Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 01/05 Archiv

The aim of this dissertation is to study the kinematics of 2-qubit pairs. A 2-qubit state is specified by the Bloch vectors for each qubit and a 3 × 3 dyadic, representing the expection values of the joint observables. In what follows the main results are listed. • The behaviour of a 2-qubit state under a local transformation is investi-gated, where we obtain a set of 9 quantities, constructed from the Bloch vectors and the cross dyadic, which are invariant under local transforma-tion. We establish a generic form for a 2-qubit state, which helps us decide if given two 2-qubit states belong to the same family or not. Using this form, which depends on the characteristic values of the cross dyadic, one can distinguish between all two-qubit families, where we obtain six classes of families of locally equivalent states. Those families classify all 2-qubit states, four of them consist of two subclasses each. • A simple criterion is obtained to check if a 2-qubit state is separable or not. This criterion does not depend on the eigenvalues of the partial trans-position of the state in question but only on three numbers, those are the coefficients of the eigenvalue equation. These numbers are written as a function of the Bloch vectors and the cross dyadic. Also using the charac-teristic values of the cross dyadic, one can decide if the CHSH inequality is obeyed or violated. • The properties of Lewenstein-Sanpera decompositions are employed to split a given state into its optimal separable and pure parts. The degree of separability is an important part in this decomposition, where a state is more useful for quantum information purposes, the smaller its degree of separability. The optimal degree of separability is obtained analytically for some important cases as a function of the Bloch vectors and the cross dyadic of the state in question: For the simple Werner state, where our result coincides with that obtained numerically. Also for the self-transposeed states, the generalized for Werner states and rank-2 states. • The technique of the rank-2 case is employed to study the case of rank-3 and the full rank, where we obtain all possible decompositions. Among them, we choose the one which has the largest splitting parameter. In this situation a numerical procedure could help in obtaining the optimal de-composition. Given a density matrix, one obtains its eigenvalues and corre-sponding eigenvectors. Using the rank-2 method to obtain all the possible decompositions, then choose the one corresponding to the largest degree of separability. If this decomposition is the optimal one, a technique is used to check the optimality. If it is not optimal, an optimization procedure is performed. • There is an important relation between the degree of separability S and what is the so called concurrence C which appears in the definition of the entanglement of formation. In general, the sum of the degree of separabil-ity and the concurrence is less than one, but equal to one for states with vanishing Bloch vectors. On the other hand both of them run from 0 to 1. • A criterion is introduced to decide if a given decomposition is the optimal one or not. Two inequalities are obeyed if the decomposition in question is the optimal one and are violated if it is not. • The effect of the unitary operators and BCNOT operations are described on the dynamical variables. An alternative presentation of the IBM and Oxford purification protocols is obtained by using theses variables. One could introduce the degree of separability as a purification parameter, where the purified state has a smaller degree of separability than the initial one. Employing the properties of the characteristic values of the cross dyadic, makes the Oxford protocol much faster.

The early universe consisted of a dense, hot and ionised gas of electrons, protons, neutrons, some light atomic nuclei and photons. The universe at that time was optically thick as the photons could not travel very far before being scattered on electrons in the dense gas. The temperature was too hot for the electrons to combine with the nuclei and form atoms. But as the universe expanded it cooled. About 300 000 years after the Big Bang, the temperature of the dense gas filling the universe was about 3000 degree Kelvin. This temperature allowed the formation of the first atoms in the universe. The electrons combined with the protons to form atoms. The probability for a photon to scatter on a neutral atom is much less than the probability to scatter on free electrons and protons. For this reason it is said that the universe got transparent when the electrons were bound to the protons. The photons continued travelling in a straight line without being scattered. About 12 billion years later some of these photons hit a detector on the planet called 'the earth'. And it provided scientists with valuable information about the origin of the universe. This radiation which has travelled more or less unchanged from the earliest times until today is called the cosmic microwave background radiation, and is the topic of this Ph.D. thesis.

