Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

Diese Arbeit beschäftigt sich mit den perizyklischen Reaktionen eines photochromen trifluorierten Indolylfulgids und verschiedenen Möglichkeiten, die Dynamik und Effizienz der Ringöffnungsreaktion durch Zuführen von zusätzlicher Schwingungsenergie zu beeinflussen.

Mittels transienter Absorptionsspektroskopie wurde die Reaktionsdynamik der Ringschluss- und Ringöffnungsreaktion dieses thermisch und photochemisch stabilen, reversiblen molekularen Schalters aufgeklärt:

Die Ringschlussreaktion ist eine ultraschnelle Reaktion aus dem S1, die ohne langlebige Intermediate auf der Subpikosekunden-Zeitskala erfolgt. Eine Abhängigkeit von der Temperatur im Bereich zwischen 12 °C und 60 °C wurde bei ihr nicht beobachtet und auch bei Variation des umgebenden Lösungsmittels wird lediglich ihre Effizienz (10 - 18%), nicht aber ihre Dynamik (0,3 ps) geändert. Als aktive Moden der Reaktion wurden niederfrequente Torsionsmoden unter 100 cm-1 identifiziert. Mittels quantenchemischer Rechnungen wurden zyklisierbare und nicht zyklisierbare Konformere der offenen Form bestimmt.

Die Ringöffnungsreaktion des trifluorierten Indolylfulgids stellt ebenfalls eine ultraschnelle Reaktion ohne langlebige Intermediate dar. Allerdings ist sie aktiviert und verläuft über zwei Barrieren im angeregten Zustand. Das verwendete Lösungsmittel ändert die Dynamik (2 - 11 ps) und Effizienz (1 - 6,7%) der Reaktion deutlich. Als aktive Moden der Reaktion findet man Schwingungen, die laut einer Normalmodenanalyse über den Bereich bis 1300 cm-1 verteilt sind.

Erhöht man die Probentemperatur, so verkürzt sich die Reaktionszeit der Ringöffnung in 1,4-Dioxan von 10,3 ps bei 12 °C auf 7,6 ps bei 60 °C und die Quanteneffizienz erhöht sich von 3,1% (12 °C) auf 5,0% (60 °C). Durch Zuführen von optischer Überschussenergie wird die Reaktion ebenfalls effizienter. Dennoch bieten diese Verfahren keine signifikanten Freiheitsgrade, den Reaktionspfad zu lenken.

Manipuliert man die Ringöffnungsreaktion hingegen dadurch, dass die geschlossenen Moleküle erst in einer vorgeschalteten Ringschlussreaktion gebildet werden, so wird die Ringöffnungsreaktion schneller, wenn die Verzögerungszeit zur vorgeschalteten Reaktion verkürzt wird. Des Weiteren weisen die transienten Absorptionssignale nichtexponentielles Verhalten auf, das mit zeitabhängigen Raten erklärt werden kann. Schließlich kann die Effizienz auf mehr als das dreifache gesteigert werden. Daraus kann geschlossen werden, dass die intramolekulare Schwingungsumverteilung nach einigen Pikosekunden noch nicht abgeschlossen ist und unterschiedliche Gruppen von Schwingungsmoden existieren, die durch die vorgeschaltete Reaktion verschieden stark populiert werden. Die in der Ringöffnungsreaktion aktiven Moden werden selektiv hoch angeregt und die Relaxation aus ihnen erfolgt auf einer Zeitskala von 5 ps.

This thesis covers the few-cycle laser-driven acceleration of

electrons in a laser-generated plasma. The so-called \emph{laser

wakefield acceleration} is a long-known concept that relies on

strongly driven plasma waves for the generation of accelerating

gradients in the range of several 100 GV/m. This value is

approximately four orders of magnitude larger than the one

attainably by classic accelerators, which is limited essentially

by electrical breakdown in the accelerating structures to

approximately 100 MV/m. Since the acceleration length necessary

for obtaining a certain electron energy is inversely proportional

to the accelerating field, this leads also to a drastic reduction

of the size and of the price of the accelerator. Furthermore, the

special properties of laser accelerated electron pulses, namely

the ultrashort pulse duration, the high brilliance, and the high

charge density, open up new possibilities in many applications of

these electron beams.

The laser system employed in this work is a new development based

on optical parametric chirped pulse amplification and is the only

multi-TW few-cycle laser in the world. It allows for the

amplification of pulses with a duration of 8 fs up to a power of

6.5 TW. In the experiment, the laser beam is focused onto a

supersonic helium gas jet which leads to the formation of a plasma

channel. The laser pulse, having an intensity of 10^19

W/cm^2 propagates through the plasma with an electron density of

2x10^19 cm^(-3) and forms via a highly nonlinear

interaction a strongly anharmonic plasma wave. The amplitude of

the wave is so large that the wave breaks, thereby injecting

electrons from the background plasma into the accelerating phase.

The energy transfer from the laser pulse to the plasma is so

strong that the maximum propagation distance is limited to the 0.1 mm

range. Therefore, gas jets specifically tuned to these

requirements have to be employed. The properties of microscopic

supersonic gas jets are thoroughly analyzed in this work. Based on

numeric flow simulation, this study encompasses several extensive

parameter studies that illuminate all relevant features of

supersonic flows in microscopic gas nozzles. This allowed the

optimized design of de Laval nozzles with exit diameters ranging

from 0.15 to 3 mm. The employment of these nozzles in the

experiment greatly improved the electron beam quality.

After these optimizations, the laser-driven electron accelerator

now yields monoenergetic electron pulses with energies up to 50

MeV and charges between one and ten pC. The electron beam has a

typical divergence of 5 mrad and comprises an energy spectrum that

is virtually free from low energetic background. The electron

pulse duration could not yet be determined experimentally but

simulations point towards values in the range of 1 fs. The

acceleration gradient is estimated from simulation and experiment

to be approximately 0.5 TV/m. The electron accelerator is

routinely operated at 10 Hz, which is a unique feature among laser

based accelerators. The light amplification technique employed in

the laser system in principle allows here improvements by several

orders of magnitude.

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. Mirror symmetry is an equivalence between the topological string A-model on a manifold X and the B-model on a mirror manifold Y, together with their deformation spaces. Deformations of the target space on the A-side are Kaehler deformations which change the volume of the manifold. Deformations on the B-side change the complex structure. The power of mirror symmetry is due to its simple physical origin which connects two different areas of mathematics, symplectic- and complex geometry. This connection has far reaching and unexpected consequences both on the mathematical and on the physical side. Physical problems can be given a precise mathematical meaning and can be solved. In this regard, quantum corrected superpotentials are computed in this work on the one hand. On the other hand the mathematical understanding of the background dependence is used to reorganize a perturbative Feynman diagram expansion in terms of a more efficient polynomial expansion. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples.

The main idea of mirror symmetry is to map the solution of simple problems to the solution of equivalent difficult problems. To do so, a mirror map is needed, which is at the heart of mirror symmetry. The computation of this map is possible thanks to a physical structure which occurs in both mathematical realizations. This structure is the vacuum bundle, together with a grading which varies over the space of deformations. In the context of the B-model the study of the variation of this grading leads to differential equations which allow the computation of the mirror map as well as other quantities which describe quantum geometry when translated to the A-side. In this thesis, the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes.

Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted.

In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps.

We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing.

Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner.

Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory.

Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record.

Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment.

Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection sc