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Themen für Bachelorarbeiten

In der Gruppe von Prof. Büchler.

Three-body bound states with Rydberg slow light polaritons

The theoretical model describing Rydberg slow light polaritons gives naturally rise to a strong three-body interaction. This means, that the bound state of two-polaritons is strongly modified in the presence of a third photon close by. The main goal of this topic is to understand the three-body bound states in such a potential. We start by analytical deriving the quantum mechanical bound states for a stepwise model potential, and then study the corrections for the realistic setup within perturbation theory.

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Robustness of topological bands towards an additional hopping term

We study polar molecules trapped in a two-dimensional deep optical lattice with quenched tunneling between the sites. The relevant degree of freedom of the polar molecules is given by two different rotational excitations, which can be transferred between different lattice sites due to the dipolar exchange interaction. It has recently been demonstrated that for a square lattice such a system gives rise to a band structure with a quadratic band touching point and even topological bands. The goal in the present thesis is to analyze the influence of additional levels in the setup.

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Stability of dipolar droplets by quantum correction to free energy

In a recent experiment, the stability of droplets with atomic gases under strong dipolar interaction was demonstrated, seemingly violating all predictions based on Gross-Pitaevski equation. A potential explanation was put forward by explaining the observed phenomena by an additional term in the energy functional describing the leading corrections due to quantum fluctuations. In this topic, we would like to understand, that such a term can indeed lead to a stabilization of the droplets within a simple variational ansatz. Furthermore, we would like to estimate the effect of the next leading term in the quantum fluctuations.

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Behavior of dephasing for Rydberg slow light polaritons

In a system of strongly interacting slow light polaritons, in many situations an additional dephasing term is present. This term accounts for fluctuating external fields, and is well described within a Lindblad master equation approach for the problem. The goal of the project is to analyze from the microscopic model the influence of such a dephasing rate onto Rydberg polaritons. In a first step, the appropriate master equation is derived in analogy to the well established approach of system bath coupling. In a next step, the behavior of the equation is studied on one hand by analytical tools as well as numerical methods. The goal is to understand the scaling for large number of particles present in the setup.

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Stability of Majorana modes under symmetry breaking terms

We recently established an exact ground state wave function of an interacting Hamiltonian in one-dimension, which gives rise to a topological phase characterized by Majorana modes at the edges of the system. However, this topological order must be protected by a symmetry, as naturally expected in one-dimension. The microscopic Hamiltonian exhibits several Z2 symmetries such as time-reversal symmetry, parity symmetry, as well as exchange of the two wires. The goal in this thesis is to analyze these symmetries and study the stability of the topological order. Especially, the goal is to design characteristic operators, which break all but one of the above symmetries and demonstrate that these operators do not destroy the topological order within lowest order perturbation theory.

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Input-output formalism for interacting slow light polaritons in an Bethe-ansatz solvable system

We analyze an exactly solvable quantum many-body sytstem in one-dimension, which can be mapped onto the problem of interacting slow-light polaritons. The main goal in this thesis is to understand the exact wave function and map them onto experimentally relevant initial states. Therefore, we start with analyzing the few photon states. The goal of this thesis is to start with a incoming two-photon wave function and exploiting the exact solvability of the model to derive the outgoing wave packet. Special focus will be on the two-body correlation function, which is expected to exhibit bunching. The main goal is to scale this up to higher number of incoming photons with the ultimate goal to understand the behavior for a incoming coherent state.

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