Research Labworks for MSc

Seeing is believing. This sentence is as true as it is tricky. Most cellular components and processes, crucial for the nuanced understanding of (human) life, are not observable by conventional light microscopy since Abbe’s Law describes their maximum resolution to roughly half the wavelength of the observed light. This law is literally set in stone in Jena. However, over the past 15 years several ways of cleverly circumventing this diffraction limit were developed and implemented, achieving three-dimensional resolutions down to the nanometer range, resulting in the ever-growing field of optical super-resolution microscopy, for which the 2014 Nobel Prize in Chemistry was awarded.

The aim of this projects is to introduce, understand and apply the principles of state of the art fluorescence microscopy techniques, used e.g. in a broad range of modern biomedical and cell-biological research. Students prepare their own, fluorescently labeled, biological samples and will image them on a variety of advanced microscopes with different (resolution) capabilities. The qualitative and quantitative comparison of acquired images will illustrate the advantages and limitations of the respective microscopy technique.

Goals and Context

• Principles and application of advanced fluorescence microscopy techniques
• Concept of diffraction-limited and super-resolution
• Preparation of fluorescently labeled, biological samples
• 3D & multi-colour imaging at the nanoscale

Methods

• Cell culture and wet lab
• Fluorescent labeling
• A selection of advanced fluorescence microscopy techniques from the IAOB toolbox:
  • Confocal Laser Scanning Microscopy
  • Array Scan Microscopy
  • Stimulated Emission Depletion (STED)
  • Structured Illumination Microscopy (SIM)
  • Single-Molecule Localization Microscopy (SMLM)
  • MINFLUX Nanoscopy
• Image analysis by Fiji/ImageJ

Prerequisites

• An open mind and motivation for independent thinking
• Students should be able to explain the general difference between confocal and widefield microscopy and have basic knowledge on the concepts of super-resolution microscopy (e.g. Abbe’s diffraction limit)
• You should know the basic principles of fluorescence

A good preparation for the course is the biophysics lecture from Prof. C. Eggeling

Person in charge: Christian Franke & Katharina Reglinski

Supervisors: Christian Franke & Katharina Reglinski         

Venue: Microscopy Labs of the IOAB in the ZAF and Abbeanum or at the IPHT (Beutenberg)

The topic is suitable for two groups with 2 students each.

Advanced techniques for stabilization of optical cavities

In the realm of advanced scientific research, the exploration of precise measurement techniques and the development of stable optical systems have emerged as crucial endeavors. These fields have witnessed remarkable progress, enabling breakthroughs in various scientific disciplines and pushing the boundaries of our understanding. Precise measurement techniques, coupled with ultra-stable optical systems, have revolutionized fields such as quantum optics, spectroscopy, and fundamental physics research. These techniques allow us to probe the fundamental properties of matter and light with unprecedented accuracy and precision. Additionally, they enable the detection and measurement of elusive phenomena such as gravitational waves, opening up new avenues for exploring the mysteries of the universe. At the heart of these precise measurement techniques and stable optical systems lie advanced stabilization methods for optical cavities and lasers. Optical cavities, with their ability to enhance light-matter interactions, play a crucial role in achieving high-precision measurements. Stabilizing these cavities ensures their reliability and accuracy, enabling precise control over photon generation and manipulation. Our focus will extend beyond specific applications and delve into the general principles and techniques involved in stabilizing these optical systems. We will explore advanced stabilization methods such as the Side-of-Fringe (SOF) locking technique and the Pound-Drever-Hall (PDH) locking technique, which are widely applicable in diverse scientific settings.

Teaching Goals and Content

• Understand the principles and importance of optical cavities in current technologies.
• Design and construction of an optical cavity.
• Calculations of the mode-matching optics of a cavity by using ABCD matrix.
• Explore the Side-of-Fringe (SOF) locking technique for cavity stabilization.
• Explore the Pound-Drever-Hall (PDH) locking technique for stabilizing optical cavities by using radiofrequency techniques.
• Compare and contrast the SOF and PDH locking techniques in terms of performance and applicability.
• Analyze the stability and reliability of the optical cavity using these locking techniques.

Experimental Techniques and Equipment

• Optical alignment of optical cavities.
• Continuous wave pump lasers at suitable wavelengths.
• Photodetectors for monitoring the cavity's reflected and transmitted light.
• Electro-optic modulators for phase modulation in the PDH technique.
• Lock-in amplifiers for demodulation and proportional-integral (PID systems) for feedback control.
• Data acquisition systems for recording and analyzing the locking signals.

Place:            Fraunhofer IOF institute

Supervision: MSc. L. Gonzalez

For this experiment two students are recommended.

Generation of single photons and Bell states has been a central concept for explaining EPR paradox, proposed by Einstein in 1935. Often termed as spooky action at a distance, this phenomenon has now become practically understandable, thanks to the development of efficient entangled photon sources in past two decades. Entangled photon sources are a powerful resource that, in addition to fundamental tests as mentioned above, have been used for state-of-the-art demonstrators of quantum enhancement in a variety of fields such as quantum imaging, quantum simulation and quantum communication.