In dieser Arbeit werden die Rauschquellen in Sperrschicht-Feldeffekttransistoren (JFETs) eingehend auf ihre Ursachen und Wirkungsweise untersucht. Das Rauschverhalten von JFETs wirkt sich beispielsweise in Halbleiter-Detektor-Verstärker-Systemen auf die Energieauflösung solcher Systeme aus, in denen JFETs aufgrund ihres geringen Rauschens oft als erste Verstärkungsstufe eingesetzt werden. Diesbezüglich wird eine Methode entwickelt, mit Hilfe derer aus Rauschmessungen an JFETs die Energieauflösung eines einfachen spektroskopischen Systems berechnet werden kann, in das der vermessene Transistor als erste Verstärkungsstufe eingebaut ist. Außerdem wird gezeigt wie aus temperaturabhängigen Rauschmessungen auf die Eigenschaften von Kristalldefekten in Halbleitern geschlossen werden kann. Im theoretischen Teil der Arbeit werden zuerst grundlegende Rauschmechanismen in Halbleitern beschrieben wie sie auch in JFETs auftreten. Auf die Herleitungen der Rauschspektren des thermischen Rauschens, des Diffusionsstrom-Rauschens, des Generations-Rekombinations-Rauschens und des „Random-Telegraph-Signal“-Rauschens (RTS-Rauschen) wird ausführlich eingegangen. Das RTS-Rauschen kommt durch den Einfang und die Emission von freien Ladungsträgern in/aus Kristalldefekte(n) hinein/heraus. Die Abhängigkeiten des RTS-Rauschens von der Lage des Kristalldefekts im Bauelement und den Eigenschaften des Kristalldefekts selbst werden detailliert analysiert. An den Beispielen eines Widerstandes und eines JFETs wurden Simulationen durchgeführt, mit Hilfe derer der Einfluß einzelner Kristalldefekte auf das Rauschverhalten des jeweils betrachteten Bauelements bestimmt werden kann. Im experimentellen Teil der Arbeit werden Messungen an verschiedenen JFETs vorgestellt, in denen das Rauschen in Abhängigkeit von der Frequenz und der Temperatur aufgenommen wurde. Auf die angeführten Rauschmessungen wird die oben erwähnte Methode angewendet, mit Hilfe derer man die Energieauflösung eines einfachen spektroskopischen Systems berechnet werden kann, in das der vermessene Transistor als erste Verstärkungsstufe eingebaut ist. Dadurch gewinnt man ein Bild vom Verhalten des betrachteten spektroskopischen Systems in Abhängigkeit von der Temperatur und der Filterzeit eines in das System integrierten Filters, der zur Optimierung des Signal-zu-Rausch-Verhältnisses dienen sollte. Daraufhin wird exemplarisch am Beispiel eines rauscharmen JFETs gezeigt, wie man anhand von Rauschmessungen die Eigenschaften und die Lage von Kristalldefekten bestimmen kann. Zum Abschluß der Arbeit werden noch Wiederholungsmessungen an einem Bauelement widergegeben, bei denen sich das Rauschverhalten von sogenannten multistabilen Kristalldefekten manifestierte. Multistabile Defekte sind Kristalldefekte, die nicht nur eine stabile sondern mehrere mögliche Konfigurationen im Kristallgitter besitzen. Übergänge zwischen den verschiedenen Zuständen können durch verschiedene Einflüsse wie z.B. durch die Temperaturbehandlung während einer Rauschmessung zustande kommen.

Coherent control of molecular dynamics deals with the steering of quantum mechanical systems with suitably shaped ultrashort laser fields. The coherence properties of the laser field are exploited to achieve constructive interference for a predefined target wave function via a phasecorrect superposition of wave functions. The goal of coherent control, the selective preparation of a target state, is an important prerequisite for mode-selective chemistry. The laser pulse tailored to drive the system from the initial to the target state as a perturbation can in general not be determined by a quantum-mechanical calculation, since usually even the Hamiltonian of the system is unknown. A practical alternative is to determine the required shape of the laser field in a feedback-controlled regulation loop which uses a signal derived from the experiment as feedback. The loop is repeated until a pulse that suits the requirements is obtained. Experiments in this area have until recently mostly been limited to the wavelength regime of Ti:Sa lasers and their fundamentals. This work deals with the fundamentals of feedback-controlled shaping of ultrashort laser pulses with respect to both establishment of its technical prerequisites and its application to suitable model systems. The feedback loop has been tested using a simple optimization experiment with known outcome; then it was applied to experiments of progressively increasing complexity. From the optimized pulses, physical insight into the optimization process has been gained. In the first part of this work, the required technology has been implemented and standardized such that control experiments might employ it as a standard tool. One of the technical prerequisites was the frequency conversion of the 800 nm Ti:Sa laser pulses to a wavelength range suited to the particular systems. To this end, non-collinear optical parametric amplifiers have been built in different designs that routinely produce tunable sub-20 fs pulses in the visible. The characterization techniques for ultrashort pulses have been implemented as well. Pulse shapers with cylindrical instead of spherical mirrors have been implemented for the modulation of broadband pulses, and their functionality has been explained both theoretically and experimentally. A new liquid crystal device, the core of our pulse shapers, has been developed in cooperation with the group of Thomas Feurer at the Universit¨at Jena and the Jenoptik GmbH which allows for the generation of more complex pulse shapes than with other commercially available devices to date. Using a pulse shaper to modulate the white light continuum that serves as the seed for the non-collinear optical parametric amplifier, generation of phase-locked two-color double pulses has been achieved, with tunable wavelengths, delays, and relative carrier phases between the single pulses. The basic principle, phase conservation during optical parametric amplification, has been demonstrated. With this setup, control experiments which require pulses with the above described attributes in electronically controllable form are possible for the first time. An evolutionary strategy used as the optimization algorithm in the feedback loop has been programmed and characterized both in simulation and experiment using a simple optimization experiment, namely pulse recompression by phase compensation. In the second part of this work, pulse recompression of ultra-broadband spectra in the sub-20fs regime serves as an example of utility of feedback-controlled optimization. This experiment simultaneously served as a further test of the feedback loop in the limit of a physically unreachable optimization goal. It has been demonstrated that a suitable parameterization of the electric field, implemented by a mapping of the optimization parameters adjusted by the algorithm to the physical parameterscontrolling the liquid crystal mask affords a means of acquiring physical knowledge from the retrieved optimal electric fields. A parameterization helps to dissect the physical processes mediating the control process, thereby assuring fast, secure convergence and robustness against signal noise. So-called ”bright” and ”dark” pulses, i.e. pulses that are absorbed by a medium or transmitted, respectively, have been demonstrated for the case of the two-photon transition Na(3s5s). The physical constraints responsible for pulses being either ”bright” or ”dark”, namely a symmetric or anti-symmetric spectral phase, have been incorporated in the parameterization with the purpose of testing the concept of parameterization for such studies. An example of mode-selective preparation of vibrational states in a polyatomic molecule is the control of the ground state dynamics in polydiacetylene. In a Raman step with a shaped Stokes pulse, the population of the backbone vibrations of polydiacetylene in its ground state could be controlled. A consecutive probe pulse in a CARS (coherent anti-Stokes Raman scattering) arrangement generates an anti-Stokes signal which, once frequency-resolved, served as feedback. Of the three or four modes, respectively, accessible within the pulse bandwidth, single modes as well as combinations of modes could be excited with high selectivity. Again, suitable parameterizations helped to identify one of the processes responsible for the control as a Tannor-Rice scheme. Since both the amplitude and the phase of each mode could be influenced, the focusing of a wave packet at a predefined time, or, equivalently, the generation of local modes represents the control of a unimolecular reaction. Starting from the control of a unimolecular reaction, the possibilities of controlling a bimolecular reaction were addressed. The NaH2 collision complex was chosen as a suitable system for the control of bimolecular reactions generally and a conical intersection in particular. First timeresolved experiments have been presented.

