
Advanced Quantum Theory (Bernuzzi/Gies)
Content
 Many particle systems, identical particles, noninteracting particles, ThomasFermi and HartreeFock approximations
 Addition of angular momenta, ClebschGordan coefficients, selection rules
 Timedependent perturbation theory, Fermis golden rule
 Scattering theory, potential scattering, partial waves, scattering of identical particles
 Introduction to relativistic quantum mechanics, Poincare transformations, Klein Gordon and Dirac equations, minimal coupling, nonrelativistic approximation
 Relativistic hydrogen atom, fine structure
 Path integrals
Intended Learning Outcomes
Knowledge of relevant facts about advanced quantum mechanics which are necessary for an understanding of quantum phenomena and their relevance in all areas of modern physics. Ability to apply methods for describing and modeling nonrelativistic and relativistic quantum systems. Ability to solve demanding problems and deal with complex physical systems.

Fundamentals of Modern Optics (Pertsch)
Content
 Basic concepts of wave optics
 Dielectric function to describe lightmatter interaction
 Propagation of beams and pulses
 Diffraction theory
 Elements of Fourier optics
 Polarization of light
 Light in structured media
 Optics in crystals
Intended Learning Outcomes
The course covers the fundamentals of modern optics which are necessary for the understanding of optical phenomena in modern science and technology. The students will acquire a thorough knowledge of the most important concepts of modern optics. At the same time, the importance and beauty of optics in nature and in technology will be taught. This will enable students to follow more specialized courses in photonics.
Recommended Reading
 B.E.A. Saleh and M.C. Teich, Fundamentals of Photonics, Wiley.
 H. Lipson, D.S. Tannhauser, S.G. Lipson, ”Optical Physics”, Cambridge.
 E. Hecht and A. Zajac, ”Optics”, AddisonWesley Longman.
 F.L. Pedrotti, L.S. Pedrotti, L.M. Pedrotti, Introduction to Optics, Pearson.
 G. Brooker, Modern Classical Optics, Oxford.

General Relativity (Brügmann)
Content
 Fundamentals of general relativity
 Einstein field equations
 Newtonian approximation
 Gravitational waves
 Black holes
 Cosmology and the big bang
Intended Learning Outcomes
Obtain knowledge of relativistic gravitational physics. Develop problem solving skills for astrophysical problems in the regime of high velocities and strong gravitational fields.

Introduction to Quantum Physics (Setzpfandt)
Content
 Relevant core concepts of atomic and solidstate physics
 Basics of lightmatterinteraction
 Basics of superconductivity
 Basics of quantum theory
 Quantum harmonic oscillator
 Perturbation theory
 Pictures of quantum mechanics
Intended Learning Outcomes
Understanding of basic concepts and methods for the description of physical systems within the framework of quantum theory. Ability to independently solve simple tasks in the area of quantum physics.

Physical Chemistry (Gräfe/Croy)
Content
 Equilibrium thermodynamics: Properties of gases, first and second law of thermodynamics, chemical equilibrium, equilibrium electrochemistry
 Transport phenomena: molecular motion in gases and liquids, diffusion, transport across biological membranes
 Chemical reactions: chemical kinetics, rate laws, temperature dependence of reaction rates, relaxation methods, kinetics of complex reactions
 Basics of quantum mechanics: wavefunctions and operators, particle in a box, harmonic oscillator, particle on a sphere, rigid rotator
 Approximations: variational principle, BornOppenheimer approximation, linear combination of atomic orbitals (LCAO) method, HartreeFock, density functional theory (DFT)
Intended Learning Outcomes
Understandig of the fundamentals of physical chemistry. Knowledge in equilibrium thermodynamics, chemical kinetics and basic molecular quantum mechanics.

Fundamentals of Quantum Information (Steinlechner/Setzpfandt/Gärttner)
Content
Concepts of quantum information processing
 Introduction to fundamental concepts and the basic formalism
 Entanglement
 Application examples
 Entanglement characterization
Hardware for quantum information processing
 Brief review of key physical concepts and applications
 Basic hardware requirements for information processing
Intended Learning Outcomes
Understanding of fundamental properties of quantum states, their applications and how to characterize them. Knowledge about basic hardware requirements for quantum information processing and example implementations.

Quantum Laboratory (Setzpfandt)
Content
Practical training in experimental quantum technology. Topics cover a broad range from quantumstate generation and characterization, the demonstration of fundamental quantum effects to applications in communication and metrology.
Intended Learning Outcomes
 Introduction to experimental techniques in quantum technology.
 Planning and preparation of a scientific measuring task.
 Carrying out scientific lab in optics together with a research team.
 Preparation of a scientific report.

