 ± 46 Hz → check for temporal drifts of the fine structure constant α Die genaueste Uhr der Welt vom LPTF/Paris in Garchinger Labor des MPQ Examples: Highest accuracy → contradictory results for proton radius 0.895(18) fm Atomic spectroscopic measurements have pushed this field (nuclear physics, QCD) again! New tools: The frequency comb In the frequency domain a train of short pulses from a femtosecond laser is the result of a interference of many continuous wave (cw) longitudinal cavity modes. These modes at ωn form a series of frequency spikes that is called frequency comb. The individual modes can be selected by phase locking other cw lasers to them. The separation between adjacent modes is constant across the frequency comb: ωn = nωr+ ωCE: The mode number n of some 105 can be counted; frequency offset ωCE lies in between 0 and ωr = 1/T. The mode spacing is thereby identified with pulse repetition rate ωr, i.e. the inverse pulse repetition time T. With the help of that equation, two radio frequencies ωr and ωCE are linked to the optical frequencies ωn of the laser. (1S-2S) = 2 466 061 102 474 851(25) Hz RY = 10 973 731.568 525(84) m-1 L1S = 8 172.840(22) MHz Example: Test of a fundamental theory Example: Test of a fundamental theory Example: Test of equivalence principle E0/T0 10.10.2011 E1 12.10.2011 T1 17.10.2011 E2 19.10.2011 T2 24.10.2011 T3 26.10.2011 - 31.10.2011 E3 02.11.2011 T4 07.11.2011 E4 09.11.2011 T5 14.11.2011 E5 16.11.2011 T6 21.11.2011 E6 23.11.2011 T7 28.11.2011 E7 30.11.2011 Motivation and introduction. Organizational issues. Atomic units. Cross sections. Coincidence measurements. Time-of-flight methods. Counting statistics. Atomic beams. Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles. Sources of singly and highly charged ions. Electron and ion detection and energy analysis. Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects No lecture Lasers, synchrotrons, free-electron lasers. Photon detection. solid-state detectors, microcalorimeters. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions Classical optical spectroscopy. Laser spectroscopy. Ultrashort pulse lasers. Frequency combs. Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients Spectroscopy outside the visible range in electron beam ion traps, and storage rings. EUV, VUV, X-ray spectroscopy, Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions Hydrogen-like ions: Quantum electrodynamics, hyperfine structure, gfactor. Few-electron ions. Spectra of many-electron ions, jj and LS coupling, advanced manyelectron approaches Photoionization and photorecombination. Quantum interference. T8 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination T9 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra: Raman, Stokes effects. T10 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, coupling of mechanical and electronic dynamics E8 14.12.2011 Electronic correlations, many-body effects and Auger decay. Bound electrons in strong fields. Collisional excitation and ionization. E9 19.12.2011 Penning and Paul ion traps. Ultra-precision mass spectrometry. E10 21.12.2011 Atom and ion traps: Laser and evaporative cooling methods. T11 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. T12 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules E11 16.01.2012 Ions and atoms in strong laser fields. E12 18.01.2012 Atomic momentum spectroscopy: COLTRIMS, reaction microscopes. T13 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green's function approach, two-photon spectroscopy E13 25.01.2012 Attophysics: Dynamic investigations of molecular vibrations and reactions T14 30.01.2012 Interaction of charged particles with matter: Statistical approach T15 01.02.2012 Basics of the density matrix theory. Mixed quantum states. Tutorial Participation in the tutorial (exercise group) is mandatory! For the moment, four groups are planned (will be more if necessary): Tuesday, 14:00-16:00, INF 501 FP Thursday, 14:00 – 16:00, INF 327 / SR Thursday, 14:00 – 16:00, INF 366 / SR Thursday, 14:00 – 16:00, INF 325 / SR Please, register for one of the groups at: http://www.physi.uni-heidelberg.de/Forschung/apix/TAP/lectures/ First tutorial will take place will take place on the week of 24 – 28 October 10 October 2011 Advanced Atomic, Molecular and Optical Physics (Theory part) 10 October 2011 Andrey Surzhykov Universität Heidelberg Physikalisches Institut Philosophenweg 12 69120 Heidelberg Phone: +49 622154 9258 Mobile: +49 151 587 38779 E-mail: surz@physi.uni-heidelberg.de Web-page: http://www.physi.uni-heidelberg.de/Forschung/apix/TAP/index.php 10 October 2011 Andrey Surzhykov Motivation Let us try to answer two questions: What did you already know (study before)? What do we intend to discuss during this course? 