10 October 2011

Advanced Atomic, Molecular and Optical Physics

(Theory part) (Experimental part)

Andrey Surzhykov

Monday 14:00-16:00KIP HS 1

José R. Crespo López-Urrutia,Ullrich Joachim,Thomas Stöhlker

Wednesday 14:00-16:00KIP HS 1

Tutorial(Theory or Experiment)

Tuesday 14:00-16:00Thursday 14:00-16:00

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 many-electron 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

Advanced Atomic, Molecular and Optical Physics

Andrey SurzhykovJosé R. Crespo López-Urrutia

Joachim UllrichThomas Stöhlker

Physikalisches Institut, HeidelbergMax-Planck-Institut für Kernphysik, Heidelberg

Gesellschaft für Schwerionenforschung, Darmstadt

• 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 theworld.

• They deliver the most accurate results in any experimental science.

• All interactions (electromagnetic, weak, strong, and gravitation) can be explored by means of atomic physicsexperiments.

• Small is beautiful!

Why atomic physics / quantum science?

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 analyticallysolvable

Experiments provide tests for theoreticalapproximations and models or new numerical(computational) methods

Time-resolved studies build the basis for themanipulation of quantum dynamics

Example: Highest accuracy

Die genaueste Uhr der Welt vom LPTF/Paris in Garchinger Labor des MPQ

•Atomic clocks run „wrong“ by 5 minutes in 13 billion years. •Time (and thus frequencies) can be measured with the highestaccuracy 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

Examples: Highest accuracy

→ contradictory results for proton radius 0.895(18) fm

Atomic spectroscopic measurementshave pushed this field (nuclear physics, QCD) again!

The mode number n of some 105 can be counted; frequency offset ωCE lies in between0 and ωr = 1/T. The mode spacing is thereby identified with pulse repetition rate ωr, i.e. the inversepulse repetition time T. With the help of that equation, two radio frequencies ωr and ωCE are linked to the opticalfrequencies ωn of the laser.

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:

New tools: The frequency comb

(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

Photoionization and photorecombination. Quantum interference.30.11.2011E7

Spectra of many-electron ions, jj and LS coupling, advanced many-electron approaches

28.11.2011T7

Hydrogen-like ions: Quantum electrodynamics, hyperfine structure, g-factor. Few-electron ions.

23.11.2011E6

Independent particle model, central field approximation, spectroscopy of few-electron atoms/ions

21.11.2011T6

Spectroscopy outside the visible range in electron beam ion traps, and storage rings. EUV, VUV, X-ray spectroscopy,16.11.2011E5

Angular momentum, coupling of momenta, angular momentum theory, Clebsch-Gordan coefficients

14.11.2011T5

Classical optical spectroscopy. Laser spectroscopy. Ultrashort pulse lasers. Frequency combs.

09.11.2011E4

Continuum-state solutions of Dirac equation, plane and distorted waves, multipole decompositions

07.11.2011T4

Lasers, synchrotrons, free-electron lasers. Photon detection. solid-state detectors, microcalorimeters.

02.11.2011E3

No lecture 31.10.2011-

Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects

26.10.2011T3

Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects

24.10.2011T2

Sources of singly and highly charged ions. Electron and ion detection and energy analysis.19.10.2011E2

Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.

17.10.2011T1

Atomic units. Cross sections. Coincidence measurements. Time-of-flight methods. Counting statistics. Atomic beams.

12.10.2011E1

Motivation and introduction. Organizational issues.10.10.2011E0/T0

Basics of the density matrix theory. Mixed quantum states.01.02.2012T15

Interaction of charged particles with matter: Statistical approach30.01.2012T14

Attophysics: Dynamic investigations of molecular vibrations and reactions

25.01.2012E13

Non-dipole effects, two and multi-photon processes, second-order perturbation theory, Green's function approach, two-photon spectroscopy

23.01.2012T13

Atomic momentum spectroscopy: COLTRIMS, reaction microscopes.18.01.2012E12

Ions and atoms in strong laser fields.16.01.2012E11

Radiative decay and absorption, evaluation of matrix elements, symmetry and selection rules

11.01.2012T12

Stark and Zeeman effects. Symmetry and mixing of electronic states. Induced transitions.

09.01.2012T11

Atom and ion traps: Laser and evaporative cooling methods.21.12.2011E10

Penning and Paul ion traps. Ultra-precision mass spectrometry.19.12.2011E9

Electronic correlations, many-body effects and Auger decay. Bound electrons in strong fields. Collisional excitation and ionization.14.12.2011E8

Quasimolecules: Ultracold atoms and ions, optical lattices, Geonium, coupling of mechanical and electronic dynamics

12.12.2011T10

Simple molecules: H2. Molecular ions. Born-Oppenheimer approximation. Rovibrational spectra: Raman, Stokes effects.

