Master's theses (modules phys910/920/930)

Research projects for master students are divided into two parts: during the first 6 months, the student must scientifically explore the master's thesis topic (module Physics910), plan the project and develop the required research methods (module Physics 920). A short report (2-4 pages) on the exploration and the planning must be handed in. The last 6 months of the research project are reserved to the master’s thesis work itself. The master’s thesis has in general 30 to 60 pages. The results of the master’s thesis are presented in a talk near the end of the research phase. The formal aspects are summarized in the Module-Handbook Master in Physics.

The research topic of the master's thesis will be discussed together with the candidate. It is possible to bring in your own ideas. Examples of research topics are listed below. Other opportunities are also available and can be discussed in person in confidential terms. Please come and talk to us. We look forward to your enthusiastic participation.

Those who are interested to join our group, please contact:

Quantum walks in two-dimensional optical lattices (13/05/21)

Ultracold atoms walking on a two-dimensional optical lattice move very differently compared to their classical counterpart. Interference among different quantum paths makes this quantum transport very intriguing. To a first approximation, atoms move like Dirac particles in two dimensions. We plan several experiments to unravel the rich physics of 2D discrete-time quantum walks.

Neutral atoms confined in optical lattice potentials are ideal candidates to perform digital quantum simulations and novel quantum computational schemes. A one-dimensional optical lattice has already been used in our group to perform discrete-time quantum walks of single atoms. With this system, we have simulated the physics of charged particles in a crystal subject to an external electric field.

For many physical problems it is important to go beyond one dimension like for quantum transport experiments (see, e.g., graphene), simulation of artificial magnetic fields (see, e.g., quantum Hall effect), disordered materials (see, e.g., Anderson localization), topological insulators (see, e.g., geometric phase), and novel paradigms of quantum information science (see, e.g., one-way quantum computer). Our original approach consists in employing two-dimensional spin-dependent transport, i.e. the ability to deterministically transport atoms depending on their internal state, in order to experimentally investigate these physical models.

Within this project, a high-power (>10W) phase-locked Ti:sapphire laser source shall be used to generate the optical lattice at the magic wavelength (866 nm), which is necessary for state-dependent transport. The 2D lattice will be placed at exactly 150 μm from the first surface of a large numerical-aperture (NA~0.9) objective lens, which is situated in a twelve-sided ultrahigh vacuum cell (see image). Two-dimensional spin-dependent transport will be performed by means of a newly developed technology, which allows to digitally synthesize the light polarization of the lattice laser beams. The final goal of the project consists in using the spin-dependent lattice to implement a two-dimensional discrete-time quantum walk with neutral atoms.

Reference person: Dr. Andrea Alberti
Image: Two-dimensional optical lattice (not to scale) in proximity of a large numerical aperture objective, which is employed to resolve and address individual lattice sites. The objective is inside an ultrahigh vacuum cell.
What you will learn: Implementation of a two-dimensional quantum walk with ultracold atoms, control of atomic states (motion and spin) using microwave and laser pulses, high-resolution fluorescence imaging with state of the art objective lens, theoretical concepts of Dirac particles on a discrete lattice.
Field of research: Discrete-time Quantum Walks
Literature:
[1] M. Karski, L. Förster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera: Quantum Walk in Position Space with Single Optically Trapped Atoms, Science 325, 174 (2009)
[2] M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede and A. Alberti: Electric quantum walks with individual atoms, Phys. Rev. Lett. 110, 190601 (2013)

Revealing quantum statistics with a pair of distant atoms (15/10/18)

We have all learned from quantum mechanics textbooks: If we swap two particles that differ only in their position but are otherwise identical in the other degrees of freedom, the quantum state acquires a phase 0 for bosons and π for fermions. We take up the challenge to validate this fundamental law of nature in a two-atom interferometer experiment.

