Physics of Light

Prof. Dr. Joly, Prof. Dr. Chekhova, 5 ECTS

• Linear properties of materials.
• Origin of the nonlinear susceptibility.
• Importance of phase-matching.
• Second harmonic generation, derivation of the set of coupled equations.
• Importance of the initial phase and case of seeding second harmonic generation. Use of birefringence to achieve phase-matching.
• Electro-optic effects.
• Nonlinear process in relation to third order nonlinearity.
• Modulation instability, soliton formation, perturbations of soliton, and supercontinuum generation.
• Application: nonlinear optics in photonic crystal fibers.

Prof. Dr. Chekhova, 5 ECTS

• Basic concepts of statistical optics
• Spatial and temporal coherence. Coherent modes, photon number per mode
• Intensity fluctuations and Hanbury Brown and Twiss experiment
• Interaction between atom and light (semiclassical description)
• Quantization of the electromagnetic field
• Quantum operators and quantum states
• Heisenberg and Schrödinger pictures
• Polarization in quantum optics
• Nonlinear optical effects for producing nonclassical light
• Parametric down-conversion and four-wave mixing, biphotons, squeezed light
• Single-photon states and single-photon emitters
• Entanglement and Bell’s inequality violation

Prof. Dr. Joly, 5 ECTS

This module naturally follows the “Basics of Lasers” module and aims at deepen the knowledge on a few specific aspects of lasers. In particular we will study the Z-cavity of one of the most popular laser system: the Titanium: sapphire laser. The purpose here is to show why simpler cavity is not possible. It requires understanding properly the concept of stability of laser cavity and introduces the problem of astigmatism. In a second stage we see how dispersion effects can hamper the properties of a mode-locked laser system and see how to circumvent this. We then study the different method used to characterize ultrashort laser pulse. This starts from basics concepts of autocorrelation but review more advanced techniques allowing to retrieve fully the amplitude and phase of a laser pulse. Towards the end of the lecture several topics are possible and it will be chosen together with the students. This can be for instance (i) the polarization and the Jones’ formalism (ii) the Maxwell-Bloch equations (iii) the origin of spontaneous emission. Finally in order to broaden the contents of the lecture the students are asked to prepare one half-an-hour presentation of the topics of their choice. The topics are discussed during the first two sessions of the lecture and must focus on a physical aspect of laser.

Prof. Dr. Hartmann, 5 ECTS

1. Introduction and Historical Overview
2. Recap of Quantum Mechanics
   States, wavefunctions and operators; time evolution and superpositions; measurements; qubits; composite quantum systems; the exponential Hilbert space; density matrices; dissipation
3. Quantum Computing Basics
   Models of quantum computation; gate model; adiabatic quantum computing
4. Quantum Algorithms for Fault Tolerant Quantum Computers
   Deutsch’s problem; classical circuits; quantum circuits; gates; some applications of the C-NOT gate; universal sets of gates; Can a quantum computer do classical computations efficiently? How hard is it to simulate a quantum computer with a classical computer? Simon’s problem; quantum Fourier transform; phase estimation; Shore’s factoring algorithm; solving systems of linear equations
5. Quantum Error Correction
   repetition code; stabilizer formalism; surface codes;  toric code; planar surface codes
6. NISQ Quantum Computing
   Today’s quantum hardware; variational algorithms; Quantum Approximate Optimization Algorithm (QAOA); quantum simulation

Prof. Dr. C. Marquardt,  Prof. Dr. Schmauß, 5 ECTS

• Introduction to quantum communication: Motivation and practical impact
• Introduction and refresh of fundamentals of quantum mechanics
• Basics of information theory
• Definition of a quantum state in quantum optics
• Fundamental principle of quantum key distribution
• Fundamental principle of quantum communication
  (classical and quantum capacity)
• Detailed steps of quantum key distribution
• Security proofs (epsilon security)
• Modulation of quantum states
• Detection of quantum states
• Electronics for coherent communication
• Error correction codes
• Practical implementations
• Combination with classical cryptography
• Fiber-based systems
• Free space and satellite-based systems
• Quantum repeaters

Prof. Dr. Eichler, 10 ECTS

The module discusses light-matter interaction in different systems as well as the quantum nature of light. Emphasis is put onto the laser. Starting from the theory of optical resonators and Gaussian beams we review the generation of laser light on a microscopic level (Maxwell-Bloch equations) and examine its principal characteristics. Various applications of laser light in quantum optics, laser spectroscopy, laser cooling and trapping of atoms and in non-linear optics are investigated. In addition we review various quantum optical phenomena like photon statistics, photon bunching/anti-bunching, multi-photon interferences, intensity interferometers and resonance fluorescence.

