In the present thesis the dynamics of the correlations between an open quantum system and its environment is investigated. This becomes feasible by means of a very useful representation of the total system-environment state. General conditions for separability and entanglement of the latter are derived, and investigated in the framework of an open quantum two-level system, which is coupled to a dissipative and a dephasing environment.

The coherent properties of semiconductor nanostructures are inherently difficult to measure and one-dimensional spectroscopies are often unable to separate inhomogeneous and homogeneous linewidths. We have refined and improved a method of performing multidimensional Fourier transform spectroscopy based on four-wave mixing (FWM) experiments in the box geometry. We have modified our system with broadband beamsplitters in all interferometer arms, high-resolution translation stages and the ability to work in reflection geometry. By improving the phase-stability of our setup and scanning pulse delays with sub-optical cycle precision, we are able to reproduce 2DFT spectra of GaAs multiple quantum wells. With the FWM signal reflected from the sample surface instead of transmitted through, we show that very low pulse powers can be used to generate coherent 2D signals from colloidal PbS quantum dots. Dephasing times are particularly difficult to measure in small colloidal quantum dots due to environmental broadening effects from the colloidal growth. We show that low-temperature pure excitonic dephasing can be measured via time-integrated measurements as well as from the cross-diagonal linewidths of 2DFT spectra. Ultrafast sub-picosecond dephasing times are measured at 5 K in 3 nm PbS quantum dots, while excitation-density-dependence is investigated in these dots. By retrieving the global phase with an all-optical method, we are able to retrieve the real-part 2D spectra of PbS quantum dots.

The phenomena of coherence and localization have gained enormous research interest during the past decades. Theoretical predictions of localization have been confirmed recently in a variety of experiments in the fields of condensed matter physics and optics. We consider the widely employed model of the one-dimensional discrete nonlinear Schrödinger equation which allows for the investigation of localization of linear and nonlinear waves. We establish a generic connection between coherence and localization by showing that localized solutions are necessarily coherent. The effects of a loss of coherence are investigated numerically by applying random dephasing. The onset of a diffusive spreading regime is observed as a generic feature for persistent dephasing, which eventually destroys localization. After finite integration times maximal delocalization is achieved for a certain rate and strength of dephasing, resulting from the competition between destroying the initial wave packet on the one hand and not suppressing spreading too much on the other. When dephasing is switched off at a certain time, a loss or gain of coherence in linear wave packets directly corresponds to delocalization or stronger localization. This leads to stable partially coherent wave packets. In contrast, localization of nonlinear waves after dephasing is connected to the efforts of establishing complete coherence, at least for asymptotically long times. On intermediate time scales, however, various interesting partially coherent regimes can be observed. / Die Phänomene von Kohärenz und Lokalisierung haben sich in den letzten Jahrzehnten zum Schwerpunkt zahlreicher Forschungsinteressen entwickelt. Erst kürzlich wurden theoretische Vorhersagen von Lokalisierung in verschiedensten Experimenten in den Bereichen der Festkörperphysik und Optik bestätigt. In dieser Arbeit wird das häufig angewendete Modell der eindimensionalen diskreten nichtlinearen Schrödingergleichung betrachtet, welches die Untersuchung der Lokalisierung von linearen und nichtlinearen Wellen ermöglicht. Eine generelle Verbindung zwischen Kohärenz und Lokalisierung wird gezeigt, wonach lokalisierte Lösungen notwendigerweise kohärent sind. Die Auswirkungen eines Verlustes von Kohärenz werden numerisch durch Anwendung unterschiedlicher Methoden eines zufälligen Dephasierens untersucht. Ein permanentes Dephasieren führt stets zum Auftreten eines diffusiven Regimes, welches letztlich die Zerstörung von Lokalisierung bedingt. Nach einer endlichen Integrationszeit wird jedoch eine maximale Delokalisierung nur durch eine bestimmte Rate und Stärke des Dephasierens bewirkt, resultierend aus einem Wettstreit zwischen möglichst schneller Zerstörung des ursprünglichen Wellenpaketes auf der einen Seite und nicht zu starker Behinderung des Zerfließens auf der anderen. Wird das Dephasieren nach einer bestimmten Zeit abgeschaltet, so entspricht ein folglicher Verlust oder Zugewinn an Kohäarenz in einem linearen Wellenpaket direkt einem Verlust oder Zugewinn von Lokalisierung. Dabei treten im allgemeinen stabile teil-kohärente Wellenpakete auf. Im Gegensatz dazu ist Lokalisierung nichtlinearer Wellenpakete stets mit den Bemühungen verbunden, vollständige Kohärenz wiederherzustellen, zumindest für asymptotisch lange Zeiten. Auf mittleren Zeitskalen können jedoch verschiedene interessante teil-kohärente Strukturen beobachtet werden.

