Covariant Phase Observables in Quantum Mechanics

The aim of this thesis is to present a solution to the quantum phase problem of the single-mode optical field. The solution is based on the use of phase shift covariant normalized positive operator measures. These measures describe realistic direct coherent state phase measurements such as the phase measurement schemes based on eight-port homodyne detection or heterodyne detection. The structure of covariant operator measures and, more generally, covariant sesquilinear form measures is analyzed in this work. Four different characterizations for phase shift covariant normalized positive operator measures are presented. The canonical covariant operator measure is definded and its properties are studied. Finally, some other suggested phase theories are introduced to investigate their connections to the covariant sesquilinear form measures.

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described

Information security and the enforcement of secrecy : the practical application of quantum key distribution

There is no doubt about the necessity of protecting digital communication: Citizens are entrusting their most confidential and sensitive data to digital processing and communication, and so do governments, corporations, and armed forces. Digital communication networks are also an integral component of many critical infrastructures we are seriously depending on in our daily lives. Transportation services, financial services, energy grids, food production and distribution networks are only a few examples of such infrastructures. Protecting digital communication means protecting confidentiality and integrity by encrypting and authenticating its contents. But most digital communication is not secure today. Nevertheless, some of the most ardent problems could be solved with a more stringent use of current cryptographic technologies. Quite surprisingly, a new cryptographic primitive emerges from the ap-plication of quantum mechanics to information and communication theory: Quantum Key Distribution. QKD is difficult to understand, it is complex, technically challenging, and costly-yet it enables two parties to share a secret key for use in any subsequent cryptographic task, with an unprecedented long-term security. It is disputed, whether technically and economically fea-sible applications can be found. Our vision is, that despite technical difficulty and inherent limitations, Quantum Key Distribution has a great potential and fits well with other cryptographic primitives, enabling the development of highly secure new applications and services. In this thesis we take a structured approach to analyze the practical applicability of QKD and display several use cases of different complexity, for which it can be a technology of choice, either because of its unique forward security features, or because of its practicability.

Influence of the (111) twinning on the formation of diamond cubic/diamond hexagonal heterostructures in Cu-catalyzed Si nanowires

The occurrence of heterostructures of cubic silicon/hexagonal silicon as disks defined along the nanowire (111) growth direction is reviewed in detail for Si nanowires obtained using Cu as catalyst. Detailed measurements on the structural properties of both semiconductor phases and their interface are presented. We observe that during growth, lamellar twinning on the cubic phase along the (111) direction is generated. Consecutive presence of twins along the (111) growth direction was found to be correlated with the origin of the local formation of the hexagonal Si segments along the nanowires, which define quantum wells of hexagonal Si diamond. Finally, we evaluate and comment on the consequences of the twins and wurtzite in the final electronic properties of the wires with the help of the predicted energy band diagram.

Frequency resolved admittance spectroscopy measurements on In0.52Al0.48As/InxGa1¿xAs/In0.52Al0.48As single quantum well structures

In this work a new admittance spectroscopy technique is proposed to determine the conduction band offset in single quantum well structures (SQW). The proposed technique is based on the study of the capacitance derivative versus the frequency logarithm. This method is found to be less sensitive to parasitic effects, such as leakage current and series resistance, than the classical conductance analysis. Using this technique, we have determined the conduction band offset in In0.52Al0.48As/InxGa1¿xAs/In0.52Al0.48As SQW structures. Two different well compositions, x=0.53, which corresponds to the lattice¿matched case and x=0.60, which corresponds to a strained case, and two well widths (5 and 25 nm) have been considered. The average results are ¿Ec=0.49±0.04 eV for x=0.53 and ¿Ec =0.51±0.04 eV for x=0.6, which are in good agreement with previous reported data.

Electrical transport quantum effects in the In0.53Ga0.47As/In0.52Al0.48As heterostructure on silicon

Electrical transport in a modulation doped heterostructure of In0.53Ga0.47As/In0.52Al0.48As grown on Si by molecular beam epitaxy has been measured. Quantum Hall effect and Subnikov¿De Haas oscillations were observed indicating the two¿dimensional character of electron transport. A mobility of 20¿000 cm2/V¿s was measured at 6 K for an electron sheet concentration of 1.7×1012 cm¿2. Transmission electron microscopy observations indicated a significant surface roughness and high defect density of the InGaAs/InAlAs layers to be present due to the growth on silicon. In addition, fine¿scale composition modulation present in the In0.53Ga0.47As/In0.52Al0.48As may further limit transport properties.

Raman scattering of InSb quantum dots grown on InP substrates

In this paper we present the Raman scattering of self-assembled InSb dots grown on (001) oriented InP substrates. The samples were grown by pulsed molecular beam epitaxy mode. Two types of samples have been investigated. In one type the InSb dots were capped with 200 monolayers of InP; in the other type no capping was deposited after the InSb dot formation. We observe two peaks in the Raman spectra of the uncapped dot, while only one peak is observed in the Raman spectra of the capped dots. In the case of the uncapped dots the peaks are attributed to LO-like and TO-like vibration of completely relaxed InSb dots, in agreement with high resolution transmission electron microscopy photographs. The Raman spectra of the capped dot suggest a different strain state in the dot due to the capping layer.

Local description of quantum inseparability

We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure product states, and can be made separable by mixing them with one or two pure product states.

Effective one-dimensional square well for two-dimensional quantum wires

The symmetrical two-dimensional quantum wire with two straight leads joined to an arbitrarily shaped interior cavity is studied with emphasis on the single-mode approximation. It is found that for both transmission and bound-state problems the solution is equivalent to that for an energy-dependent one-dimensional square well. Quantum wires with a circular bend, and with single and double right-angle bends, are examined as examples. We also indicate a possible way to detect bound states in a double bend based on the experimental setup of Wu et al.

Systematic trends in self-consistent calculations of linear quantum wires

Systematic trends in the properties of a linear split-gate heterojunction are studied by solving iteratively the Poisson and Schrödinger equations for different gate potentials and temperatures. A two-dimensional approximation is presented that is much simpler in the numerical implementation and that accurately reproduces all significant trends. In deriving this approximation, we provide a rigorous and quantitative basis for the formulation of models that assumes a two-dimensional character for the electron gas at the junction.

Current-density-functional approach to large quantum dots in intense magnetic fields

Within current-density-functional theory, we have studied a quantum dot made of 210 electrons confined in a disk geometry. The ground state of this large dot exhibits some features as a function of the magnetic field (Beta) that can be attributed in a clear way to the formation of compressible and incompressible states of the system. The orbital and spin angular momenta, the total energy, ionization and electron chemical potentials of the ground state, as well as the frequencies of far-infrared edge modes are calculated as a function of Beta, and compared with available experimental and theoretical results.

Structure and far-infrared edge modes of quantum antidots at zero magnetic field

We have investigated edge modes of different multipolarity sustained by quantum antidots at zero magnetic field. The ground state of the antidot is described within a local-density-functional formalism. Two sum rules, which are exact within this formalism, have been derived and used to evaluate the energy of edge collective modes as a function of the surface density and the size of the antidot.