Advanced Quantum Information (Steinlechner/Setzpfandt/Gärttner)
Content
Hardware for quantum information processing
 Superconducting qubits, gates, control, manipulation, readout
 Lightmatter interaction
 Semiconductor qubits (quantum dots, defects)
 Atoms / quantum gases
 Foundations of quantum sensing (sensitivity, noise, standard quantum limit)
 Optomechanics
Concepts of quantum information processing
 Decoherence
 Quantum error correction
 Manybody entanglement
Intended Learning Outcomes
Knowledge of all eminent concepts for implementing quantuminformation systems. Understanding advanced concepts that enable treatment of nonideal quantum systems.

Advanced Seminar Gravitational and Quantum Physics (Brügmann/Gies)
Content
 Systematic development of specialized knowledge in the fields of gravitation theory and quantum theory
 Presentation and discussion of current problems of gravitation theory and quantum theory
Intended Learning Outcomes
 Familarisation with a specific topic in gravitation or quantum theory
 Independent discovery and evaluation of scientific literature
 Presentation of scientific facts in form of a talk
 Indepth knowledge in the fields of gravitation theory and quantum theory

Computational Physics II (Brügmann)
Content
 Introduction to Unix and higherlevel programming languages (e.g.: C/C++, Fortran)
 Numerical solution of partial differential equations
 Monte Carlo method
 Molecular dynamics methods
 Minimization problems
Intended Learning Outcomes
Teaching the basic algorithms and practical skills for the numerical solution of complex physical problems and visualization of large amounts of data.

Electronic Structure Theory (Peschel)
Content
 Introduction to the manybody problem
 Wavefunctionbased approaches for electronic structure
 Density functional theory
 Electronic excitations: beyond density functional theory
Intended Learning Outcomes
Electronic structure theory is a successful and evergrowing field, shared by theoretical physics and theoretical chemistry, that takes advantage from the increasing availability of highperformance computers. Starting only from the knowledge of the types of atoms that constitute a material (molecule, solid, nanostructure,..) we will learn how to determine without further experimental input, i.e. using only the laws of quantum physics, its structural and electronic properties.The lecture will initiate the students to the stateoftheart theoretical and computational approaches used for electronic structure calculations. In the practical classes the students will learn through tutorials to use different software for electronic structure simulations. During the last month they will realize a small independent scientific project.

Molecular Quantum Mechanics / Quantum Chemistry I (Gräfe/Croy)
Content
In lecture and tutorial, students are taught basics and concepts describing the dynamics of (open) quantum systems (wave packets, density matrix, quantum master equations). Furthermore, aspects of multiparticle physics of molecules are covered, i.e. e.g. multielectron wave functions, the HartreeFock approximation and the role of basis sets.
Intended Learning Outcomes
Become familiar with the fundamentals of open quantum systems and "ab initio" methods for performing quantum chemical calculations with respect to molecular and nanoscale systems.

Nanomaterials and Nanotechnology (Ronning)
Content
 Dimension effects
 Quantisation of electrons
 Singleelectron transistor
 Synthesis of nanomaterials
 Characterization of nanomaterials
 Material systems: carbon nanotubes, graphene, magnetic nanomaterials, bionanomaterials
 Application and technology of nanomaterials
Intended Learning Outcomes
Indepth knowledge in the field of solidstate physics.

Optoelectronics (Schmidl)
Content
 Semiconductors
 Optoelectronic devices
 Photodiodes
 Light emitting diodes
 Semiconductor optical amplifier
Intended Learning Outcomes
In this course the student will learn the fundamentals of semiconductor optical devices such as photodiodes, solar cells, LEDs, laser diodes and semiconductor optical amplifiers.
Semiconductors
Optoelectronic devices
Photodiodes
Light emitting diodes
Semiconductor optical amplifier

Semiconductor Nanomaterials (Staude)
Content
 Review of fundamentals of semiconductors
 Optical and optoelectronic properties of semiconductors
 Effects of quantum confinement
 Photonic effects in semiconductor nanomaterials
 Physical implementations of semiconductor nanomaterials, including epitaxial structures, semiconductor quantum dots and quantum wires
 Advanced topics of current research, including 2D semiconductors and hybrid nanosystems
Intended Learning Outcomes
This course aims to convey a fundamental understanding of the physics governing the optical and optoelectronic properties of semiconductor nanomaterials. First, the fundamental optical and optoelectronic properties of bulk semiconductors are reviewed, deepening and extending previously obtained knowledge in condensed matter physics. The students will then learn about the effects of quantum confinement in semiconductor systems in one, two or three spatial dimensions, as well as about photonic effects in nanostructured semiconductors. Finally, several relevant examples of semiconductor nanomaterial systems and their applications in photonics are discussed in detail. After successful completion of the course, the students should be capable of understanding present research directions and of solving basic problems within this field of research.