In nature elementary particles are either bosons or fermions depending on whether their angular momentum is an integer number or a half-integer number of ħ. This classification of particles into two large families has deep physical consequences in relation to identical particles. The spin-statistics theorem states that when we exchange two particles – namely, when we transport one particle into the position of the other and vice versa – we obtain the same two-particle quantum mechanical state except for a quantum phase [1]. This phase is 0 for bosons and π for fermions. The different exchange phase between bosons and fermions can be revealed with a new type of two-particle interferometry experiment, which probes the spin-spin correlations between the two particles. The scheme illustrated in the figure is robust against decoherence mechanisms and can be implemented with bosons and fermions.

Reference person: Dr. Andrea Alberti
Image: Two-atom interferometer scheme to measure the exchange phase with a pair of distant atoms.
What you will learn: Laser cooling of atoms into the quantum mechanical ground state of motion, Ramsey atom interferometry, advanced experiment automation techniques with sub-µs microwave and laser polarization control to swap exactly two atoms.
Field of research: Few-atom quantum systems
Literature:
[1] A. Jabs, Connecting Spin and Statistics in Quantum Mechanics, Foundations of Physics 40, 776 (2009).
[2]  M. Berry and J. Robbins, Quantum indistinguishability: Spin-statistics without relativity or field theory? AIP Conf. Proc. 545, 3 (2000)
[3] C. K. Hong, Z. Y. Ou, and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett. 59, 2044 (1987).
[4] C. F. Roos, A. Alberti, D. Meschede, P. Hauke, and H. Häffner, “Revealing Quantum Statistics with a Pair of Distant Atoms,” Phys. Rev. Lett. 119, 160401 (2017).

Optimized Faraday Rotators for Applications in Photonics (08/02/19)

There is significant interest in reducing size and cost of Faraday Isolators, key components in high performance laser diode laser systems, and a basic question is: what permanent magnet configuration optimizes ∫Bdz? This project comprises an innovation project with industrial relevance and addresses the theoretical solution of the basic optimization task, analysis of cost and technical constraints and realization of a practical device.

Requirements: Master specialization in quantum optics/photonics; interest in computer simulations for applications in photonics and their experimental realization; interest in contacts to research within the industrial world.
Background: Diode lasers are sensitive to backscattered light. Spectral performance suffers already at return levels of 10-3. A well-known concept is the usage of optical diodes, known as Faraday-Isolators. An axial magnetic field acting on the Faraday rotator crystal makes the polarization rotate 45°, and the rotation is always clockwise as seen in propagation direction. Recent progress in manufacturing technology and permanent magnet configurations have led to improved designs with smaller footprint. Several configurations have been discussed, however no systematic evaluation of a permanent magnet configuration has been performed.
Questions this thesis seeks to answer: Which spatially restricted (box or cylinder) permanent magnet configuration maximizes ∫Bdz? This question has already been addressed for the simple cases, and analytical solutions were presented. The cylindrical symmetry of the actual problem motivates investigation of an analytic solution. If this turns out not to be feasible, a numeric optimization shall be performed. They shall give an answer to questions like: how to theoretically arrange NdFeB M52 permanent magnet material with 1.4 T magnetization to achieve 45° Faraday rotation with TGG crystals with minimum footprint? What is the dependence upon changes of the restricting length and diameter? How to balance cost vs performance?
Reference persons: Prof. Dr. Dieter MeschedeDiese E-Mail-Adresse ist gegen Spambots geschützt! JavaScript muss aktiviert werden, damit sie angezeigt werden kann.
Image: Faraday isolator concept (adapted after SDM Magnetics).
What you will learn: Magnet physics and photonics, software based optimization with ie COMSOL Multiphysics, cooperation with industry.
Field of research: Photonics / Quantum optics / Quantum Technology
Literature:
[1] V. Frerichs, W. G, Kaenders, and D. Meschede: Analytic Construction of Magnetic Multipoles from Cylindric Permanent Magnets, Appl. Phys. A 55, 242 (1992).
[2] Gérard Trénec, William Volondat, Orphée Cugat, and Jacques Vigué: Permanent magnets for Faraday rotators inspired by the design of the magic sphere, App. Opt. 50, 4788 (2011).