TU Darmstadt Physik Institut für Angewandte Physik Theoretische Quantendynamik Forschung/Research Abgeschlossene Projekte / completed projects

**Antje Neumann **

Matter-wave interferometry enables high-precision measurements of rotation and acceleration, applicable for inertial navigation and fundamental physics, like testing Einstein's weak equivalence principle. We are part of the QUANTUS (QUANTengase Unter Schwerelosigkeit) collaboration, where atom interferometry is the central method of their free-fall experiments, just like within the MAIUS (Materie-Wellen-Interferometer Unter Schwerelosigkeit) mission, where the first BEC in space was generated in 2017.

Like in optical systems all matter wave devices exhibit imperfections and the amount of these aberrations must be quantified. Therefore, we analytically and numerically study the performance of 3D atomic beam splitters and mirrors. Describing these central components of a matter-wave interferometer as realistic as possible, we consider spatio-temporal laser beam envelopes and in the quasi Bragg regime we take into account the velocity dispersion as well as losses into unobserved momentum orders.

This work is supported by the German Aerospace Center (DLR) through grant 50 WM 1557, 1957.

Three-level energy diagram for Calcium-40 ions. Laser 1 induces eg transitions and laser 2 couples the em transition.

**Antje Neumann**

The velocity distribution of a hot ionic beam can be filtered with a narrow stimulated Raman process to prepare a colder subensemble, as substantiated in this theoretical analysis. Using two counterpropagating far-detuned lasers, we can define a pi-pulse for the resonant velocity to transfer atoms within the linewidth of the Raman resonance between the ground states of a Lambda-system. Spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise, diminishes the efficiency of the filter. From a comprehensive master equation, we obtain conditions for the optimal frequency pair of lasers and evaluate the filter performance numerically as well as analytically. If we apply this analysis to current ^{40}Ca^{+} ion experiments, we obtain a sensitivity for measuring high ion acceleration voltages on the ppm level or below.

This work is published as Editor's Suggestion in Physical Review A: Raman velocity filter as a tool for collinear laser spectroscopy.

It is supported by the German Aerospace Center (DLR) through grant 50 WM 1557, 1957.

During the last years, spectrally broadband emitting superluminescent diodes (SLDs) became essential elements in modern research due to their high potential in industrial applications, e.g. in optical coherence tomography or fiber sensor technology. Here, light generation arises at the transition of spontaneous to stimulated emission, the range of amplified spontaneous emission (ASE). The delicate choice of waveguide geometry and gain medium, here quantum dots (QDs), enables large spectral widths of some THz as well as spatial coherence.

From a theoretical point of view, characterization of ASE generated by QD-SLDs and investigation of their photon statistical behavior (especially at a particular temperature regime, where a reduction of the intensity correlation down to 1.33 is observable), represents an interesting and challenging project of research, which we analyze on a microscopic level.

Radial effective box potential with angular momentum l=3 (black). Wave functions of the radial Schrödinger equation for a bound molecular state (green) with negative energy E < 0, a scattering state (red) with positive energy E > 0 and a quasi bound state (blue), also with positive energy.

Bose-Einstein-Condensation of dilute alkali gases has dominated the past decade of AMO research. With the condensation of noble gases (He*) a new phase has started. Currently, many experiments are geared towards the condensation of other noble gases, rare-earth gases and composite molecules. In the research group of G. Birkl (http://www.iap.tu-darmstadt.de/apqneu/) significant effort is spent on the investigation of the possibility to condense metastable neon (Ne*).

In the present research project we will examine the binary scattering physics of metastable neon atoms. Starting from simple and analytically solvable model potentials we investigate the basic principles of multichannel scattering theory. This is generalized to realistic extended potentials in order to evaluate the scattering matrix and inelastic loss rates. Eventually, we will address the loss rates due to a fragmentation process (penning ionization) which could be obstacle towards Bose-Einstein-Condensation.

Observing freely falling objects has been the cornerstone of Isaac Newton's mechanics and has also led to the modern understanding of space-time as formulated by Albert Einstein. Recently, the QUANTUS collaboration (QUANTen Gase Unter Schwerelosigkeit) has realised a free-fall experiment with Bose-Einstein condensates (BECs) from a height of 110 m.

For such long expansion times in free fall of 1 s, the approximation of non-relativistic quantum mechanics becomes a less accurate description. Thus it becomes relevant to employ general relativity and quantum field theory in curved space-time to model the evolution of BECs and to quantify the relativistic corrections. The goal of this PhD project is to extend the dynamical evolution of BECs to General Relativity and to model and quantify the arising corrections.

Iso-surfaces of the spatial linear gain distribution inside the laser medium are shown. The central orange region provides gain while the blue surfaces represent increased absorption. The non-trivial structure of the gain medium arises from the wave vector configuration of external driving fields (green and blue arrow) with respect to the lasing field (violet arrow). This configuration shields the spectrally narrow gain peak against Doppler broadening.

For conventional lasers population inversion on the lasing transition is a necessity. This renders direct lasing in the UV regime impossible since the required pumping power for population inversion is not accessible for these wavelengths. However, in the 1990s a class of techniques was developed that circumvents this limitation by exploiting atomic coherence effects induced by external fields. These techniques are referred to as lasing without inversion (LWI). Even though multiple prove of principle experiments have demonstrated LWI, a UV laser operating on this principle is yet to be build. We analyze the experimental feasibility of a promising scheme [1] for LWI at ?=254 nm in mercury [2] and work in cooperation with the research group of T. Walther towards an experimental realization.