07.12.2011T9

Photoionization and recombination, atomic collisions, Coulomb ionization and excitation, dielectronic recombination

05.12.2011T8

10 October 2011

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 FPThursday, 14:00 – 16:00, INF 327 / SRThursday, 14:00 – 16:00, INF 366 / SRThursday, 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 HeidelbergPhysikalisches Institut

Philosophenweg 1269120 Heidelberg

Phone: +49 622154 9258Mobile: +49 151 587 38779

E-mail: surz@physi.uni-heidelberg.deWeb-page: http://www.physi.uni-heidelberg.de/Forschung/apix/TAP/index.php

Andrey Surzhykov

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

Basics of atomic physicsDuring the course we will often recall basic information/knowledge on atoms/molecules (the level of Experimental Physics IV: Atomic Physic):

Spectroscopy of hydrogen (quantum numbers, transitions)

Idea of angular momentum

Basic experiments: Zeeman, Stark, Stern-Gerlach

10 October 2011

Basics of quantum quantum mechanicsErwin Schrödinger

In Quantum physics, Schrödinger equation describes how the quantum state of physical system evolves with time:

),(ˆ),( tHtti rr ψψ =

∂∂

hHamiltonian operator

Wave function

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:

If Hamiltonian does not depend on time, one can easily derive time-independent Schrödinger equation:

),()(),(2

),( 22

tUtmt

ti rrrr ψψψ +∇−=∂

∂ hh

kinetic term potential term

)()()()(2

22

rrrr ψψψ EUm

=+∇− h

We have to solve eigenproblem!

10 October 2011

Schrödinger equation in 1D case

WavefunctionPotential

⎩⎨⎧∞

≤≤=

otherwiseLx

xU00

)(

2)(

2kxxU =

⎩⎨⎧ ≤≤

=otherwise

LxUxU

00

)(

0

Pictures from HyperPhysics

Schrödinger equation opened a way of systematic analysis of quantum phenomena:

• tunneling• particle confinement• molecular vibrations• hydrogen structure• many-electron ions• ….

Schrödinger equation (time-independent):

)()()()(2 2

22

xExxUxdxd

mψψψ =+− h

10 October 2011

Schrödinger equation: Spherical problem

Schrödinger equation opened a way of systematic analysis of quantum phenomena:

• tunneling• particle confinement• molecular vibrations• hydrogen structure• many-electron ions• ….

Schrödinger equation (time-independent):

)()()(2

22

2

rrr ψψψ ErZe

m=−∇− h

Coulomb potential

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?

11 October 2010

Plan of lectures

0. 11.10.2011 Introduction and motivation

1. 17.10.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.2. 24.10.2011 Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects.3. 26.10.2011 Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects.4. 07.11.2011 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 function 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

Plan of lectures

0. 11.10.2011 Introduction and motivation

1. 17.10.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.2. 24.10.2011 Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects.3. 26.10.2011 Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects.4. 07.11.2011 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 function 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

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 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.2. 24.10.2011 Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects.3. 26.10.2011 Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects.4. 07.11.2011 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 function 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

Many-electron ions and atoms: Interelectronic interaction effects

( ) ∑=Ψ,...,,

333

222

111

21

............

............

...)()()(

...)()()(

...)()()(

):,...,,(!

1,...,cba

cccbbbaaa

cccbbbaaa

cccbbbaaa

jnjnjn

jnjnjn

jnjnjn

ccbbaa JMjjjdN μμμ

μμμ

μμμ

μμμ

ψψψψψψψψψ

μμμ rrrrrrrrr

rr

11 October 2010

Plan of lectures

0. 11.10.2011 Introduction and motivation

1. 17.10.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.2. 24.10.2011 Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects.3. 26.10.2011 Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects.4. 07.11.2011 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 function 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

Molecular systems

0. 11.10.2011 Introduction and motivation

1. 17.10.2011 Spin and relativity, from Schrödinger to Dirac equation. Solutions with negative energy, Dirac sea, antiparticles.2. 24.10.2011 Bound-state solutions of Dirac equation, spectroscopy, fine-structure effects.3. 26.10.2011 Higher-order corrections to Dirac equation: QED, hyperfine-structure and isotope shift effects.4. 07.11.2011 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 function 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

Plan of lectures

11 October 2010

Atomic dynamics: Collisions, interaction with EM fields, penetration trough matter

rrεαrεα krkr deeM ai

bai

bab )()( ψψψψ ∫ +≡=ε

10 October 2011

Organization of the lectures

10 October 2011

Our “road map”-light

“computer” part “blackboard” part (tutorial)

will be available in I-net

10 October 2011

Literature and I-net sources

11 October 2010

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”

OrJ. 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

10 October 2011

Problems: Theory 1

11 October 2010