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:

**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.

[1] M. Karski, L. Förster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera:

[2] M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede and A. Alberti:

**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.

[1] A. Jabs, Connecting Spin and Statistics in Quantum Mechanics, Foundations of Physics

[2] M. Berry and J. Robbins, Quantum indistinguishability: Spin-statistics without relativity or field theory? AIP Conf. Proc.

[3] C. K. Hong, Z. Y. Ou, and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett.

[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.

**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.**

[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).