Solid State Optics I (H. Schmidt)
Content
 Electronic, dielectric, and optical properties of solids
 Mueller matrix polarimetry
 Electrooptics and magnetooptics
 Photodetectors and optical systems
 Quantum optics and quantum technology
Intended Learning Outcomes
The course covers basic and advanced topics of solid state optics, with a special focus on the relation between electronic and optical properties. An effort is made to treat electro and magnetooptical effects and quantum optical effects as rigorous as possible through the Mueller matrix approach and through quantum mechanical approaches, respectively.

Supraconductivity (Schmidl)
Content
 Basic effects of superconductivity
 Characteristics of superconductors
 Josephson effects
 Superconducting materials (classes, structure, properties)
 Fabrication (single crystals, solid material, layers, wires, ribbons)
 Modification of the materials (doping, pinning)
 Applications of superconductivity
Intended Learning Outcomes
 Unterstanding the basic concepts and concepts of superconductivity, sperconducting materials and their application
 Creation of readytouse basic knowledge
 Ability to independently redeepen the subject
 Ability to participate in a scientific discussion

Quantum Computing (Eilenberger/Steinlechner/Pertsch)
Content
 Basic introduction to algorithms and computing
 The Qubit and entanglement thereof
 Basics of quantum algorithms
 Advanced quantum algorithms
 Implementation of QuBits and quantum computers
 Handson circuits
Intended Learning Outcomes
After active participation in the course, the students will be familiar with the basic concepts of quantum computation and the implementation of quantum algorithms. They will be able to apply their knowledge in the assessment and creation of quantum algorithms and the development of quantum information systems. The intended learning outcome is to introduce the students to the basic usage of quantum bits for information processing. To provide further insight, the course will expand this concept on multipartite systems and introduce the concept of entanglement. In a further step we shall see how individual quantum operations tie together to create algorithms. Important algorithms, such as the quantum Fourier transformation, the algorithms of Shor and Grover will be discussed. To relate the abstract knowledge on quantum algorithms to practical applications, realworld implementations of quantum computers will be discussed.

Quantum Communication (Steinlechner/Eilenberger)
Content
 Basic introduction to quantum optics
 Quantum light sources
 Encoding, transmission and detection of information with quantum light
 Quantum communication and cryptography
 Quantum communication networks
 Outlook on Quantum metrology and Quantum imaging
Intended Learning Outcomes
Goals: The course will give a basic introduction into the usage of quantum states of light for the exchange of generation of quantum light and schemes that leverage these states for the exchange of information, ranging from fundamental concepts and experiments to state of the art implementations for secure communication networks. The course will also give an outlook to aspects of Quantum metrology and imaging. After active participation in the course, the students will be familiar with the basic concepts and phenomena of quantum information exchange and some aspects related to the practical implementation thereof. They will be able to apply their knowledge in the assessment and setup of experiments and devices for applications of quantum information processing

Quantum Field Theory (Ammon)
Content
 Principles of relativistic quantum field theories
 Quantization of KleinGordon , Dirac , and electromagnetic fields
 Perturbation theory and Feynman diagrams
 S matrix and cross sections
 Functional integrals
 Effective effects and correlation functions
 Regularization and renormalization
Intended Learning Outcomes
Teaching the basic principles and structures of quantum field theories. Obtaining abilities to describe the interactions of elementary particles and to calculate important scattering and decay processes.

Quantum Imaging and Sensing (Setzpfandt/Pertsch)
Content
 Basic introduction to relevant concepts of quantumoptics
 Generation of photon pairs
 Fundamentals of twophoton interference
 Applications of twophoton interference
 Optical quantum metrology
 Ghost Imaging
 Quantum microscopy
Intended Learning Outcomes
The course will give a basic introduction into the usage of quantum light, in particular photon pairs, for imaging and sensing. To this end, many basic concepts and applications will be introduced and discussed. Furthermore, students will learn how to mathematically describe quantum sensing schemes in order to understand and predict their propreties. After active participation in the course, the students will be familiar with the basic concepts and phenomena of quantum imaging and sensing and will be able to apply the derived formalism to similar problems.

