Trajectories and the corresponding wavefronts of a matter wave in a Mach-Zehnder interferometer.

**Jan Teske**

In 1934 Frits Zernike discovered the orthogonal `Kreisflächenpolynome' to describe the optical path difference between light waves and a spherical reference wavefront. Understanding the phase differences and minimizing the optical aberrations laid the base for the first phase-contrast microscope for which he was awarded the Nobel Prize in Physics 1953. Nowadays, the Zernike polynomials are widely used in optical system design as a standard description of imperfections in optical imaging. In contrast to visible light, massive particles have a much smaller de Broglie wavelength and therefore a possible higher resolving power. In particular matter-wave interferometry with ultracold atoms is paving the way to a new era of quantum technologies.

In this project, we develop a schematic aberration analysis for matter-wave optics with Bose-Einstein condensates. Following Zernike's idea, we introduce a set of orthogonal basis functions to quantify deviations from a chose reference state in terms of aberration coefficients. We study long expansion times that can be achieved in microgravity environments (QUANTUS, MAIUS, ISS) as well as the effect of Delta-kick collimation with real anharmonic magnetic chip trap potentials. Both are essential to understand the condensates' phase evolution which is necessary for a precise description of matter-wave interferometry.

(Top) Distribution of a complex Gaussian field and (bottom) intensity noise suppression depending on the temperature, calculated with a stochastic model.

**Kai Hansmann**

We develop a novel approach to the investigation of quantum dot superluminescent diodes using stochastic methods. Under the assumption, that the emission of such diodes results as a superposition of independent, stochastically fluctuating emitters, we numerically simulate the complex electric field amplitude emitted by the diode. From this, key optical properties like first- and second-order temporal correlation functions and the spectral power density of the emission are calculated.

Suppression of intensity fluctuations in incoherent semiconductor light sources has been observed by Blazek et al. in 2011. We use our stochastic approach to explain the noise suppression mechanisms in such diodes to match experimental facts. The results give an insight into general noise suppression processes in semiconductor diodes and open up the opportunity to customize noise-reduced broadband light sources.

Sketch of a Z-trap, including the resulting trap minimum. The sphere of radius R describes the region in which the multipole moments are evaluated.

**Tobias Liebmann**

Magnetic chip traps are standard devices to trap cold atoms via the Zeemann-potential. This work is part of the QUANTUS collaboration, using such trapping configurations for Bose-Einstein Condensates (BECs) in microgravity. With MAIUS the first space-borne BEC was created in 2017. While magnetic chip traps exhibit pleasant confinement potentials, they are not necessarily harmonic. The Zeemann-potential exerted by a chip trap's magnetic induction field is only relevant in a limited space around the trap minimum. In this region, the magnetic induction field is described in terms of a magnetic potential, which satisfies Laplace's equation. The magnetic potential itself can be expressed as a series of regular solid harmonics, allowing for a complete description of the magnetic induction field by the multipole moments of the magnetic potential. Starting from a standard Z-trap configuration, the goal of this work is the description of its observed anharmonicities in terms of the corresponding multipole moments and reduce them by introducing a variation to the shape of the Z-trap's wires.

Prof. Dr. Reinhold Walser

Theoretische Quantendynamik

Institut für Angewandte Physik

Fachbereich 05 - Physik

Technische Universität Darmstadt

Hochschulstr. 4a

D-64289 Darmstadt

+49 6151 16-20320

+49 6151 16-20402

Reinhold.Walser@tu-...

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