[1] www.sciencedirect.com/science/article/pii/S0030401899007312

Immersing carbon nano-tubes in a cigar shaped BEC.

Mean-field theory is a valuable tool to model interacting bosonic atoms in an external trap at zero temperature. It is well described by the Gross-Pitaevskii equation, a non-linear Schrödinger wave equation approximating the many-body state. Its dynamics is subject to the competition between binary collisions and quantum-mechanical dispersion. In many experimental settings, however, the Gross-Pitaevskii mean-field theory is itself an approximation which only describes observable physics on a certain scale.

The dynamics of interacting atoms deep inside a big BEC cloud is dominated by collisions, making the quantum pressure negligible. Thus, the cloud of condensed atoms behaves as a classical non-viscous fluid (superfluid). This approximation provides an excellent base for building successively more detailed models, e.g. like introducing the non-condensed fraction (quantum depletion). Currently, we are evaluating a simple yet powerful model to describe the physics of hybrid systems: carbon nanotubes immersed in BECs (see illustration).

Molecular dynamics simulation of 2^14 Rubidium atoms in a trap.

Evaporative cooling is of essential importance for reaching quantum degeneracy in atomic gases. Yield, speed and efficiency of this mechanism is usually optimized in the laboratory by trial and error.

The QUANTUS-experiment aims to produce degenerate quantum gases in weightlessness via free-fall-experiments. Thus the time of every single experiment is limited to ten seconds. Quickly producing cold samples is therefore of outmost importance. In the current project we are optimizing the evaporation trajectories with these constraints. The dynamics of n interactive particles in a trap is studied with molecular dynamic methods which benefit from the parallelization on modern graphic cards.

Field intensity behind a double slit along the propagation direction.

The Young double slit is the key experiment to analyze interference of wave phenomenon. It exists in wave optics as well as in wave mechanics for examples: electrons, neutrons, atoms, coherent Bose-Einstein-Condensates. In this project, we analyze a realistic setup of a double slit starting from a partially, coherent source, real masks in two dimensions and the propagation to the detector. As a method we use the Wigner function to represent partially, coherent fields (see picture)

Normalized resonance fluorescence spectrum of a driven and damped two level atom calculated with 5000 trajectories of Monte Carlo wave function simulation (red line) and compared to an analytic solution (blue line) found by solving the master equation and applying quantum regression theorem.

The Monte-Carlo method is a class of computational algorithms using repeated random events to estimate probabilistically determined calculations. In quantum optics there is a method to determine the time evolution of the density matrix equation (Lindblad form) by effectively simulating many stochastic Schrödinger equations. The conception of this method has led to tremendous progress in the understanding of laser cooling. Our particular interest is in the simulation for n-level-atomic systems interacting with a reservoir of the electromagnetic field and the prospect for parallelizing this code on modern hardware.

From "Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations"

Interacting cold atomic gases are an interesting topic to study many aspects of classical and quantum-many-body dynamics.

Starting in the thermal regime we have an ensemble of classical particles, which are trapped in confining potentials and interact via short range binary forces. For example, this is exploited in the process of evaporative cooling. Therefore, studying classical molecular dynamics (MD) is a very relevant topic. In this bachelor thesis we will study the different behavior of numerical integration scheme for solving the coupled Newtonian equations of motion that are commonly used in MD- Simulations:

e.g. multi-step-predictor corrector methods, Runge-Kutta integrators and most favorably structure preserving symplectic integrators.

Intensity distribution of light on a CCD detector calculated via raytracing through a system of optical elements.

All experiments in the field of cold atomic matter waves rely crucially on perfectly designed optical systems. The imaging of an atomic cloud inside an ultrahigh vacuum chamber requires a multitude of optical elements and perfectly controlled laser fields. The design of such a system and in particular the optimization of the imaging quality depends on many parameters, which is a daunting task.

In this project, we employ the optical design software ZEMAX to model and optimize the imaging quality of a Bose Einstein condensate expanding freely, while dropping in microgravity (http://www.dlr.de/desktopdefault.aspx/tabid-3228/5011_read-26903/).

Carbon nanotubes have a range of extraordinary properties such as huge length-to-diameter aspect ratio, high electrical and thermal conductivity, high mechanical strength, atomic-scale-perfection (single-walled carbon nanotubes) similar to graphene. These qualities make them very fascinating materials.

Currently, particular interest is focused to the immersion of carbon nanotubes in quantum degenerate atomic gases. In this combination the properties of the quantum and classical worlds are merged into a hybrid quantum system. We investigate the interaction of carbon nanotubes with a bath of ultracold gases or Bose-Einstein-Condensates. Moreover, the possibilities of sympathetic cooling of carbon nanotube vibrations down to the ground state mode are considered. This theory relates to experiments performed in the research group of Prof. Dr. Fortagh at the Center for Collective Quantum Phenomena, University of Tübingen, Germany.

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-...

- BEC auf ISS , (FAZ 13.6.20)
- Editors choice: Raman velocity filter for laser spectroscopy (26.5.20)
- Dissertationspreis 2019 für Dr. Martin Sturm
- Exploring the Universe with matter waves

- Erstes BEC im All: Erfolgreicher Raketenstart von MAIUS 1

- Exotischer Quantenzustand im All erzeugt (Spiegel Online)

- Seit 1.1.14 ist die NAG Lizenz campusweit und permanent zugänglich