Quantum Optics (Setzpfandt)
Content
 Basic introduction to quantum mechanics
 Quantization of the free electromagnetic field
 Nonclassical states of light and their statistics
 Experiments in quantum optics
 Semiclassical and fully quantized lightmatter interaction
 Nonlinear optics
Intended Learning Outcomes
The course will give a basic introduction into the theoretical description of quantized light and quantized lightmatter interaction. The derived formalism is then used to examine the properties of quantized light and to understand a number of peculiar quantum optical effects. After active participation in the course, the students will be familiar with the basic concepts and phenomena of quantum optics and will be able to apply the derived formalism to other problems.

Theory of Nonlinear Optics (Peschel)
Content
 Types and symmetries of nonlinear polarization
 Coupling between optical fields and nonlinear matter
 Solutions of nonlinear evolution equations
 Frequency conversion in crystals with quadratic nonlinearity
Intended Learning Outcomes
The course provides the theoretical background to understand nonlinear optics.
Recommended Reading
… on nonlinear materials
 Butcher and Cotter, The Elements of Nonlinear Optics, Cambridge University Press, 1990.
 Richard Lee Sutherland, Handbook of nonlinear optics, 2003.
 Govind Agrawal, Contemporary nonlinear optics, Academic Press 1992.
…on general nonlinear optics
 Schubert and Wilhelmi, Nonlinear optics and quantum electronics, 1986.
 Jerome V. Moloney and Alan C. Newell, Nonlinear optics, 1990.
 Bahaa Saleh and Malvin C. Teich, Fundamentals of Photonics, Wiley, 2007.

Internship (individually choosen)
Module Components
Practical course of 300 h. Depending on the topic this total workload should be distributed approximately as: 50 h introduction to the research topic (study of relevant literature, …), 190 h research work (in the lab for experimental topics and atcomputer etc. for theoretical topics), 50 h preparation of the final report, and 10 h preparation and carrying out presentation of the results
Intended Learning Outcomes
Carrying out scientific labwork in photonics together with a research team; preparation of a written scientific report; presentation and defense of the results in an oral presentation.

Research Project (individually choosen)
tba

2D Materials (Soavi)
Content
 Graphene: electrical and optical properties; Applications in electronic and optoelectronic
 Semiconducting 2D materials: Coulomb screening and the concept of excitons; Optical spectroscopy of excitons; Optoelectronic applications
 Heterostructures: electron and exciton interactions in layered heterostructures
Intended Learning Outcomes
 Mastering the basics and methods of twodimensional materials
 Ability to work independently on problems in the field of twodimensional materials

Advanced Quantum Field Theory (Ammon)
Content
 Anomalies in quantum field theory
 Quantum field theory at finite temperature and density
 Nonequilibrium dynamics of field theories
 (Quantum) phase transitions
 Introduction to compliant field theory
 Topological objects in quantum field theory
Intended Learning Outcomes
Impart thorough knowledge of advanced methods in quantum field theory.

Atomic Physics at High Field Strenghts (Stöhlker)
Content
 Strong field effects on the atomic structure
 Relativistic and QED effects on the structure of heavy ions
 Xray spectroscopy of highZ ions
 Application in xray astronomy
 Penetration of charged particles through matter
 Particle dynamics in of atoms and ions in strong laser fields
 Relativistic ionatom and ionelectron collisions
 Fundamental interaction processesScattering, absorption and energy loss
 Detection methods
 Particle creation
Intended Learning Outcomes
The Module provides insight into the basic techniques and concepts in physics related to extreme electromagnetic fields. Their relevance to nowadays applications will be discussed in addition. The Module also introduces the basic interaction processes of highenergy photon and particle beams with matter, including recent developments of high intensity radiation sources, such as free electron lasers and modern particle accelerators. Experimental methods and the related theoretical description will be reviewed in great detail.

Atomic Theory (S. Fritzsche)
Content
 Short review of hydrogenic atoms
 Independentparticle model & HartreeFock theory
 Interaction with the radiation field
 Correlated manybody theory
 Atomic collision theory
 Basics of the density matrix theory
 Atoms and forces in (intense) light fields
 Laser cooling and trapping; ions traps
 Rotatingwave approximation
Intended Learning Outcomes
Learning the basics of atomic structure and atomic collision processes.