In the present thesis the dynamics of the correlations between an open quantum system and its environment is investigated. This becomes feasible by means of a very useful representation of the total system-environment state. General conditions for separability and entanglement of the latter are derived, and investigated in the framework of an open quantum two-level system, which is coupled to a dissipative and a dephasing environment.

Nous avons mis en place un dispositif permettant l’acquisition d'échos de photons stimulés infrarouges à l’échelle femtoseconde. Le but est d'examiner la dynamique vibrationnelle aux temps courts de métaux carbonyles (W(CO)₆ and Fe(CO)₅) piégés en matrice cryogénique (4-50 K). Cet environnement solide, issu de la condensation d'un mélange gazeux contenant une impureté et un gaz inerte (N₂, CH₄, Ar, etc.), est propice à l’étude de systèmes dans leur état fondamental. L’excitation d’une vibration moléculaire s’atténue toujours temporellement, ce qui correspond dans le domaine spectral à un élargissement des raies d’absorption. L’étude de la dynamique vibrationnelle vise à examiner les causes physiques à l’origine de cet élargissement spectral. Typiquement, elles sont de trois sortes : phénomènes intramoléculaires, interactions entre molécules piégées et interactions entre la molécule piégée et l’environnement. Les échos de photons permettent de distinguer les contributions homogènes et inhomogènes de l’élargissement spectral et de caractériser les processus de déphasage, de relaxation des populations et de diffusion spectrale. Parmi les résultats obtenus, nous avons mis en évidence l'influence des phonons spécifiques aux matrices moléculaires (ex : libration de N₂ et rotation de CH₄ ) sur le déphasage vibrationnel ainsi que l’influence de la transition de phase du méthane solide à 20 K sur la dynamique vibrationnelle. Nous avons également montré que la dynamique vibrationnelle était dépendante du site cristallographique dans lequel est piégée la molécule. Enfin, en excitant plusieurs modes de vibration simultanément, nous avons pu examiner les couplages intramoléculaires. / We built an experimental set-up in order to generate infrared stimulated photon echoes at the femtosecond timescale. The purpose is to examine the short time vibrational dynamics of metal carbonyls (W(CO)₆ and Fe(CO)₅) trapped in cryogenic matrices (4-50 K). This environment, resulting from the condensation of a gas mixture containing the impurity and an inert gas (N₂, CH₄, Ar, etc.), is well suited to study systems in their ground state. An excited molecular vibration is always damped in the time domain. It corresponds in the frequency domain to a broadening of the absorption line. The study of the vibrational dynamics aims at examining the physical causes of this spectral broadening. Typically, there are three kinds of causes: intramolecular phenomena, interactions between trapped molecules and interactions between the impurity and the environment. Photon echoes allow distinguishing between the homogeneous and the inhomogeneous contributions of the spectral broadening and characterizing dephasing process, population relaxation and spectral diffusion. Among the obtained results, we highlighted the influence of phonons that are specific to molecular matrices (ex: N₂ libration and CH₄ rotation) on the vibrational dephasing. Moreover, we observed the influence of the phase transition of solid methane at 20 K on the vibrational dynamics. We also showed that the vibrational dynamics depends on the site in which the molecule is trapped. Finally, when exciting several vibrational modes, we are also able to study intramolecular couplings.