The work at hand presents a comprehensive investigation of solid-state lasers based on thin films of a disordered organic semiconductors (OS). The high luminescence yield of OS together with their conductivity and the ease of processing them into sub-micron thick films on substrates of virtually any shape and size open vast opportunities both for the realization of novel devices and for the exploration of innovative resonator geometries. Within the course of this work optically pumped lasers with spatially distributed feedback were fabricated by deposition of a thin film of an OS on a nanopatterned substrate. Upon optical excitation with femtosecond laser pulses laser operation is observed. It is characterized using time-integrated and time-resolved spectroscopy. As active medium two of the most promising electroluminescent organic materials were employed, namely the conjugated polymer MeLPPP and the composite molecular system Alq3:DCM. Owing to their large gain coefficient low-threshold light-amplification by stimulated emission can be observed from slab waveguides formed by a thin layer of the OS on a planar substrate. In periodically modulated waveguides Bragg scattering gives rise to distributed feedback. Utilizing UV-embossed plastic substrates with an appropriate onedimensional surface corrugation, edge- and surface-emitting lasers were fabricated. Excellent agreement is found between the performance of these 1D-DFB lasers and the predictions of a quantitative numerical modeling. Unless further precautions are taken these lasers operate on a continuum of lateral modes, characterized by a broad emission spectrum and a large beam divergence. A significantly improved performance is achieved by application of a two-dimensional corrugation. The specific properties of light-propagation in the resulting 2D photonic crystal give rise to monomode laser operation, accompanied by a reduction of the laser threshold, an increased differential efficiency, and by the emission of a circularly shaped, diffractionlimited laser beam. It is demonstrated that the emission linewidth is (time-bandwidth) transform limited by the duration of the laser pulse. The mechanism leading to monomode operation at low excitation density as well as the photonic band structure at high excitation density is revealed by a Laue model for the feedback in such a 2D photonic crystal laser. By use of a self-assembly technique waveguide structures with stochastically distributed scatter centers were fabricated. Lasing with resonant feedback is observed and attributed to the formation of random closed loop cavities (random lasing). The underlying process of recurrent light-scattering is made possible by the strong scattering, the reduced dimensionality of the waveguide geometry, and the large gain of the organic semiconductor material. In order to explore the technological potential of organic semiconductor lasers two alternative concepts for electrical operation were examined. In a hybrid concept an OS DFB laser is merely used as a tunable solid-state laser source. Thanks to the low laser threshold a very compact setup can be realized utilizing a microchip pump laser with a repetition rate of several kilohertz. In the approach of making an organic diode laser the low mobility of disordered organic semiconductors imposes severe constraints on the device architecture. Several structures were developed and fabricated that concurrently permit large current densities and possess a low laser threshold. As a result, optically pumped lasing is for the first time demonstrated in structures that are suitable for electrical excitation.