Computational Quantum Physics (S. Fritzsche)
Content
 Coulomb problem
 Particles with spin
 Qubits, quantum registers and quantum gates
 Representation of pure and mixed states (Bloch sphere)
 Composite systems, indistinguishable particles
 HartreeFock method
 Coupling of angular momenta
Intended Learning Outcomes
 Learning computer algebraic and numerical methods in the description of simple quantum models
 Ability to independently solve simple models and tasks, formulate pseudocode and deal with computer algebra systems more efficiently

Computational Physics III and IV (Brügmann)
Content
Computational Physics III
 Partial Differential Equations
 Fundamentals of differential equations
 Introduction to elliptic, parabolic and hyperbolic differential equations
 Explicit and Implicit procedures, stability analysis
 Poisson equation, diffusion equation, advection equation, wave equation
 Shocks
 Difference method
 Pseudo spectral methods
 Multiple Grids
Computational Physics IV
 Machine Learning in Physics
 Basics of Machine Learning, Neural Networks and Deep Learning
 Sample Applications in Physics, Pattern Recognition, Time Series Analysis, Monte Carlo Methods
Partial Differential Equations:
• Fundamentals of differential equations
• Introduction to elliptic, parabolic and hyperbolic differential equations
• explicit and implicit procedures, stability analysis
• Poisson equation, diffusion equation, advection equation, wave equation,
• shocks;
• difference method,
• pseudo spectral methods,
Partial Differential Equations:
• Fundamentals of differential equations
• Introduction to elliptic, parabolic and hyperbolic differential equations
• explicit and implicit procedures, stability analysis
• Poisson equation, diffusion equation, advection equation, wave equation,
• shocks;
• difference method,
• pseudo spectral methods,
Partial Differential Equations:
• Fundamentals of differential equations
• Introduction to elliptic, parabolic and hyperbolic differential equations
• explicit and implicit procedures, stability analysis
• Poisson equation, diffusion equation, advection equation, wave equation,
• shocks;
• difference method,
• pseudo spectral methods,
Intended Learning Outcomes
Computational Physics III
Mastering the basics and methods of partial differential equations and machine learning in physics
 Mastering the basics and methods of partial differential equations and machine learning in physics
 Ability to work independently on a numerical project
Computational Physics IV
 Mastering the basics and methods of machine learning in physics
 Ability to work independently on a numerical project

Experimental nonlinear optics (Paulus)
Content
 Propagation of light in crystals
 Properties of the nonlinear susceptibility tensor
 Description of light propagation in nonlinear media
 Parametric effects
 Second harmonic generation
 Phasematching
 Propagation of ultrashort pulses
 Highharmonic generation
 Solitons
Intended Learning Outcomes
This course gives an introduction to optics in nonlinear media and discusses the main nonlinear effects.

Fundamentals of Modern Optics (Pertsch)
Content
 Basic concepts of wave optics
 Dielectric function to describe lightmatter interaction
 Propagation of beams and pulses
 Diffraction theory Elements of Fourier optics
 Polarization of light
 Light in structured media
 Optics in crystals
Intended Learning Outcomes
The course covers the fundamentals of modern optics which are necessary for the understanding of optical phenomena in modern science and technology. The students will acquire a thorough knowledge of the most important concepts of modern optics. At the same time the importance and beauty of optics in nature and in technology will be taught. This will enable students to follow more specialized courses in photonics.

Innovation Methods in Physics (Pertsch/Kretzschmar)
Content
 Rapid prototyping technology in photonics
 Innovation management and design thinking
 Handson/practical examples of photonics prototyping
 Entrepreneurial skills and business modelling
 Basics of intellectual property rights
Intended Learning Outcomes
The students will learn how the results of their scientific research can be turned into relevant innovations as an important part of their future career. On the one hand, the course will enable students to understand and to drive innovation processes in photonics companies. On the other hand, students will develop an entrepreneurial skill set for the independent economical exploitation of scientific ideas. Therefore, the course introduces the basic knowledge on innovation management, entrepreneurship, and intellectual property rights. To practice their skills, the students will also conduct their own photonics innovation project during the semester by working handson in small teams in the photonics makerspace Lichtwerkstatt. During this practical part, they acquire and apply a thorough knowledge of photonic rapid prototyping technology (e.g. 3d scanning and printing, laser cutting, microcontrollers, ...) and the most important creativity methods and project management skills. To cover this range of topics, the course will be supported by guest lecturers from different sectors (academia, industry).