The aim of this lab work is to give an intuitive understanding of single photon generation with non-linear materials and quantum entanglement from an experimental point of view. An analysis of factors like phase matching conditions for non-linear materials and their tuning with temperature, optical alignment, evaluation of correlation functions and analysis of single photon and entangled state.

Teaching Goals and Content 

• Bell states of light and their generation: Concepts with an overview of the course
• Fundamentals of designing a single photon source: Hardware and opto-mechanics selection, calculations of various beam parameters, optical alignment
• Characterizing a source: In terms of spectra, photon generation rate and efficiency
• Demonstration of two-photon interference-The Hong Ou Mandel (HOM) effect: Determining the purity of single photons and computation of coherence time of single photons
• Transitioning to an Entangled photon source (EPS): Employing birefringent media to achieve an entangled state and entangled state division into two channels for further analysis
• Characterization of the EPS: Development of a polarization analysis module, Indistinguishability analysis in polarization mutually unbiased basis for the above two channels.

Experimental Techniques and Equipment 

• Nonlinear crystals- periodically poled ppktp and crystal heating oven for photon generation and temperature tuning, respectively.
• Optics-lenses, mirrors, polarizers, waveplates, beam displacers, birefringent media (ppktp, YVO4, calcite), for setup construction and subsequent operation.
• Michelson Interferometer- design and illustration of operation.
• Grating spectrometer for spectral data recording.
• Si avalanche single photon detectors and timing correlator (Time tagger) for correlation measurements.

Supervisors:   MSc. Purujit Singh Chauhan, MSc. Sabine Hausler

Place:            Fraunhofer IOF institute and ACP labs

Literature:

1.      Basic knowledge on the behaviour of light under optical elements like – lens, waveplates, beam splitter, polarizer
2.      Gaussian beam propagation- theory is widely available online as well in IAP Masters course lectures
3.      The experimental work is based on the following review paper-Entangled Photon-Pair Sources based on three-wave mixing in bulk crystals (https://arxiv.org/abs/2007.15364)

For this experiment two groups of two students are recommended.

Nowadays the generation of ultra-short laser pulses with a duration down to some femto seconds is state of the art. Such pulses find their application not only in the field of scientific research to investigate ultra-fast processes, to perform ultra-precise spectroscopy, or to generate extreme electrical and magnetic fields through ultra-high light intensities, but they are also applied in material processing, medicine, especially in ophthalmology. Nevertheless, the generation and metrology of ultra-short pulses require complex measurement techniques. The basics to understand the underlying effects of pulse generation, stretching and compression as well as their measurement will be taught here. Some of these effects are based on non-linear optics and frequency conversion, that requires phase matching to get reasonable efficiencies. Second harmonic generation and two-photon absorption are used for pulse characterization by auto-correlation here. The limitations of the auto-correlation for the reconstruction of the temporal behavior of the laser field will be investigated in more detail.   

Teaching goals and content 

• Working principle and properties of solid-state lasers (Ti:sapphire)
• Cavity stability and longitudinal cavity modes
• Dependence of output power on pump power
• Generation of femtosecond pulses by Kerr-lens mode-locking
• Compensation of group velocity dispersion in optical cavities
• Impact of spectral phase on pulse duration and temporal pulse shape
• Measurement of band-width and duration of laser pulses
• Application of Fourier-Transform to explain pulse stretching and compression
• Interferometric and intensity auto-correlation and their limitations for pulse characterization
• Measurement of group velocity dispersion (GVD) of several materials

Experimental techniques and equipment

• diode-pumped, frequency-doubled 5W Nd:YV0₄-laser as pump source
• homemade Ti:sapphire femtosecond laser with prism GVD compensation
• external prism pulse compressor
• optical spectrometer
• second harmonic generating auto-correlator
• photodiodes, powermeter and oscilloscope

Supervisor:   Dr. Joachim Hein

Place:            F-Praktikum

For this experiment two students are recommended.

In modern optical imaging, precise methods for investigating micro- and nanoscale structures are of great importance. Diffraction imaging revolutionizes optical imaging by foregoing traditional optics and instead relying on computer algorithms to create high-resolution images. Despite its potential, there are significant challenges in reconstructing images from diffraction patterns.

The main focus of this project is to investigate the optical diffraction imaging in the visible range. The various influences such as the size of the illumination spot, the coherence, the structure size, the monochromaticity or bandwidth and the overlap with other beams in the visible spectral range will be taken into account. A particular focus will be on exploring the convergence of reconstruction algorithms as a function of the above parameters. In particular, multicolor diffraction still raises many fundamental questions.

Teaching Goals and Content 

• Design and construction of an optical test setup
• Basics of diffraction imaging and ptychography
• Influence of various light sources on imaging
• Development and application of reconstruction algorithms
• Experimental applications and diagnostic methods

Prerequisites

• Basics in optics, Fourier optics, and image processing
• Interest in modern imaging and algorithm development
• Experimental skill and problem-solving ability
• Basic knowledge in programming, ideally in Python or Matlab

Supervisor: Dr. Martin Wünsche and Dr. Jan Rothhardt

Place:         Max-Wien-Platz 1 and Albert-Einstein-Str. 6

The topic is suitable for two groups with 2 students each.

