title: Ultrafast correlated many-body dynamics in magnetic and nonmagnetic quantum nanostructures
Creators: name: Ungar, Florian Roland
Publisher: name: University of Bayreuth
Year: 2019
Subjects: subject: Correlated Systems, Excitons, Spin Dynamics, Diluted Magnetic Semiconductors, Quantum Kinetics, Quantum Dots, Path Integrals
subject: 530

description: In a time where CPU frequencies have stagnated and a limit to shrinking transistor sizes is within reach, the exploration of novel computing methods in terms of new materials as well as fundamentally different computing techniques becomes ever more important. In this cumulative thesis, two possible avenues are explored in that regard which fall into the category of spintronics and photon-based quantum computing realized in magnetic and nonmagnetic quantum nanostructures, respectively. While the former seeks to combine the spin and charge degrees of freedom of carriers to achieve a more robust fundamental logical unit, the latter approach aims to explicitly harness superpositions of quantum states using nonclassical quantum algorithms. Both of these approaches require a thorough theoretical understanding of ultrafast processes to which this thesis contributes by theoretically investigating the correlated many-body dynamics in diluted magnetic semiconductors and nonmagnetic quantum dots on a level beyond the effective single-particle approximation. Since two distinct types of materials are investigated, this thesis is divided into two parts, each of which focuses on the influence of many-body correlations on typical observables of interest. In diluted magnetic semiconductors, the many-body physics is due to the interaction between the magnetic doping atoms and the carriers in the material, whereas the many-body problem in quantum dots originates from the carrier-phonon coupling. Part I of this thesis introduces the material system of diluted magnetic semiconductors and specifically focuses on the ultrafast spin dynamics of excitons in the presence of magnetic impurities in quantum-well nanostructures. To this end, a quantum kinetic theory is developed that allows an explicit treatment of exciton-impurity correlations based on a previously studied model for quasi-free particles. In contrast to the predominant theoretical description in the literature, the predicted spin-decay rates agree well with experimental findings and their dependence on an external magnetic field features similar nonmonotonic tendencies. Furthermore, it is shown how the correlation energy indicative for the deviation from the bare exciton picture can be extracted from the linear absorption spectrum and how the presence of correlations affects the occupation of excited exciton states. To highlight nonMarkovian effects, the quantum kinetic results are generally compared with the Markov limit of the theory, which corresponds to vanishing correlations and agrees with standard theoretical models based on Fermi’s golden rule. After extending the theory by also accounting for carrier-phonon scattering, its impact on the spin dynamics of optically generated excitons as well as a highly nonequilibrium distribution of hot excitons is investigated. Albeit the scattering with magnetic impurities is found to dominate the spin dynamics, phonons do have a significant impact on the exciton distribution and can even cause a ratchet-like dynamics at low temperatures in suitably high magnetic fields. Finally, it is shown that radiative decay as well as correlations can lead to significant spin overshoots and that, depending on the specific semiconductor, spin-orbit interaction in the conduction band can have a pronounced impact on the spin dynamics of hot excitons. Part II of this thesis focuses on semiconductor quantum dots embedded in a cavity and makes use of a real-time path-integral description to fully account for the phonon coupling in terms of a pure-dephasing model. First, an existing version of the algorithm is refined by grouping all states with the same phonon coupling, thereby reducing the numerical demand by several orders of magnitude and paving the way towards a study of many-level systems, which have so far been out of reach due to their high numerical demand. Specifically, the modified algorithm is applied to a 41-level system with up to twenty photons in the cavity, revealing highly unconventional photon statistics as a function of time. Since multitime correlation functions are an important tool in the characterization of photon states in general, it is also shown how such quantities can be evaluated within the path-integral framework without relying on additional approximations and, most importantly, without neglecting the phonon-induced memory. Applying this scheme to calculate the single-photon purity after pulsed excitation of the quantum dot, it is shown that a high-quality single-photon source whose emission frequency is spectrally separated from the laser frequency can be achieved by off-resonant phonon-assisted excitation. Finally, the biexciton cascade in quantum-dot cavity systems is discussed regarding the generation of entangled photon pairs. Due to the somewhat ambiguous way of quantifying entanglement via properties of the reduced two-photon density matrix using the notion of concurrence, this quantity is first analyzed with respect to its different appearances throughout the literature. Subsequently, the concurrence of simultaneously-emitted photon pairs is compared for different quantum-dot cavity configurations and it is shown that, quite contrary to the general belief that phonons always lead to a degradation of entanglement, phonon-enhanced entanglement can occur for certain parameters.