Gauge Theories (Gies)
Content
 Gauge symmetry
 Classical YangMills theory
 Quantization of gauge theories / BRST formalism / Gribov problem
 Perturbation theory
 Semiclassical expansions
 Topological configurations
 Confinement criteria and scenarios
Intended Learning Outcomes
Comprehension of concepts and methods, and acquiring technical skills for the theoretical treatment of gauge theories with applications in particle physics.

Integrated Quantum Photonics (Gili/Pertsch)
Content
The lecture will cover a significant part of integrated quantum photonics, which is one of the pillars of the current quantum technology development. In particular, the lecture will cover the following topics
 Integrated optics on a single photon level
 Generation and manipulation of quantum states of light using integrated waveguides
 Overview over integrated photonic platforms and fabrication of passive and active waveguide structures
 Quantum walks in linear and nonlinear waveguide lattices
 Introduction to photonic quantum computation and simulation
 Measurements using superconducting nanowire single photon detectors and transition edge sensors
Intended Learning Outcomes
The course should provide the participating students with a profound knowledge on the state of the art of integrated optics used for the realization of quantum optical devices. After active participation in the course, the students will be familiar with the basic concepts and phenomena of integrated quantum photonics and will be able to develop own concepts for integrated quantum circuitry. The intended learning outcome is that the students are introduced to the basics on the field of integrated quantum optics and its applications. Therefore, course starts with an overview on the generation of nonclassical states of light with special attention on integrated solutions. Afterwards several integrated photonic platforms will be discussed ranging from fabrication to performance and useability. Based on that the onchip manipulation of nonclassical states of light will be discussed. This starts with the very general concept of quantum walks and continues towards quantum simulation. It ends with an introductory to photonic quantum computing with a clear focus on practical implementation of quantum photonic gate structures. The course closes with the discussion on nonclassical light detection in integrated photonics.

Introduction to Nanooptics (Pertsch)
Content
 Surfaceplasmonpolaritons
 Plasmonics
 Photonic crystals
 Fabrication and optical characterization of nanostructures
 Photonic nanomaterials / metamaterials / metasurfaces
 Optical nanoemitters
 Optical nanoantennas
Inteded Learning Outcomes
The course provides an introduction to the broad research field of nanooptics. The students will learn about different concepts which are applied to control the emission, propagation, and absorption of light at subwavelength spatial dimensions. Furthermore, they will learn how nanostructures can be used to optically interact selectively with nanoscale matter, a capability not achievable with standard diffraction limited microscopy. After successful completion of the course the students should be capable of understanding present problems of the research field and should be able to solve basic problems using advanced literature.

Introduction to String Theory and AdS/CFT (Ammon)
Content
Introduction to concepts of string theory and AdS/CFT correspondence, in particular:
 Relativistic bosonic string and its quantization
 Open strings and Dbranes
 Aspects of conformal field theory
 Polyakov path integral
 Scattering of strings
 Low energy effective action
 Dualities in string theory
 Compactification scenarios
 Introduction to AdS / CFT
 Main tests of AdS / CFT
 Extension and application of AdS / CFT
Intended Learning Outcomes
Impart thorough knowlege of string theory and AdS/CFT duality.
Impart thorough knowledge of string theory and AdS/CFT duality
Introduction to concepts of string theory and AdS/CFT correspondence, in particular:
• relativistic bosonic string and its quantization
• open strings and Dbranes
• aspects of conformal field theory
• Polyakov path integral
• scattering of strings
• low energy effective action
• dualities in string theory
• compactification scenarios
• introduction to AdS / CFT
• main tests of AdS / CFT
• extension and application of AdS / CFT
Introduction to concepts of string theory and AdS/CFT correspondence, in particular:
• relativistic bosonic string and its quantization
• open strings and Dbranes
• aspects of conformal field theory
• Polyakov path integral
• scattering of strings
• low energy effective action
• dualities in string theory
• compactification scenarios
• introduction to AdS / CFT
• main tests of AdS / CFT
• extension and application of AdS / CFT

Lattice Field Theory (Wipf)
Content
 Path integral for quantum field theories
 Euclidean formulation and quantum field theories in thermal equilibrium
 Lattice field theory as spin models in Statistical Physics
 Rigorous results and approximations
 Stochastic methods, Monte Carlo simulations
 Renormalization group, critical phenomena
 Gauge theories on a spacetime grid
 Quantumchromodynamic on a lattice
Intended Learning Outcomes
 The course covers theoretical concepts and methods necessary to understand (discretized) Quantum Field Theories.
 The students will learn stochastical and numerical methods to simulate spin models and lattice field theories.
 They will aquire skills to independently develop numerical algorithms to calculate observables in Elementary Particle Physics, Quantum Field Theory and Statistical Physics.