Development of a spectroscopic ellipsometer and investigation of the measurement uncertainty

Ellipsometry is a non-invasive optical measurement technique used to characterise thin layers on surfaces. It is based on the analysis of the change in the plane of polarisation of light reflected from a surface. By measuring the changes in polarisation, important parameters such as layer thickness, refractive index and layer structure of materials can be determined. Ellipsometry is used in various fields such as materials science, semiconductor manufacturing, surface coating and nanotechnology to accurately characterise and control the properties of thin films.

One focus of the practical course is the creation of a digital twin of the ellipsometer, which enables the device to be virtually simulated and its performance analysed under various conditions. This will be used to test the evaluation software and analyse the influence of various system parameters such as alignment, detector noise and deviation of the optical elements on the measurement uncertainty.

The main goals of this experiment are:

1. Understanding the concept of ellipsometry and its significance in nanoscience and materials science.
2. Develop a flexible digital twin of the ellipsometer
3. Apply the digital twin to improve the available software and investigate the uncertainty
4. Experimentally validation of the findings

Prerequisites:

• Basic Understanding of Polarization
• Basic knowledge of Phyton programming
• Good laboratory skills
• Interest in designing a students’ experiment

Supervisor: Dr. Thomas Siefke

Language: Python, C, C++

Venue: F-Praktikum

The topic is suitable for one or two students.

Fiber Bragg gratings (FBG) play a key role in modern fiber optics. They consist of a modulated refractive index in the fiber core and act as narrow-bandwidth filters or in-fiber reflectors. Their application spans from cavity mirrors or dispersion control in fiber lasers to signal filtering in quantum optics and astro photonics.  They are also commonly used as strain or temperature sensors. In comparison to normal FBGs, that have a constant grating period, chirped FBGs have a varying(increasing) grating period, meaning different spectral components will be reflected at different spatial positions within the grating. This enables dispersion control in the fiber. To realize FBGs, a femtosecond pulsed laser system is used.

The main focus of this project will be the investigation of the influence of different inscription parameters on the dispersion on the resulting FBG.  To do this, a simple in-fiber interferometric measurement setup has to be built and characterized. Then, the dispersion of several FBGs is measured with an inhouse software. Finally, the results are to be analyzed and compared.

Teaching goals and content

• Basics of FBGs and chirped FBGs and their inscription by femtosecond pulsed laser
• Fiber handling and preparation
• Setup and characterization of a simple interferometric fiber-based setup
• Measurement of dispersion of multiple different FBGs
• Basic signal processing and analysis

Prerequisites

• Basics in optics
• Minimal experimental skills
• Basic knowledge in programming, ideally in Python or Matlab
• Interest in integrated fiber optics and their application

Supervisor:         Ria Krämer & Georg Schwartz

Place:                   Institute of Applied Physics (IAP, Beutenberg)

The topic is suitable for two students.

Interaction of intense ultrashort laser pulses with crystalline solids might excite a coherent vibrational motion in the lattice having ultrafast time scale – from several tenses to several hundreds of femtoseconds. The physical mechanism of the excitation is typically the Raman excitation, when nuclear motion is triggered by the electron polarization driven by intense laser pulses, whereas the type of the excited vibrational modes depends on relative orientation of the laser polarization in respect to the symmetry axes of the crystal.

The goal of the suggested project is the experimental investigation of time-dependent dynamics of lattice vibrations in a very novel magnetic semiconductor layered material CrSBr excited by intense, ultrashort laser pulses. The experiments are based on a pump-probe technique when an intense, ultrashort laser pulse excites vibrational motion of the lattice via the resonant stimulated Raman scattering, and the corresponding phonon dynamics is probed by a weak pilot ultrashort pulse. Specifically, a novel detection scheme will be used, that is based on the dynamically changing birefringence, induced in the material due to the lattice motion. This detection scheme involves a box-car integrator and lock-in amplifier detection to achieve a very high sensitivity. The spectrum and the temporal evolution of the coherent phonons will be measured as a function of crystal orientation and the intensity of the pump laser pulses.

Prerequisites

• Basics knowledge in optics
• Good experimental skills
• LabView as highly desirable skill

Supervisor:         Dr. Daniil Kartashov

Place:                  Institute of Optics and Quantum Electronics (IOQ, Max-Wien-Platz 1)

The topic is suitable for one or two students.

According to de Broglie matter has not only particle but also wave character. It was shown that electrons, due to their rest mass, already exhibit wavelengths of around 1 angstrom at acceleration voltages of about 150 V, which is in the range of atomic distances in solids. Crystals therefore represent natural diffraction gratings for accelerated electrons, just as they do for X-rays of similar wavelengths. However, due to the strong inelastic interaction between electrons and atoms, the inelastic mean free path of electrons in solids ranges from less than 1 to several 100 nm which is thus considerably smaller than for X-rays. This makes electron diffraction especially suited for the investigation of crystalline surfaces and thin layers.

The aim of this projects is to understand principles of electron diffraction, especially reflection high energy electron diffraction (RHEED) and low-energy electron diffraction (LEED), which are a widely used characterization method for inorganic compounds with the ability of in situ growth monitoring of thin films. Students prepare their own samples, starting from cleaning single-crystal surfaces, followed by the deposition of films via molecular beam epitaxy as well as their structural characterization by means of RHEED and LEED. All preparation and analyzing steps are performed under ultrahigh vacuum (UHV) conditions.