In this thesis, theoretical and computer simulation studies of vibrational phase relaxation in various molecular liquids are presented. That includes liquid nitrogen, both along the coexistence line and the critical isochore, binary liquid mixture and liquid water. The focus of the thesis is to understand the dependence of the vibrational relaxation on the density, temperature, composition and the role of different interactions among the molecules. The density fluctuation of the solute particles in a solvent is studied systematically, where the computer simulation results are compared with the mode coupling theory (MCT). The classical density functional theory (DFT) is used to study the vibrational relaxation dynamics in molecular liquids with an aim to understand the heterogeneous nature of the dynamics commonly observed in experiments. Chapter 1 contains a brief overview of the earlier relevant theories, their successes and shortcomings in the light of the problems discussed in this thesis. This chapter discusses mainly the basic features of the vibrational dynamics of molecular liquids and portrays some of the theoretical frameworks and formalisms which are widely recognized to have contributed to our present understanding. Vibrational dephasing of nitrogen molecules is known to show highly interesting anomalies near its gas–liquid critical point. In Chapter 2, we present the results of extensive computer simulation studies and theoretical analysis of the vibrational phase relaxation of nitrogen molecules both along the critical isochore and the gas–liquid coexistence line. The simulation includes the different contributions (density (ρ), vibration–rotation (VR), and resonant transfer (Rs)) and their cross–correlations. Following Everitt and Skinner, we have included the vibrational coordinate (q) dependence of the inter–atomic potential, which is found to have an important contribution. The simulated results are in good agreement with the experiments. The linewidth (directly proportional to the rate of the vibrational phase relaxation) is found to have a lambda shaped temperature dependence near the critical point. As observed in the experimental studies, the calculated lineshape becomes Gaussian–like as the critical temperature (Tc) is approached while being Lorentzian–like at the temperatures away from Tc. Both the present simulation and a mode coupling theory (MCT) analysis show that the slow decay of the enhanced density fluctuations near the critical point (CP), probed at the sub–picosecond timescales by the vibrational frequency modulation, and an enhanced vibration–rotation coupling, are the main causes of the observed anomalies. Dephasing time (тv) and the root mean square frequency fluctuation (Δ) in the supercritical region are calculated. The principal results are: 1. a crossover from a Lorentzian–like to a Gaussian–like lineshape is observed as the critical point is approached along the critical isochore, 2. the root mean square frequency fluctuation shows a non–monotonic dependence on the temperature along the critical isochore, 3. the temperature dependent linewidth shows a divergence–like (λ–shaped) behavior along the coexistence line and the critical isochore. It is found that the linewidth calculated from the time integral of the normal coordinate time correlation function (CQ(t)) is in good agreement with the known experimental results. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous effects of several factors, (i) the enhancement of the negative cross–correlations of ρ with VR and Rs and (ii) the large density fluctuations as the critical point (CP) is approached. Due to the negative cross–correlations of ρ with VR and Rs the total decay becomes faster (correlation times are in the femtosecond scale). The reason for the negative cross–correlation between ρ and VR is explored in detail. A mode coupling theory (MCT) analysis shows a slow decay of the enhanced density fluctuations near the critical point. The MCT analysis demonstrates that the large enhancement of VR–coupling near CP may arise from a non–Gaussian behavior of the equilibrium density fluctuations. This enters through a non–zero value of the triplet direct correlation function. Many of the complex systems found in nature and used routinely in industry are multi–component systems. In particular, binary mixtures are highly non–ideal and play an important role in the industry. The dynamic properties are strongly influenced by composition fluctuations which are absent in the one component liquids. In Chapter 3, isothermal–isobaric (NPT) ensemble molecular dynamics simulation studies of vibrational phase relaxation (VPR) in a model system are presented. The model considers strong attractive interaction between the dissimilar species to prevent phase separation. The model reproduces the experimentally observed non–monotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time (т c) at a mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of the mean square frequency modulation ((Δω2(0))) with тc indicates that the present model is in the intermediate regime of the inhomogeneous broadening. The non–monotonic composition (χ) dependence of тv is found to be primarily due to the non–monotonic χ dependence of тc, rather than due to a similar dependence in the amplitude of (Δω2(0)). The probability distribution of Δω shows a markedly non–Gaussian behavior at intermediate composition (χ - 0.5). We have also calculated the composition dependence of the viscosity (η∗) in order to explore the correlation between the viscosity with that of тv and тc. It is found that both the correlation times essentially follow the nature of the composition dependence of the viscosity. A mode coupling theory (MCT) analysis is presented to include the effects of the composition fluctuations in binary mixture. Water is an interesting and attractive object for research, not only because of its great importance in life processes but also due to its unusual and intriguing properties. Most of the anomalous properties of water are related to the presence of a three–dimensional network of hydrogen bonds, which is constantly changing at ultrafast, sub–picosecond timescales. Vibrational spectroscopy provides the means to study the dynamics of processes involving only certain chemical bonds. The dynamics of hydrogen bonding can be probed via its reflection on molecular vibrations, e.g., the stretching vibrational mode of the O–H bond. Recently developed femtosecond infrared vibrational spectroscopy has proved to be valuable to study water dynamics because of its unique temporal resolution. Recent studies have shown that the vibrational relaxation of the O–H stretch of HDO occurs at an extremely fast timescale with time constant being less than 100 femtosecond. Here, in Chapter 4, we investigate the origin of this ultrafast vibrational dephasing using computer simulation and appropriate theoretical analysis. In addition to the usual fast vibrational dynamics due to the hydrogen bonding excitations, we find two additional reasons: (a) the large amplitude of angular jumps of the water molecules (with 30–40 fs time intervals) provide large contribution to the mean square vibrational frequency and (b) the projected force along the O–H bond due to the solvent molecules, on the oxygen (FO(t)) and hydrogen (FH (t)) atoms of the O–H bond exhibit a large negative cross–correlation (NCC) between FO(t) and FH (t). This NCC is shown to be partly responsible for a weak, non–Arrhenius temperature dependence of the relaxation rate. In the concluding note, Chapter 5 starts with a brief summary of the outcome of this thesis and ends up with suggestions of a few relevant problems that may prove worthwhile to be addressed in the future.

