Ab initio approaches to x-ray cavity QED : From multi-mode theory to nonlinear dynamics of Mössbauer nuclei

In this thesis, a theoretical framework for x-ray cavity QED with Mössbauer nuclei is developed. First, it is shown how Jaynes-Cummings-like few-mode models for open resonators can be derived from first principles, which has been an open question in the quantum optics literature. The resulting ab initio few-mode theory is applied to the x-ray cavity case, generalizing a previous phenomenological model. In addition, a second orthogonal approach is developed to enable the numerically efficient treatment of complex cavity geometries. It is shown that one can thereby directly derive a nuclear ensemble Master equation using Green’s functions to encode the cavity environment. This approach provides an ab initio quantum theory for the system, which resolves previous discrepancies and allows to semianalytically calculate cavity-modified nuclear level schemes without the need for a fitting procedure. On the basis of the two developed theories, multi-mode effects resulting from large losses in leaky resonators are investigated. A general criterion is introduced to identify and classify such multi-mode effects, which demonstrates that they are responsible for previously observed signatures in x-ray cavity experiments and can be harnessed to artificially tune nuclear quantum systems. Further interesting cusp features in nuclear Fano interference trajectories of x-ray cavities with overlapping modes are reported. Finally, the gained insights are employed to investigate nonlinear excitation dynamics of Mössbauer nuclei in the presence of strong x-ray driving fields. The feasibility of inverting nuclear ensembles at upcoming facilities and the possibility of using focused pulses in combination with x-ray cavities for intensity boosting is analyzed

Molecular mechanisms of crystal nucleation and growth at ferritin/oxide Interfaces : a theoretical investigation

The biomimetic production of micro- and nanostructures from magnetic materials is a suitable way to replace conventional methods with an environmentally friendly and sustainable solution. Biomineralization is nature's way of synthesizing inorganic materials through living organisms. One of the best-known representatives is the protein ferritin, which is found in many organisms and serves as an iron store. Ferritin consists of a total of 24 subunits, which are arranged in the form of a hollow sphere in which iron is biomineralized in the form of iron oxide hydroxide. These subunits were used in this theoretical work and supporting experiments to allow magnetic layers of iron oxide hydroxide to grow without spatial limitations. In this work the different substrate/protein/mineral interfaces, the crystal growth process as well as structure and composition of the resulting mineral phase are analyzed by classical Molecular Dynamic (MD) simulations and quantum mechanical (QM) modelling

Effective field theories for strongly correlated fermions - Insights from the functional renormalization group

'There are very few things that can be proved rigorously in condensed matter physics.' These famous words, brought to us by Nobel laureate Anthony James Leggett in 2003, summarize very well the challenging nature of problems researchers find themselves confronted with when entering the fascinating field of condensed matter physics. The former roots in the inherent many-body character of several quantum mechanical particles with modest to strong interactions between them: their individual properties might be easy to understand, while their collective behavior can be utterly complex. Strongly correlated electron systems, for example, exhibit several captivating phenomena such as superconductivity or spin-charge separation at temperatures far below the energy scale set by their mutual couplings. Moreover, the dimension of the respective Hilbert space grows exponentially, which impedes the exact diagonalization of their Hamiltonians in the thermodynamic limit. For this reason, renormalization group (RG) methods have become one of the most powerful tools of condensed matter research - scales are separated and dealt with iteratively by advancing an RG flow from the microscopic theory into the low-energy regime. In this thesis, we report on two complementary implementations of the functional renormalization group (fRG) for strongly correlated electrons. Functional RG is based on an exact hierarchy of coupled differential equations, which describe the evolution of one-particle irreducible vertices in terms of an infrared cutoff Lambda. To become amenable to numerical solutions, however, this hierarchy needs to be truncated. For sufficiently weak interactions, three-particle and higher-order vertices are irrelevant at the infrared fixed point, justifying their neglect. This one-loop approximation lays the foundation for the N-patch fRG scheme employed within the scope of this work. As an example, we study competing orders of spinless fermions on the triangular lattice, mapping out a rich phase diagram with several charge and pairing instabilities. In the strong-coupling limit, a cutting-edge implementation of the multiloop pseudofermion functional renormalization group (pffRG) for quantum spin systems at zero temperature is presented. Despite the lack of a kinetic term in the microscopic theory, we provide evidence for self-consistency of the method by demonstrating loop convergence of pseudofermion vertices, as well as robustness of susceptibility flows with respect to occupation number fluctuations around half-filling. Finally, an extension of pffRG to Hamiltonians with coupled spin and orbital degrees of freedom is discussed and results for exemplary model studies on strongly correlated electron systems are presented

Interfacing Rydberg atoms with light and observing their interaction driven dynamics

This thesis investigates new phenomena that arise when light is strongly coupled to an interacting atomic gas. For this, a new apparatus has been built which allows to create ultracold and dense atomic samples and to detect individual atoms in high-lying atomic states, so-called Rydberg atoms. Strong light-matter coupling is achieved using the collective coupling of the atomic cloud to the light field under conditions of electromagnetically induced transparency (EIT). In experiments on EIT involving non-interacting Rydberg states, we characterize the light-matter coupling and demonstrate the first combined optical and matter based probing of EIT. By coupling to strongly-interacting Rydberg states, we investigate the effect of interactions which we observe as a strong nonlinear optical response of the atomic gas as well as in the emergence of strong correlations between the hybrid quasiparticles associated with the strong light-matter coupling. We employ the nonlinear response of the atomic cloud to image Rydberg atoms immersed in the atomic cloud. In a theoretical proposal, we show that this novel imaging technique allows to investigate many-body Rydberg states with single particle sensitivity. Using the proposed imaging method, we demonstrate imaging of small numbers of Rydberg atoms with high time-resolution in single shot experiments. In experiments exploiting the dipolar exchange interaction between Rydberg atoms, we employ the new imaging technique to follow dipole-mediated transport of Rydberg excitations through the cloud. The transport dynamics is determined by the continuous spatial projection of the electronic quantum state under observation and features an emergent spatial scale of micrometer size induced by Rydberg-Rydberg interactions