Goals and context

• principles and application of electron diffraction in two dimensions (2D)
• concept of reciprocal space
• preparation of atomically clean single crystals and two dimensional materials
• highly-ordered ultrathin layers by molecular beam epitaxy
• vacuum technology (pumps, gauges, rest gas analysis etc.)

Methods

• UHV chambers with:
  
  • RHEED device (electron gun, phosphor screen, camera)
  • MCP-LEED (electron gun, phosphor screen, micro channel plates, camera)
  • sputter gun and sample heater
  • vacuum pumps (roughing, turbo, ion getter, and titanium pump)
• metal single crystals as sample substrates
• effusion cells for deposition

Supervisor: Dr. Felix Otto    

Venue: Labs of AG Fritz (ZAF)

The topic is suitable for two students.

Two dimensional materials show some unique optical properties, many of which arising from the quantum confinement that leads to a strong binding of excited electrons and the positively charged hole. Some experiments, e.g. for the study of nonlinear optics and many body physics, require high laser excitation powers which leads to a problem that has so far not been studied in detail: local heating by the laser radiation. This is especially crucial in experiments where the excitation power is scanned from low and high, since the different temperatures will lead to secondary effects that make any interpretation difficult. To mitigate the heating effects or include the heating into the models appropriately, we first need to learn more about the magnitude of said temperature increase. In our labs we work with many different materials, wavelength-ranges and temperatures from ambient down to 14 K and it can be expected that each configuration will be unique, but for our first investigation that will be detailed below, we will pick the class of 2D materials known as transition metal dichalchogenides (TMDs), because they possess a Raman peak that is known to be temperature sensitive.

In the experiment we will place the sample on a thermostat and perform a measurement of this Raman peak with very low excitation power which is expected to leave the temperature nearly unchanged. By tuning the temperature of the thermostat, a correlation of peak position and temperature can be established. After that, we repeat the experiments, only this time the thermostat remains fixed at the lowest temperature and the excitation power is increased. Again, the peak position is monitored, which yields the correlation between laser powerand peak position. By combining the two results we can determine the influence of laser power on temperature.

Objectives

• Temperature dependence of Raman mode in TMDs
• Laser induced heating in TMD

Experimental techniques

• Raman scattering
• Cryostat/thermostat
• Two-dimensional materials

Supervisor: M.Sc. Muhammad Hussain

Venue: GUFOS, IFK (Room E011)

The topic can be worked on by one or two students. Supervision is possible in English only.

Nonlinear optics is a vital part of science and technology, widely used for frequency conversion, self-referencing of frequency combs, spectroscopy, sensing and ultrashort pulse characterization. Two-dimensional materials are ideal for nonlinear optics because they offer a strong optical response with nearly unlimited bandwidth. Additionally, due to their deep-sub wavelength thickness, flexibility and strength, they can be easily integrated into photonic platforms.

In this series of experiments, we will investigate the nonlinear optical properties, namely second harmonic (SH) and third harmonic (TH) generation, of atomically thin semiconductors belonging to the category of transition metal dichalcogenides (TMDs). We will theoretically and experimentally study the SH and TH nonlinear response of TMDs, focusing in particular on their power and polarization dependence. In addition, we will discuss how the latter can be understood in a more general framework considering point group symmetries. We will study how SHG can be used for the characterization of crystal orientation and number of layers in naturally stacked TMDs. Finally, we will discuss the concept of angular momentum of light and we will experimentally study SHG and THG in TMDs when the fundamental beam is tuned from linear to circular polarization.

Working plan:

Weeks 1 -4: introduction to SHG in TMDs, dependence of SHG on layer number, input power and stacking, polarization resolved SHG (six fold patterns, resolving crystal axes and strain)

Weeks 5-8: introduction to THG in TMDs, dependence of THG on layer number, input power and polarization, in comparison to SHG

Weeks 9-12: angular momentum of light, SHG & THG for linear à circular polarization

Objectives

• 2D Materials and TMDs: band structure, optical properties and crystal symmetry
• Nonlinear optics: basic theory, nonlinear susceptibility tensors for SHG and THG
• Polarization optics (Quarter wave plate, half wave plate…..)

Experimental techniques

• Second harmonic generation (SHG)
• Third harmonic generation (THG)
• Low noise and lock-in detection
• Precise control and detection of the polarization state of light

Supervisor: Sebastian Klimmer

Venue: GUFOS, IFK (Room E002)

The topic can be worked on by one or two students. Supervision is possible in English and German

The particle-in-a-box model is a simplified but powerful representation used to explain quantum confinement effects. In this model, a particle, such as an electron, is imagined to be confined within a one-dimensional potential energy well, often resembling a rectangular box. The dimensions of the box, particularly its length, determine the quantized energy levels of the confined particle.

Similar to electrons within a potential well, electrons within organic molecules can exhibit quantized energy states due to quantum confinement. Consequently, energy levels in molecules depend on their size and structural characteristics. Experimental evidence for the particle-in-a-box model shall thus be provided by means of absorption and photoluminescence measurements on suitable organic molecules.