10 October 2011 Basics of atomic physics During the course we will often recall basic information/knowledge on atoms/molecules (the level of Experimental Physics IV: Atomic Physic): Spectroscopy of hydrogen numbers, transitions) (quantum Idea of angular momentum Basic experiments: Zeeman, Stark, SternGerlach 10 October 2011 Basics of quantum quantum mechanics Erwin Schrödinger In Quantum physics, Schrödinger equation describes how the quantum state of physical system evolves with time: ∂ψ (r , t ) ˆ ih = Hψ ( r , t ) ∂t Wave function Hamiltonian operator Define your system, define its initial state and you can find the state of the system in any moment of time t. By the way, what is the wavefunction? 10 October 2011 Schrödinger equation for single particle For single particle Schrödinger equation reads: ∂ψ (r , t ) h2 2 ih =− ∇ ψ (r , t ) + U (r )ψ (r , t ) ∂t 2m kinetic term potential term If Hamiltonian does not depend on time, one can easily derive time-independent Schrödinger equation: h2 2 − ∇ ψ (r ) + U (r )ψ (r ) = Eψ (r ) 2m We have to solve eigenproblem! 10 October 2011 Schrödinger equation in 1D case U ( x) Schrödinger equation (time-independent): ⎧0 0 ≤ x ≤ L =⎨ ⎩∞ otherwise h2 d 2 − ψ ( x) + U ( x)ψ ( x) = Eψ ( x) 2 2m dx Potential Wavefunction kx 2 U ( x) = 2 Schrödinger equation opened a way of systematic analysis of quantum phenomena: • tunneling • particle confinement • molecular vibrations • hydrogen structure • many-electron ions • …. U ( x) ⎧U =⎨ 0 ⎩0 Pictures from HyperPhysics 10 October 2011 0≤ x≤ L otherwise Schrödinger equation: Spherical problem Schrödinger equation (time-independent): h2 2 Ze 2 − ∇ ψ (r ) − ψ ( r ) = Eψ ( r ) 2m r Coulomb potential Schrödinger equation opened a way of systematic analysis of quantum phenomena: • tunneling • particle confinement • molecular vibrations • hydrogen structure • many-electron ions • …. 10 October 2011 Motivation Let us try to answer two questions: What did you already know (study before)? What do we intend to discuss during this course? 10 October 2011 Plan of lectures 0. 11.10.2011 Introduction and motivation 1. 17.10.2011 antiparticles. 2. 24.10.2011 3. 26.10.2011 4. 07.11.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects. Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions. 5. 14.11.2011 Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients. 6. 21.11.2011 Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions. 7. 28.11.2011 Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches. 8. 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination. 9. 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra of molecules: Raman, Stokes. 10. 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, superheavy molecules, coupling of mechanical and electronic degrees of freedom. 11. 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. 12. 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules. 13. 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green’s approach, two-photon spectroscopy. 14. 30.01.2012 Interaction of charged particles with matter: Statistical approach. 15. 01.02.2012 Basics of the density matrix theory. 11 October 2010 function Plan of lectures 0. 11.10.2011 Introduction and motivation 1. 17.10.2011 antiparticles. 2. 24.10.2011 3. 26.10.2011 4. 07.11.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects. Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions. 5. 14.11.2011 Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients. 6. 21.11.2011 Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions. 7. 28.11.2011 Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches. 8. 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination. 9. 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra of molecules: Raman, Stokes. 10. 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, superheavy molecules, coupling of mechanical and electronic degrees of freedom. 11. 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. 12. 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules. 13. 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green’s approach, two-photon spectroscopy. 14. 30.01.2012 Interaction of charged particles with matter: Statistical approach. 15. 01.02.2012 Basics of the density matrix theory. 11 October 2010 function One electron heavy ions: Strong fields, relativity, QED www.gsi.de www.mpg.de 11 October 2010 Plan of lectures 0. 11.10.2011 Introduction and motivation 1. 17.10.2011 antiparticles. 2. 24.10.2011 3. 26.10.2011 4. 07.11.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects. Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions. 5. 14.11.2011 Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients. 6. 21.11.2011 Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions. 7. 28.11.2011 Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches. 8. 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination. 9. 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra of molecules: Raman, Stokes. 