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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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