In order to include this experiment in the students’ lab (F-Praktikum) in the future, instructions shall be written that include background information, experimental procedures, materials needed, methods, safety precautions, and learning objectives. Designing and conducting experiments for students can not only deepen your own skills but also be a valuable contribution to the educational experience of future students.

The main goals of this experiment are:

1. Understanding the concept of quantum confinement and its significance in nanoscience and materials science.
2. Relating the particle-in-a-box model to the quantization of energy levels in confined systems.
3. Performing absorption and photoluminescence spectroscopy
4. Experimentally validation the quantum confinement model by observing and interpreting optical spectra
5. Improve an instructional guide for conducting the particle-in-a-box model experiment in a students’ lab

Prerequisites:

• Basic Understanding of Quantum Mechanics
• Electronic structure and properties of molecules (energy levels, etc.)
• Knowledge about optical spectroscopy
• Good laboratory skills and great care when experimenting with chemicals
• Interest in designing a students’ experiment

Supervisor: Dr. Marco Grünewald

Language: German

Venue: F-Praktikum

The topic is suitable for one or two students.

Thin layers are layers with thicknesses in the micrometer and nanometer range. Their physical parameters such as electrical conductivity often deviates from that of the bulk material, allowing for altered, tailored properties and new functionalities. In addition, the material savings are often of great economic importance. Well known is the application in the field of protection against environmental conditions, e.g. against corrosion or oxidation. However, thin layers are most important in microelectronics, where almost all components are manufactured using thin-film technology. In optics, thin layers and layer stacks are used to influence the reflection and transmission behavior, but also the polarization. In particular, layer systems play a prominent role in X-ray optics.

In the internship, metallic layers are usually deposited and characterized by different methods. Concrete topics and goals, amongst others taken from current research projects, are proposed by the supervisor at the beginning of the internship, but can be discussed and adapted depending on the interests.

Learning goals and content

• Deposition of thin metal layers by means of various coating methods (sputter coating, thermal evaporation)
• Characterization of the layer properties (e.g., composition, roughness, crystalline properties) depending on substrate properties and coating parameters (e.g. chamber pressure, residual gas composition, process times, substrate heating)
• Introduction and application of various analysis methods
  • Scanning Electron Microscopy (SEM) and Energy Dispersive X-Ray Analysis (EDX)
  • Scanning Tunneling or Atomic Force Microscopy (STM, AFM)
  • Auger Electron Spectroscopy (AES)
  • X-ray diffractometry (in cooperation with the X-ray group)

Experimental equipment

• Sputter coating system from Oxford Instruments
• Thermal evaporation system (self-made)
• Mass Spectrometer for residual gas analysis
• Quartz layerthickness monitor
• Scanning Electron Microscope
• Atomic Force Microscope
• Scanning Tunneling Microscope
• Auger Electron Spectrometer

Supervisor:   Dr. Thomas Siefke

Venue:           F-Praktikum

The topic is suitable for one or two students.

Single crystalline metal layers on natural mica are often used in electronic devices such as transistors, solar cells, and sensors, due to their high electrical conductivity and mechanical stability. Additionally, they can be used as a substrate for growing other single crystalline materials, such as semiconductors, which can be used in electronic devices as well. The high thermal and chemical stability of natural mica also makes it an ideal substrate for a wide range of applications, such as in the aerospace and automotive industries. Overall, the cost-effective fabrication of single crystalline metal layers on natural mica can have a significant impact on the development of new technologies and the improvement of existing ones.

The experiment aims to fabricate and investigate the properties of single crystalline metal layers using a thermal evaporation method. In this process, the metal material will be thermally evaporated onto a substrate of natural mica under specific conditions, such as temperature, pressure, and evaporation rate, to achieve single crystalline growth. The substrate will be carefully chosen, cleaned and prepared to ensure optimal growth conditions.

The characterization of the fabricated metal layers will be done using a combination of techniques including atomic force microscopy (AFM) and x-ray diffraction studies (XRD). The AFM will be used to observe the surface morphology of the metal layers, including the thickness, uniformity, and surface roughness. The XRD will be used to determine the crystal structure of the metal layers, including the crystal size, lattice spacing, and crystal orientation, as well as to identify any defects or impurities in the crystal structure.

The goal of the experiment is to understand how the thermal evaporation fabrication method and process conditions affect the properties of single crystalline metal layers and how such layers can be used in various applications such as electronics, catalysis, and sensing. The experiment will also help in understanding the relationship between the growth conditions and the crystal structure and will provide a better understanding of the fundamental physics of metal growth.

The main goals of this experiment are:

• Fabrication of single crystalline metal layers using thermal evaporation
• Investigation of the structural and morphological properties

Prerequisites:

• Familiarity with basic laboratory techniques
• Basic understanding of crystal growth and crystal structure

Methods:

• Thermal evaporation setup
• Atomic force microscopy (AFM)
• X-ray diffraction studies (XRD)

Supervisor: Dr. Marco Grünewald and Dr. Berit Marx

Language: German or English

Venue: F-Praktikum and labs of the IOQ

The topic is suitable for one or two students.