10. 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, superheavy molecules, coupling of mechanical and electronic degrees of freedom. 11. 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. 12. 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules. 13. 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green’s approach, two-photon spectroscopy. 14. 30.01.2012 Interaction of charged particles with matter: Statistical approach. 15. 01.02.2012 Basics of the density matrix theory. 11 October 2010 function Many-electron ions and atoms: Interelectronic interaction effects Ψ (r1 , r2 ,... ) = 1 N! 11 October 2010 μa , ∑ μ μ b , ψn ψn d ( j a μ a , j b μ b , j c μ c ,... : JM ) ψ n c ,... a ja μ a a ja μ a a ja μ a ψn ( r2 ) ψ n ( r3 ) ψ n ( r1 ) b jb μ b ( r1 ) b jb μ b ( r2 ) b jb μ b ( r3 ) ψn ψn ψn c jc μ c ( r1 ) ... c jc μ c ( r2 ) ... c jc μ c ( r3 ) ... ... ... ... ... ... ... ... ... Plan of lectures 0. 11.10.2011 Introduction and motivation 1. 17.10.2011 antiparticles. 2. 24.10.2011 3. 26.10.2011 4. 07.11.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects. Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions. 5. 14.11.2011 Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients. 6. 21.11.2011 Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions. 7. 28.11.2011 Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches. 8. 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination. 9. 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra of molecules: Raman, Stokes. 10. 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, superheavy molecules, coupling of mechanical and electronic degrees of freedom. 11. 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. 12. 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules. 13. 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green’s approach, two-photon spectroscopy. 14. 30.01.2012 Interaction of charged particles with matter: Statistical approach. 15. 01.02.2012 Basics of the density matrix theory. 11 October 2010 function Molecular systems 11 October 2010 Plan of lectures 0. 11.10.2011 Introduction and motivation 1. 17.10.2011 antiparticles. 2. 24.10.2011 3. 26.10.2011 4. 07.11.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects. Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects. Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions. 5. 14.11.2011 Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients. 6. 21.11.2011 Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions. 7. 28.11.2011 Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches. 8. 05.12.2011 Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination. 9. 07.12.2011 Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra of molecules: Raman, Stokes. 10. 12.12.2011 Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, superheavy molecules, coupling of mechanical and electronic degrees of freedom. 11. 09.01.2012 Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions. 12. 11.01.2012 Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules. 13. 23.01.2012 Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green’s approach, two-photon spectroscopy. 14. 30.01.2012 Interaction of charged particles with matter: Statistical approach. 15. 01.02.2012 Basics of the density matrix theory. 11 October 2010 function Atomic dynamics: Collisions, interaction with EM fields, penetration trough matter M ab = ψ b α ε e ikr ψ a ≡ ∫ ψ b+ ( r ) α ε e ikr ψ a ( r ) d r ε 11 October 2010 Organization of the lectures 10 October 2011 Our “road map”-light “computer” part will be available in I-net 10 October 2011 “blackboard” part (tutorial) Literature and I-net sources 10 October 2011 Basic literature B.H. Bransden and C.J. Joachin “Physics of Atoms and Molecules” H. A. Bethe and E. E. Salpeter “Quantum Mechanics of One- and Two-Electron Atoms” J. Eichler and W. E. Meyerhof “Relativistic Atomic Collisions” Or J. Eichler “Lectures on Ion-Atom Collisions” 11 October 2010 Additional literature R. Zare “Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics” K. Blum “Density Matrix Theory and Applications” H.F. Beyer and V.P. Shevelko “Introduction to Physics of Highly Charged Ions” 11 October 2010 Lectures in Internet Please, find PPT/PDF files at: http://www.physi.uni-heidelberg.de/Forschung/apix/TAP/lectures/ (password: dirac2012) 11 October 2010 Mathematica library Set of Mathematica programs will be provided for: • • • • Calculation of the energy levels Evaluation of the nonrelativistic as well as relativistic wavefunctions Cross section calculations …. The programs will be available for downloading from: http://www.physi.uni-heidelberg.de/Forschung/apix/TAP/lectures/ 11 October 2010 Mathematica library 11 October 2010 Problems: Theory 1 10 October 2011 11 October 2010

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