Prof. Dr. Götzinger, Prof. Dr. Joly, 5 ECTS

• Photonic Crystal Optics
• Laser/ Pulsed light / pulse propagation
• Guided wave optics
• Fiber optics
• Photonic crystal fibers
• Optical resonators / microresonators
• Acousto optics/spatial light modulator
• Metamaterials
• Orbital angular momentum
• Superresolution

Prof. Dr. Joly, Prof. Dr. Chekhova, 5 ECTS

• Nonlinear propagation in solid-core photonic crystal fibres (modulation instability, four-wave mixing, soliton dynamics, supercontinuum generation) and in hollow-core photonic crystal fibres (generation of tunable dispersive waves, plasma in fibres)
• Nonlinear optical effects (parametric down-conversion, four-wave mixing, modulation instability) for the generation of nonclassical light (entangled photons, squeezed light, twin beams, heralded single photons).
• Nonlinear effects for generating high energy sub cycle pulses (kerr-lens mode-locking, Yb:YAG laser technology, optical parametric amplification, pulses synthesis, attosecond pulse generation)

Prof. Dr. C. Marquadt, 5 ECTS

In this module we will introduce and discuss fundamental concepts of quantum communication and talk about recent developments. Topics include: Introduction to quantum information concepts, quantum optics: preparation and measurement of quantum states, concepts of quantum cryptography and the BB84 protocol, quantum key distribution with discrete variables: modern protocols, QKD with continuous variables, modern quantum key distribution security proofs, quantum repeaters, quantum communication with satellites, quantum random number generation

After the module students

• comprehend an interesting physical topic in a short time frame
• identify and interpret the appropriate literature
• select and organize the relevant information for the presentation
• compose a presentation on the topic at the appropriate level for the audience
• use the appropriate presentation techniques and tools
• criticize and defend the topic in a scientific discussion

Prof. Dr. Chekhova, 5 ECTS

• Two-photon absorption with entangled photons
• Fibre sources of nonclassical light
• Nanoscale quantum nonlinear optics
• Sensing ‘with undetected photons’
• Nonlinear optics with noble gases
• The ’simplest‘ nonlinear optical system: a single atom
• Quantum optics with parabolic mirrors
• Machine Learning for Quantum State Estimation
• Artificial Intelligence for Designing Quantum Optics Experiments and Photonic Devices

Prof. Dr. F. Marquardt, 5 ECTS

This module aims at covering a few special topics in the interactions between quantum matter (atoms, molecules) and quantum light. The first part of the course will present fundamental aspects such as light field quantization, spontaneous emission, stimulated emission and absorption, cavity quantum electrodynamics. The second part of the course makes use of the introduced concepts to allow the understanding of laser theory, laser cooling, cavity cooling and cavity optomechanics. The mathematical tools involved are quantum master equations and quantum Langevin equations.

Prof. Dr. Chekhova, 5 ECTS

• Polarization of light: definition, brief history, role in photonics
• Jones vector and Jones matrices
• Stokes parameters and Müller matrices
• Poincare sphere representation: states, transformations
• Optical elements that we use in the lab
• Geometrical phase
• Crystal optics: birefringence, Fresnel surfaces, uniaxial and biaxial crystals, walkoff
• Polarization in nonlinear optics: phase and group matching
• Polarization in quantum optics: operators-0 Polarization in quantum optics: states
• Quantum key distribution with polarized photons.

Prof. Dr. Hartmann, 5 ECTS

The course provides an introduction to quantum computing. The development of quantum hardware has progressed substantially in recent years and has now reached a level of maturity where first industrial applications are being explored. This course will introduce the fundamental ingredients of quantum algorithms, quantum bits and quantum gates, the most important hardware implementations and in particular algorithms that can run on near term hardware implementations of so called Noisy Intermediate Scale Quantum (NISQ) devices. The course will be completed with introductions to the basic concepts of error correction, which is needed in the next stage of development to fully exploit the potential of this emerging computing technology. Prerequisites: the main concepts of quantum theory, including quantum states, the Schrödinger equation, unitary evolution and measurements.

Dr. Roland Gillen, 5 ECTS

The lecture series will discuss modern (and less modern) theoretical methods for the simulation of optical spectra of crystalline materials. A focus will lie on the proper description of excitonic and trionic contributions, which are important in one- and two-dimensional materials. Examples in the form of calculations and paper reviews will be integrated into the lectures.

Selected topics are:

• Excitons in solid, particularly one- and two-dimensional materials

• Effective mass-based approaches

• Tight-binding

• Modern ab initio methods, such as density-matrix based approaches and the excitonic Bethe-Salpeter Equation

Reading material containing the contents of the lecture and recordings from a previous lecture series will be available on StudOn.

Prof. Dr. Schmidt, 5 ECTS

The nobel prize is the most prestigious award in physics. Here we focus on nobel prizes for the quantum theory of light and matter. This field is an important cornerstone of modern physics and the largest research pillar of our physics department. Goal of this seminar is to gain an understanding and overview of the most prominet topics in this field.