Ion sources are applied in a wide range of processes for e.g. doping, quantum dot fabrication and the creation of buried layers. For theses purposes, broad beam ion sources can be utilized to maintain fast processing times even on large implantation areas.

In 2022, operation of a unique four-grid accelerator broad ion source (4GABIS) started at the IAP Jena. Within 4GABIS, ions are accelerated from a plasma source with voltages of up to 30 kV in a beam of around 180 mm diameter. Currently, 4GABIS is not completely characterized for all of the available acceleration parameters. Hence, the first goal of the experiments is to investigate the effect of grid voltages on the resulting shape of the beam profile. This will be measured both directly with a movable faraday cup and indirectly via resulting sputter rates. The insights of this will subsequently be applied to establish ratios between the flux of ions hitting the target and the faraday cup in measurement position, respectively. Next to that, the impact of neutralisation of ions during their flight via charge transfer will be measured. From this, charge transfer cross sections can be calculated and compared with the literature. The combined results are to be integrated into a pre-existing LabVIEW program to allow for in-situ measurement of ion flux.

Summary of the main goals for this experiment:

1. Understanding the shaping of a hot-cathode glow discharge plasma
2. Investigation of grid voltage parameters to affect the resulting ion beam
3. Measurement of charge transfer cross section for collisions of ions and residual gas
4. Combining parameters necessary for in-situ monitoring of ion flux

Prerequisites:

• Basic understanding of hot cathode glow discharge and ion acceleration
• Basic knowledge of LabVIEW programming
• Good laboratory skills
• Interest in operating a unique ion source

Supervisor: Johannes Kaufmann

Venue: Institute of Applied Physics, Beutenberg Campus (Albert-Einstein-Str. 15)

The topic is suitable for one or two students.

Micro- and nanotechnology forms the basis for a growing number of everyday objects and current scientific research. Many physical systems require a direct examination or at least a basic understanding of this technology chain.

The theoretical foundations are already taught at the FSU as part of the Micro/Nanotechnology lecture in the Physics or Photonics Master's programme and the associated seminar. Practical training has not yet been provided. This gap is to be closed by expanding the programme of the lab course.

The aim of this offer is to gain initial experience with an existing lithography line in the clean room and to jointly develop a concept for how this can be used for future teaching.

Supervisor:   Dr. Thomas Siefke

Venue:           Clean room of the IFK and F-Praktikum

The topic is suitable for one or two students.

Context and goals:

In this project, mutual gravitational perturbations in systems containing stars, planets, and minor bodies are studied. Depending on the scenario and configuration, these perturbations can lead to different types of short and long-term phenomena: resonances and chaotic behavior as well as secular effects. Possible examples for specific scenarios include: capture in and release from orbital resonances; long-term stability of planetary systems; Lyapunov exponent and chaotic motion; influence of small perturbers on chaotic systems; secular perihelion drift in multi-planet systems; Kozai mechanism. For each specific problem, analytic approximations are available and can be used for comparison with the numerical results.

Methods:

 A handful of numerical integrators is available, covering a set of different algorithms (Bulirsch­-Stoer, Runge-Kutta, Everhart, (hybrid) symplectic) and scenarios. The integrators can be compared with respect to their precision and speed. Simulation results can then be visualized and statistically examined with self-made programs/scripts.

Instructor:    Dr. Torsten Löhne

Venue:          Astrophys. Inst. and Unisternwarte, Haus 2 (Schillergässchen 3)

The complex topic can be worked on by one or multiple students. The actual tasks will be adapted.

Goals and context

• Basic concept of hyperbolic partial differential equations (PDEs) and the initial-boundary value problem (IVBP)
• Finite differencing methods for derivative approximation
• Method-of-line for time-domain PDEs with Runge-Kutta timesteps
• Numerical implementation of methods to solve multi-D PDEs
• Concepts of numerical stability and convergence

Methods

The students will solve the IBVP with the wave equation in 1+1 and 2+1 dimensions (one time dimension and one and two spatial dimensions) numerically. The project has different sequential steps:

• Wave equation and reduction to first order system
• Characteristic analysis and well-posedness
• Finite differencing approximation of derivatives and convergence
• Runge-Kutta time integrators
• Solution of IBVP withthe 1+1 wave equation and periodic boundaries using the method of lines
• Stability and convergence
• IBVP with open boundaries and Sommerfeld boundary conditions
• Wave equation with a potential: the Regge-Wheeler equation, scattering of graviational waves off a black hole and quasi-normal modes
• More spatial dimensions: the 2+1 wave equation

Students can code in their preferred language, although Python is strongly recommended (open sources, simple and optimal for visualizations).

Prerequisites

• Basic knowledge of partial differential equations
• Basic programming skills

Organisation

Person of charge: Prof. Dr. S. Bernuzzi

Supervision: 

Place: Abbeanum, Fröbelstieg 1 or PAF Computerpool

Per term, one or two or three students may work on the topic.