Molecular Quantum Mechanics / Quantum Chemistry II (Gräfe/Croy)
Content
Building on Module PAFMQ100, indepth and advanced knowledge of advanced methods of theoretical chemistry is taught. This includes (timedependent) density functional theory as well as an introduction to numerical methods, concepts and algorithms for the description of molecular systems that exchange energy and/or charge with their environment.
Intended Learning Outcomes
Familiarization with advanced methods and concepts, such as DFT/TDDFT. Understanding numerical methods, concepts and algorithms for describing open quantum systems and their application to molecular and nanoscale systems.

Nano Engineering (Höppener/Schubert)
Content
 Building with Molecules
 Selforganization and selfassembled coatings
 Chemically sensitive characterization methods
 Nanomaterials for optical applications
 Nanowires and nanoparticles
 Nanomaterials in optoelectronics
 Bottomup synthesis strategies and nanolithography
 Polymers and selfhealing coatings
 Molecular motors
 Controlled polymerization techniques
Intended Learning Outcomes
A large diversity of nanomaterials can be efficiently produced by utilizing chemical synthesis strategies. The wide range of nanomaterials, i.e., nanoparticles, nanotubes, micelles, vesicles, nanostructured phase separated surface layers etc. opens on the one hand versatile possibilities to build functional systems, on the other hand also the large variety of techniques and processes to fabricate such systems is also difficult to overlook. Traditionally the communication in the interdisciplinary field of nanotechnology is difficult, as expertise from different research areas is combined. This course aims on the creation of a common basic level for communication and knowledge of researchers of different research fields and to highlight interdisciplinary approaches which lead to new fabrication strategies. The course includes basic chemical synthesis strategies, molecular selfassembly processes, chemical surface structuring, nanofabrication and surface chemistry to create a pool of knowledge to be able to use molecular building blocks in future research projects.

Optical Metrology and Sensing (Staude)
Content
 Basic principles
 Wave optical fundamentals
 Sensors
 Fringe projection, triangulation
 Interferometry and wave front sensing
 Holography
 Speckle methods and OCT
 Phase retrieval
 Metrology of aspheres and freeform surfaces
 Confocal methods
Intended Learning Outcomes
This course covers the main principles of optical measurements and surface metrology.

Particles and Fields (Gies)
Content
 Introduction: examples of classical field theories
 Aspects of classical field theory: Lagrange and Hamilton formalism, Noether theorem and charges
 Nonlinear scalar field theories: O(N) models, spontaneous symmetry breaking, Goldstone theorem
 Fields / particles as representations of the Lorentz group: classification of representations, spinors, construction of free theories
 Interactive theories: Yukawa models, QED, Abelian Higgs models
 Current aspects of field theories in particle physics
Intended Learning Outcomes
Comprehension of concepts and methods, and acquiring technical skills for the theoretical treatment of field theories with applications in particle physics.

Particles in Strong Electromagnetic Fields (Stöhlker)
Content
 Electrons in constant fields
 Electrons in electromagnetic pulses
 Radiation produced by particles in extreme motion
 Radiation reaction
 QED effects in strong laser fields
Intended Learning Outcomes
This course is devoted to the dynamics of charged particles in electromagnetic fields. Starting with motion of electrons in constant magnetic and electric fields, the course continues with the electron motion in electromagnetic pulses (i.e. laser pulses) of high strength (i.e. when laser pressure becomes dominant). Radiation produced by electrons in extreme motion will be calculated for several most important cases: synchrotron radiation, Thomson scattering, undulator radiation. Effects of radiation reaction on electron motion will be discussed. The last part of the course will briefly discuss the QED effects in strong laser fields: stochasticity in radiation reaction, pair production by focused laser pulses and QED cascades. Analytical framework will be complemented with the help of numerical calculations.

Physics of the Quantum Vacuum in Strong Fields (Gies)
Content
 Theoretical foundations of quantum electrodynamics (QED) in strong electromagnetic fields
 Derivation of elementary signatures of the strong field QED
 Discussion of proposals for their demonstration with current experimental methods
Intended Learning Outcomes
Imparting concepts and methods and gaining the skills to deal with quantum electrodynamics issues in strong electromagnetic fields.

