A novel integrated modeling methodology for NEMS is presented. Nano scale device models include typical effects found, at this scale, in various domains. The methodology facilitates the insertion of quantum corrections to nanoscale device models when they are simulated within multi-domain environments, as is performed in the MEMS industry. This methodology includes domain-oriented approximations from ab-initio modeling. In addition, the methodology includes the selection of quantum mechanical compact models that can be integrated with basic electronic circuits or non-electronic lumped element models. Nanoelectronic device modeling integration in mixed signal systems is reported. The modeling results are compatible with standard hardware description language entities and building blocks. This methodology is based on the IEEE VHDL-AMS, which is an industry standard modeling and simulation hardware description language. The methodology must be object oriented in order to be shared with current and future nanotechnology modeling resources, which are available worldwide. In order to integrate them inside a Learning Management System (LMS), models were formulated and adapted for educational purposes. The electronic nanodevice models were translated to a standardized format for learning objects by following the Shareable Content Object Reference Model (SCORM). The SCORM format not only allows models reusability inside the framework of the LMS, but their applicability to various educational levels as well. The model of a molecular transistor was properly defined, integrated and translated using SCORM rules and reused for educational purposes at various levels. A very popular LMS platform was used to support these tasks. The LMS platform compatibility skills were applied to test the applicability and reusability of the generated learning objects. Model usability was successfully tested and measured within an undergraduate nanotechnology course in an electrical engineering program. The model was reused at the graduate level and adapted afterwards to a nanotechnology education program for school teachers. Following known Learning Management Systems, the developed methodology was successfully formulated and adapted for education.

The exponential nature of Moore's law has inadvertently created huge data storage complexes that are scattered around the world. Data elements are continuously being searched, processed, erased, combined and transferred to other storage units without much regard to power consumption. The need for faster searches and power efficient data processing is becoming a fundamental requirement. Quantum computing may offer an elegant solution to speed and power through the utilization of the natural laws of quantum mechanics. Therefore, minimal cost quantum circuit implementation methodologies are greatly desired. This thesis explores the decomposition of group functions and the Walsh spectrum for implementing quantum canonical cascades with minimal cost. Three different methodologies, using group decomposition, are presented and generalized to take advantage of different quantum computing hardware, such as ion traps and quantum dots. Quantum square root of swap gates and fixed angle rotation gates comprise the first two methodologies. The third and final methodology provides further quantum cost reduction by more efficiently utilizing Hilbert spaces through variable angle rotation gates. The thesis then extends the methodology to realize a robust quantum circuit synthesis tool for single and multi-output quantum logic functions.

In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

Energy harvesting using rectennas for infrared radiation continues to be a challenge due to the lack of fast switching diodes capable of rectification at THz frequencies. Metal insulator metal diodes which may be used at 30 THz must show adequate nonlinearity for small signal rectification such as 30 mV. In a rectenna assembly, the voltage signal received as an output from a single nanoantenna can be as small as ~30µV. Thus, only a hybrid array of nanoantennas can be sufficient to provide a signal in the ~30mV range for the diode to be able to rectify around 30THz. A metal-insulator-metal diode with highly nonlinear I-V characteristics is required in order for such small signal rectification to be possible. Such diode fabrication was found to be faced with two major fabrication challenges. The first one being the lack of a precisely controlled deposition process to allow a pinhole free insulator deposition less than 3nm in thickness. Another major challenge is the deposition of a top metal contact on the underlying insulating thin film. As a part of this research study, most of the MIM diodes were fabricated using Langmuir Blodgett monolayers deposited on a thin Ni film that was sputter coated on a silicon wafer. UV induced polymerization of the Langmuir Blodgett thin film was used to allow intermolecular crosslinking. A metal top contact was sputtered onto the underlying Langmuir Blodgett film assembly. In addition to material characterization of all the individual films using IR, UV-VIS spectroscopy, electron microscopy and atomic force microscopy, the I-V characteristics, resistance, current density, rectification ratio and responsivity with respect to the bias voltage were also measured for the electrical characterization of these MIM diodes. Further improvement in the diode rectification ratio and responsivity was obtained with Langmuir Blodgett films grown by the use of horizontally oriented organic molecules, due to a smaller tunneling distance that could be achieved in this case. These long chain polymeric molecules exhibit a two-dimensional molecular assembly thereby reducing the tunneling distance between the metal electrodes on either side of the insulating layer. Rectification ratios as high as 450:1 at ±200mV were obtained for an MIM diode configuration of Ni-LB films of Arachidic Acid films-(Au/Pd). The bandwidth of the incident radiation that can be used by this rectenna assembly is limited to 9.5% of 30THz or ±1.5THz from the center frequency based on the antenna designs which were proposed for this research. This bandwidth constraint has led to research in the field of frequency selective emitters capable of providing a narrowband emission around 30THz. Several grating structures were fabricated in the form of Ni-Si periodic arrays, in a cleanroom environment using photolithography, sputtering and deep reactive ion etching. These frequency selective samples were characterized with the help of focusing optics, monochromators and HgCdTe detectors. The results obtained from the emission spectra were utilized to calibrate a simulation model with Computer Simulation Technology (CST) which uses numerous robust solving techniques, such as the finite element method, in order to obtain the optical parameters for the model. Thereafter, a thorough analysis of the different dimensional and material parameters was performed, to understand their dependence on the emissivity of the selective emitter. Further research on the frequency selectivity of the periodic nano-disk or nano-hole array led to the temperature dependence of the simulated spectra, because the material parameters, such as refractive index or drude model collision frequency, vary with temperature. Thus, the design of frequency selective absorbers/emitters was found to be significantly affected with temperature range of operation of these structures.

<p>In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.</p>

<p>This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.</p>

<p>Quantum entanglement is employed as a resource throughout quantum information science. However, before entanglement can be put to intelligent use, the issues of its production and detection must be considered. This thesis proposes four schemes for producing the bound entangled Smolin state. Three of these schemes produce the Smolin state by means of general quantum gates acting on different initial states - an all-zero state, a GHZ-state and two combined Bell states. The fourth scheme is based on one-qubit operations acting on two-photon states produced by SPDC. Furthermore, a maximum overlap entanglement witness detecting entanglement in the Smolin state is derived. This witness is measurable in three measurement settings with the maximal noise tolerance p=2/3. Lastly, simplified entanglement witnesses for the 4-, 6- and 8-qubit unitary invariant states are derived. These witnesses are measurable in three measurement settings with noise tolerances p=0.1802..., p=0.1502... and p=0.0751..., respectively.</p>

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work. / Graduation date: 2012

Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time. / QC 20100810

In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.