Die vorliegende Arbeit beschäftigt sich mit der Herstellung und Charakterisierung von verdünnten magnetischen II-VI und III-V Halbleiter-Dünnschichten. Diese Systeme bieten vereinfachte optische kohärente Kontrolle von Spin-basierten Prozessen und eignen sich hervorragend für den Einsatz in zukünftigen opto-magnetischen Anwendungen. ZnO-, ZnXO-, GaN- und GaXN-Proben (X = Mangan, Cobalt) sind mit Hilfe der naßchemischen Sol-Gel Synthese hergestellt worden. Sie werden mit Hilfe der Photolumineszenzspektroskopie untersucht. Die spektrale Position der elektronischen Niveaus in der Nähe der Bandkante dieser Materialien wird bestimmt, um in weiteren Experimenten die freien und gebundenen Exzitonen einzeln abzufragen. Mit der Methode der zeitaufgelösten differentiellen Transmissionsspektroskopie (TRDT) werden die Lebensdauern dieser Ladungsträger bestimmt und mit ultraschnellen Prozessen der optischen Anregung und Relaxation in Verbindung gebracht. Die Methode der zeitaufgelösten Faraday-Rotation-Spektroskopie (TRFR) wird angewandt, um die kohärente Spindynamik des optisch angeregten Teilchenensembles zu beschreiben. Die Kohärenz unterliegt den Störeinflüssen verschiedener Streumechanismen, die in der vorliegenden Arbeit identifiziert und quantitativ beschrieben werden. Bei einigen untersuchten Materialsystemen (ZnCoO, ZnMnO und GaMnN) wird die jeweilige spezifische Elektron-Ion Austauschenergie N0α bestimmt, welche die Kopplungsstärke der elektronischen Spins zu denen der Dotierionen beschreibt.