Quantum Information Theory (Gärttner/Sondenheimer)
Content
 Basic introduction to quantum optics
 Quantum light sources
 Encoding
 Transmission and detection of information with quantum light
 Quantum communication and cryptography
 Quantum communication networks
 Outlook on Quantum metrology and Quantum imaging
Contributed lectures by Dr. Sondenheimer
 Open quantum systems, Density matrix formalism, Generalized measurements, Quantum channels
 Superdense coding, quantum teleportation
 Entanglement theory
 Bell inequalities, CHSH inequalities
 Quantum circuits, universal gates
 Quantum error correction
Intended Learning Outcomes
The course will give a basic introduction into the usage of quantum states of light for the exchange of information. It will introduce contemporary methods for the generation of quantum light and schemes that leverage these states for the exchange of information, ranging from fundamental concepts and experiments to state of the art implementations for secure communication networks. The course will also give an outlook to aspects of Quantum metrology and imaging. After active participation in the course, the students will be familiar with the basic concepts and phenomena of quantum information exchange and some aspects related to the practical implementation thereof. They will be able to apply their knowledge in the assessment and setup of experiments and devices for applications of quantuminformation processing.

Solid State Optics II (H. Schmidt)
tba

Structure of Matter (Stenzel)
Content
 Classical interaction of light with matter
 Basic knowledge on quantum mechanics
 Einstein coefficients and Plancks formula
 Selection rules
 Hydrogen atom and helium atom
 Introduction to molecular spectroscopy
 Dielectric function and linear optical constants
 KramersKronigRelations
 Linear optical properties of crystalline and amorphous solids
 Basic nonlinear optical effects
Intended Learning Outcomes
The course is an introduction to the principles of the optical response of materials.

The Standard Model of Particle Physics (Wipf)
Content
Overview of the standard model of particle physics including:
 Symmetries, quantum electrodynamics
 Strong interaction
 The quark model and quantum chromodynamics
 Hadrons and asymptotic freedom
 Weak interactions and the Higgs effect
 Scattering experiments
 Limits of the Standard Model
Intended Learning Outcomes
Impart thorough knowledge of particle physics phenomenology and its fundamental concepts.

Theoretical Solid State Physics (Peschel)
Content
 Crystal structures and elastic properties of solids
 Electronic properties of crystals
 Approximate methods for electronic band structure
 Semiconductors and defect physics
 Pn junctions
 Microscopic description of charge transport
 Properties of alloys
 Nanostructures and interfaces
 Optical and dielectric properties of solids
 Magnetism and superconductivity
Intended Learning Outcomes
The course covers advanced topics of solid state physics, with a specific focus on the theoretical understanding of the properties of electrons in crystals. An effort is made to remain as rigorous as possible in the theoretical and mathematical treatment, while keeping the presentation at an accessible level through the presentation of interesting applications to experiments and advanced technology. After completion of the course the students will master the relation between electronic structure of crystalline solids and their dielectric, optical, transport, magnetic properties.

Symmetries in Physics (Wipf)
Content
 Symmetries and groups
 Space and spacetime symmetries
 Conserved currents and charges
 Discrete groups and continuous Liegroups
 Representations of groups, theory of characters, reductions of representation
 Invariant integration on LieGroups
 Liealgebras and their representations
 Classification of semisimple Liealgebras
 Selected application of group theory and representation theory in solid state physics, atomic and molecular physics, quantum field theory and particle physics
Intended Learning Outcomes
The course covers theoretical concepts of discrete and continuous groups, Liealgebras and their representations with relevant applications in physics. The students will learn how to exploit symmetry principles to simplify or even solve problems in all branches of physics where symmetry principles play a role.

Supersymmetry (Wipf)
Content
 Supersymmetric quantum mechanics
 Symmetries and spinors
 Wess Zumino models
 Supersymmetry algebra and representations
 Superspace and superfields
 Supersymmetric YangMills theories
Intended Learning Outcomes
The students will learn the structure and properties of supersymmetric theories and the basics for understanding developments in particle physics and string theory. They will aquire skills to calculate simple processes in supersymmetric theories.

Topics of Current Research: Quantum Field Theory (Ammon)
Content
 Further, indepth topics in the field of quantum field theory
 Topics from current areas of research
Intended Learning Outcomes
 Specialisation in a special field of quantum field theory
 Independent handling of exercises
 Ability of literature review

Topics of Current Research: Gravitational Theory (Brügmann)
Content
 Further, indepth topics in the field of gravitation theory
 Topics from current areas of research
Intended Learning Outcomes
 Specialization in the special field of gravitation theory
 Independent handling of exercises
 Ability of literature review

Master degree thesis (individually choosen)
tba