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:

**We have learned from quantum mechanics textbooks: If we swap two particles that differ only in their position but are otherwise identical in the other degree 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 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.

[4] C. F. Roos, A. Alberti, D. Meschede, P. Hauke and H. Häffner, Revealing quantum statistics with a pair of distant atoms, arXiv:1706.04231 [quant-ph] (accepted in Phys. Rev. Lett.), (2017)

**Ultracold atoms walking on a two-dimensional optical lattice move very differently than does their classical counterpart. Interference among different quantum paths makes this quantum transport very intriguing. To a first approximation, atoms move like 2D Dirac particles. 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. For instance, a one-dimensional optical lattice has been used in our group to perform discrete-time quantum walks of single atoms, thus demonstrating an elementary quantum cellular automaton. With this system, we have recently 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 graphene), simulation of artificial magnetic fields (see quantum Hall effect), disordered materials (see Anderson localization), topological insulators (see geometric phase), and novel paradigms of quantum information science (see 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 commercial 4W 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:

**How far can we coherently split a single particle preserving quantum coherences? We intend to use spin-dependent optical lattices to transport the electron spin-up and the electron spin-down components of a single atom by 1 mm apart, and recombine them together to observe interference fringes.**

State-dependent optical lattices are periodic potentials created by laser fields, which we use to transport atoms along a direction determined by their qubit state, which can either be spin up or spin down. With this system we could, for instance, demonstrate the splitting of a single atom at two spatial locations separated by 10 μm.

In order to achieve even larger distances, we have recently developed a new technology for transporting atoms over arbitrary long distances. The new system is based on a digital synthesis of light polarization, which is use to control the state-dependent optical lattice. The state-dependent transport of single atoms is controlled by digitally programming the phase of a RF signal through a direct digital synthesizer (DDS). The new technology allows us to shape arbritrary transport shape.

The project consists in applying the concept of quantum optimal control theory to optimize the atom transport over large disances while preserving the very fragile quantum "coherences". We aim at demonstrating a macroscopic single-atom interferometer, where atoms are coherently split over hundreds of lattice sites (1 lattice site = 433 nm). We will interface a fast FPGA with the DDS chip to program complex transport sequences in real time. This will allow us to tailor the interferometer geometry with ultrahigh spatiotemporal control, ultimately achieving a spatial and temporal resolution of 100 pm and 10 ns, respectively.

[1] Analog Devices Direct Digital Synthesizer AD9910.

[2] A. Steffen, A. Alberti, W. Alt, N. Belmechri, S. Hild, M. Karski, A. Widera and D. Meschede: A digital atom interferometer with single particle control on a discretized spacetime geometry, PNAS

[3] J. Werschnik and E. K. U. Gross: Tutorial on Quantum optimal control theory, J. Phys. B: At. Mol. Opt. Phys.

[4] G. de Chiara, T. Calarco, M. Anderlini, S. Montangero, P. J. Lee, B. L. Brown, W. D. Phillips, and J. V. Porto: Optimal control of atom transport for quantum gates in optical lattices, Phys. Rev. A

The exact manipulation of quantum states is crucial for realizing quantum devices for information processing [1]. Quantum tomography is a well established method that allows to fully characterize the action of an arbitrary quantum devices [2].

During the master thesis an experimental setup shall be implemented to perform quantum tomography on the polarization degree of freedom of single photons. The student contributes to work towards an atom-cavity based quantum memory for optical qubits.

[1] “Quantum Computation and Quantum Information”, Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press, Cambridge, UK, 20000.

[2] “Prescription for experimental determination of the dynamics of a quantum black box”, I. L. Chuang and M. A. Nielsen, Journal of Modern Optics,

- Alberti
- 20/12/18
- Ott
- 16/10/18
- Reichel
- 09/10/18
- Nir Davidson
- 29/08/18
- Tommaso Calarco
- 12/06/18
- Hannes Pfeifer
- 05/06/18
- Steffen Wirth
- 29/05/18
- Claudiu Genes
- 08/05/18
- Eschrig
- 19/12/17
- Alexander Pukhov
- 05/12/17
- Dagmar Bruss
- 14/11/17