Context

The strong interaction that binds the elementary particles in nuclear matter is responsible for most the mass of visible matter. The mass is generated due to the interaction strength and it is hence essential for the formation of our universe. Nevertheless its charges can not be observed at the scales of our everyday live due to confinement: at low energies, a free charge of the theory can not exist and only bound states of fundamental particles are observed. At high enough energies, on the other hand, the theory is rather simple due to a phenomenon called asymptotic freedom. This simple fundamental theory is specified by the guiding principle of local gauge invariance, a generalization of the gauge principle of electrodynamics.

The confinement is an essential property of the theory, but it is not accessible by analytic perturbative methods. Some decades ago, the numerical techniques of Monte Carlo simulations on a space-time lattice have been developed. They are by now the most important methods to investigate the theory especially in the confined regime. This low temperature regime of bound state particles is separated by a deconfinement transition form a high temperature regime at which the fundamental constituents, the quarks and gluons, become relevant degrees of freedom.

The aim of this project is to understand the theoretical foundations of gauge theories and explore properties of the theory in numerical simulations.

Goals of the project

• obtain understanding of theoretical foundations of gauge theories and strong interactions
• understand the basics of lattice Monte Carlo simulations in quantum field theory
• derive a program code for the simulation of SU(2) pure gauge theory (some skeleton code and examples are provided)
• investigate the deconfinement transition
• optional extensions: improved algorithms, static quark-antiquark potential and further observables

Prerequisites:

• basic knowledge of quantum field theory
• programming skills (C++, C, Fortran)

Contact:

Supervision: Dr. Georg Bergner, Theoretisch-Physikalisches Institut

Where: Theoretisch-Physikalisches Institut, Fröbelstieg 1 (Abbeanum)

Per term, one or two students may work on the project

Possible topics within this project are:

• Entanglement and its entropy measures in quantum mechanics
• Supersymmetric quantum mechanics
• Magnetic monopoles and quantization of electric charge
• Magnetic monopoles in theoretical condensed matter physics: From the Berry phase in quantum mechanics to the field theoretical description of Weyl semimetals
• Do particles exist interpolating between a fermionic and a bosonic behaviour? Anyons and their description in terms of Chern-Simons theory.
• Hawking radiation and evaporating quantum black holes*
  
  *basic knowledge of general relativity and quantum field theory required.

Contact

Supervision: Prof. Dr. Martin Ammon

Venue: Theoretisch-Physikalisches Institut, Fröbelstieg 1 (Abbeanum)

One or two students may work on this topic per term.

Goals and context

The strong coupling of light to quantum systems relies on the confinement of electromagnetic fields to sub-wavelength volumes. This can be achieved by hybrid nanophotonic quantum systems, in which photonic nanostructures support tightly confined electromagnetic resonances. Computer simulations are an essential part of this research since the fabrication of nanoscopic structures is challenging and the experimental characterization of optical fields at the few photon level with nanometer resolution is equally complicated. Therefore, reliable simulation methods are required to calculate the electromagnetic response of nanostructured matter in advance. Since we are dealing with structures in the sub-wavelength range, "rigorous" methods are needed, which solve Maxwell´s equations without any approximation. Different approaches have explored for certain classes of nanophotonic structures (micro and nano cavities, metasurfaces, nanoantennas).

Methods

The students will implement and use a rigorous numerical method (FDTD or FEM) for the solution of electrodynamic problems. They will either use one of the existing professional implementations of such methods or will be working on their own implementation in a programming language suitable for high-performance computing. The method will be used to simulate the behavior of a nanophotonic structure and to investigate the coupling to quantum systems.

Programming can be done in any language preferred by the students, but Python and Matlab are supported by existing implementations.

Prerequisites

• Basic knowledge of electrodynamics and related partial differential equations
• Basic knowledge of optics
• Basic knowledge of numerical methods
• Familiar with at least one programming language supporting numerical simulations (preferred Python or Matlab)

Organization

Person in charge: Prof. Dr. Thomas Pertsch

Supervisor: Dr. Ángela Barreda

Place: Abbe Center of Photonics, Campus Beutenberg

Per term, one group of one or two students may work on the topic.

Context and goals

Computational Fluid Dynamics (CFD) is a central part of computational physics and has been a driver for the development of modern numerical methods. It involves solving flow mechanical problems that cannot be solved analytically and are expensive to study experimentally by integrating generally nonlinear, partial differential equations.

In this project, the students will apply numerical methods to solve the Navier-Stokes-Equations for the case of an incompressible fluid to study flow within a cavity and flow around obstacles.

Methods

Timestepping schemes for integration of hyperbolic equations as well as a relaxation scheme for solving elliptic equations will be employed to solve the Navier-Stokes-Equations numerically on a staggered grid in two dimensions. The stability and convergence behavior of these schemes will be examinated.

The students will use C/C++, Python or Matlab to implement these methods.

