Creating Experimental Setups

Mario Krenn, Xuemei Gu, Anton Zeilinger

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

Jamie Ryan Gardner

Aidan Moran-Bates

Our research is centered around the creation of a generalized and universal system that can replicate the soliton generaton found in walking droplets. This experimental setup has been realized and uses a programmable motor to create the initial wave, which is then propagated throughout the system via a connection of AC synchronous motors, torsion springs, and gears. Further work into this system will be to show that this soliton generation can be used to create a Turing-complete machine capable of logic gate functionality.

Mitsuyoshi Kamba

Shahin Tajik

Martin Göbel

This thesis describes the design and realization of a novel experimental setup for the investigation of ultracold Bose-Fermi mixtures. The new setup combines a mixture experiment of 40K and 87Rb with one-dimensional trapping geometries that are accessible in the miniaturized wire traps of an atom chip. By additionally coupling the internal states of magnetically trapped atoms with radio-frequency (rf) fields, versatile state-selective and species-selective potentials can be created. One special case is the deformation of the static one-dimensional trap to a novel two-dimensional geometry in which the atoms are confined to the walls of a straight tube. An extensive numerical and experimental analysis of this trapping geometry with the aim of minimizing the variations in the trapping potential was performed. This leads to a new improved spatial arrangement for the wires that create the rf fields. The optimized wire layout was implemented in the new experimental setup and will allow the first realization of such a two-dimensional trap configuration with periodic boundary conditions. Results of experiments performed with a simplified arrangement of the rf wires allowed the observation of the two-dimensional regime with thermal atoms.