Die vorliegende Arbeit beschäftigt sich mit der Herstellung und Charakterisierung von verdünnten magnetischen II-VI und III-V Halbleiter-Dünnschichten. Diese Systeme bieten vereinfachte optische kohärente Kontrolle von Spin-basierten Prozessen und eignen sich hervorragend für den Einsatz in zukünftigen opto-magnetischen Anwendungen. ZnO-, ZnXO-, GaN- und GaXN-Proben (X = Mangan, Cobalt) sind mit Hilfe der naßchemischen Sol-Gel Synthese hergestellt worden. Sie werden mit Hilfe der Photolumineszenzspektroskopie untersucht. Die spektrale Position der elektronischen Niveaus in der Nähe der Bandkante dieser Materialien wird bestimmt, um in weiteren Experimenten die freien und gebundenen Exzitonen einzeln abzufragen. Mit der Methode der zeitaufgelösten differentiellen Transmissionsspektroskopie (TRDT) werden die Lebensdauern dieser Ladungsträger bestimmt und mit ultraschnellen Prozessen der optischen Anregung und Relaxation in Verbindung gebracht. Die Methode der zeitaufgelösten Faraday-Rotation-Spektroskopie (TRFR) wird angewandt, um die kohärente Spindynamik des optisch angeregten Teilchenensembles zu beschreiben. Die Kohärenz unterliegt den Störeinflüssen verschiedener Streumechanismen, die in der vorliegenden Arbeit identifiziert und quantitativ beschrieben werden. Bei einigen untersuchten Materialsystemen (ZnCoO, ZnMnO und GaMnN) wird die jeweilige spezifische Elektron-Ion Austauschenergie N0α bestimmt, welche die Kopplungsstärke der elektronischen Spins zu denen der Dotierionen beschreibt.

No description available.

We present the development of a novel, UHV-compatible device fabrication strategy for the realisation of nano- and atomic-scale devices in silicon by harnessing the atomic-resolution capability of a scanning tunnelling microscope (STM). We develop etched registration markers in the silicon substrate in combination with a custom-designed STM/ molecular beam epitaxy system (MBE) to solve one of the key problems in STM device fabrication ??? connecting devices, fabricated in UHV, to the outside world. Using hydrogen-based STM lithography in combination with phosphine, as a dopant source, and silicon MBE, we then go on to fabricate several planar Si:P devices on one chip, including control devices that demonstrate the efficiency of each stage of the fabrication process. We demonstrate that we can perform four terminal magnetoconductance measurements at cryogenic temperatures after ex-situ alignment of metal contacts to the buried device. Using this process, we demonstrate the lateral confinement of P dopants in a delta-doped plane to a line of width 90nm; and observe the cross-over from 2D to 1D magnetotransport. These measurements enable us to extract the wire width which is in excellent agreement with STM images of the patterned wire. We then create STM-patterned Si:P wires with widths from 90nm to 8nm that show ohmic conduction and low resistivities of 1 to 20 micro Ohm-cm respectively ??? some of the highest conductivity wires reported in silicon. We study the dominant scattering mechanisms in the wires and find that temperature-dependent magnetoconductance can be described by a combination of both 1D weak localisation and 1D electron-electron interaction theories with a potential crossover to strong localisation at lower temperatures. We present results from STM-patterned tunnel junctions with gap sizes of 50nm and 17nm exhibiting clean, non-linear characteristics. We also present preliminary conductance results from a 70nm long and 90nm wide dot between source-drain leads which show evidence of Coulomb blockade behaviour. The thesis demonstrates the viability of using STM lithography to make devices in silicon down to atomic-scale dimensions. In particular, we show the enormous potential of this technology to directly correlate images of the doped regions with ex-situ electrical device characteristics.