Prerequisites

• Basic knowledge of partial differential equations
• Basic knowledge of numerical methods
• Familiarity with at least one of the suggested programming languages

Organisation

Person in charge: Prof. Dr. Bernd Brügmann

Supervision: Diana Nitzschke

Place:  Abbeanum, Fröbelstieg 1 or PAF Computerpool

One or two students may work on this project

Quantum many-particle systems usually required both, a numerical and (very) efficient treatment. In practice, therefore, they request the use of a modern programming language in order of have proper support of vector and matrix algebra, an extended type system or parallelization. --- Julia is such a language, suitable for scientific computing, which includes many useful features like dynamic types, optional type annotations, type-specializing, just-in-time compilation of code, or garbage collection, to name just a few. When compared with other programming languages, Julia's type system is known as one of its strongest features, in which abstract data types help establish a hierarchy of relationships between data and actions and, hence, to model “behavior” of the code by just providing (concrete) subtype arguments.

In this project, we wish to apply (and implement) simple features of Julia in order to accelerate an established atomic (structure) code and, in particular, to parallelize the setup and diagonalization of the associated Hamiltonian matrix. Emphasis will be placed on the  different interatomic interactions and their corresponding terms in the many-electron Hamiltonian.

Goals of the project

• Get use to and understand the basic features of Julia (and how they compare with regard to Python or C)
• Explore the efficient use of packages suitable for linear-algebra operations
• Understand the many-electron Hamiltonian in terms of (its) one- and two-particle interactions
• Diagonalize the (block-diagonal) Hamiltonian, both in a sequential and parallel mode
• Optional: Account for the rotational symmetry of atoms and ions by using a decomposition in spherical tensor operators

Prerequisites:

• basic knowledge of quantum mechanics and/or atomic physics.
• programming skills (Python, Julia, C)

Contact:

Supervision:  Prof. Stephan Fritzsche, Theoretisch-Physikalisches Institut

Where: Theoretisch-Physikalisches Institut & Helmholtz-Institut Jena, Frauenhoferstr. 8.

Per term, one or two students may work on the project

In quantum mechanics, the “density matrix” is an alternative and often more complete concept (than the well-known wave function) in order to describe the quantum state of a physical system. It enables one to compute quantum probabilities for the outcome of measurements, if the quantum system is in a mixed state. The density matrix is particularly useful, if the initial state of the system is not fully known or if it interacts and becomes entangled with some environment. Density matrices have therefore been found crucial in many research areas, such as atomic and molecular physics, quantum information or the study of decoherence.

In this project, we wish to apply the (atomic) density matrix theory to study the photo-ionization of simple, i.e. hydrogenic or few-electron, atoms. The density matrix is appropriate here, if we need to analyze the angular distribution or spin polarization of the emitted electron, and if the photoion remains unobserved. The great advantage of atomic density matrices are that they can readily be limited to the physical states of interest and, hence, are low-dimensional.

Goals of the project

• Recall the treatment of quantum systems in terms of wave functions and density matrices
• Explore the SO₃ rotational symmetry of atoms and ions
• Describe the interaction of atoms with a weak radiation field
• Develop a program for the setup of small density matrices and their analysis for possible observables
• Optional: Describe the interaction of atoms and molecules in terms of a multipole expansion of the radiation field (spherical tensors)

Prerequisites:

• basic knowledge of quantum mechanics
• programming skills (Python, Julia, C)

Contact:

Supervision:  Prof. Stephan Fritzsche, Theoretisch-Physikalisches Institut

Where: Theoretisch-Physikalisches Institut & Helmholtz-Institut Jena, Frauenhoferstr. 8.

Per term, one or two students may work on the project

Contents and learning objectives

Stars are mostly born in open clusters and spend a significant part of their lives as a member of a cluster. An open cluster contains dozens or hundreds of stars formed at nearly the same time from the same nebula and loosely bound by mutual gravitational attraction. The cluster members share similar distance, age, metallicity, extinction, and velocity; hence they are the key objects in stellar evolution studies. Therefore, the differences in apparent brightness among members are due only to their intrinsic luminosities, thus their masses. The distances and the transverse velocities of the stars can be derived from the astrometric parallax and proper motion values respectively, measured by the Gaia Satellite. The color-magnitude (Hertzsprung-Russell) diagram of the cluster members indicates the age, metallicity and the extinction. The most massive and hottest stars of the cluster evolve faster, move away from the main sequence in the color-magnitude diagram and become cooler giants and/or supergiants. The position of the turn-off from the main sequence can be used to estimate the age of the cluster. To identify the properties of the members as well as the cluster variables, the color-magnitude diagram is fitted by a theoretical isochrone calculated for certain stellar evolution models and initial mass functions. However, the parameters determined by the isochrones must be tested by spectroscopic observations of the cluster members. The atmospheric parameters of the members derived from their spectra narrow down the uncertainty of theoretical isochrones. 

This project aims to teach students how to determine the properties of the open clusters using astronomical catalogs, stellar evolution models, stellar kinematics, observations, data reduction and analysis.

Tasks

• Selection of cluster members regarding their positional and kinematic properties.
• Setting the color-magnitude diagram using optical and near-infrared photometry from various catalogs.
• Spectral observation, data reduction and analysis of the brightest members.
• Measuring the effective temperature, surface gravity and metallicity of the stars.
• Determination of the extinction and the cluster age by the isochrone fitting.

Supervisor: Dr. Baha Dincel

Location (night observation): University Observatory in Großschwabhausen

Location (data reduction and analysis): Astrophysical Institute, Schillergäßchen 2, Jena

The tasks can be worked on by up to 2 students.