271 research outputs found
Coherent control and decoherence of charge states in quantum dots
This Chapter contains a review of the recent results, both experimental and
theoretical, related to optical control of carriers confined in semiconductor
quantum dots. The physics of Rabi oscillations of exciton and biexciton
occupations, as well as time-domain interference experiments are discussed.
Next, the impact of carrier--phonon interaction in a semiconductor structure is
described and modern methods of theoretical description of the carrier--phonon
kinetics and of the resulting dephasing are presented.Comment: An introductory review chapter to appear in a book published by World
Scientifi
On the convergence of a matrix splitting algorithm for the symmetric linear complementarity problem
Cover title.Includes bibliographical references (p. 45-48).Partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems) DAAL03-86-K-0171 Partially supported by the Office of Naval Research. N00014-84-K-0519 (NR64-003) Partially supported by the National Science Foundation. NSF-ECS-8519058by Zhi-Quan Luo, Paul Tseng
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ON QUASI-NEWTON FORWARD{BACKWARD SPLITTING: PROXIMAL CALCULUS AND CONVERGENCE
We introduce a framework for quasi-Newton forward{backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal � rank-r symmetric positive de�nite matrices. This special type of metric allows for a highly e�cient evaluation of the proximal mapping. The key to this e�ciency is a general proximal calculus in the new metric. By using duality, formulas are derived that relate the proximal mapping in a rank-r modi�ed metric to the original metric. We also describe e�cient implementations of the proximity calculation for a large class of functions; the implementations exploit the piece-wise linear nature of the dual problem. Then, we apply these results to acceleration of composite convex minimization problems, which leads to elegant quasi-Newton methods for which we prove convergence. The algorithm is tested on several numerical examples and compared to a comprehensive list of alternatives in the literature. Our quasi-Newton splitting algorithm with the prescribed metric compares favorably against state-of-the-art. The algorithm has extensive applications including signal processing, sparse recovery, machine learning and classi�cation to name a few.</p
Higher dimensional time-energy entanglement
Judging by the compelling number of innovations based on taming quantum mechanical effects, such as the development of transistors and lasers, further research in this field promises to tackle further technological challenges in the years to come. This statement gains even more importance in the information processing scenario. Here, the growing data generation and the correspondingly higher need for more efficient computational resources and secure high bandwidth networks are central problems which need to be tackled. In this sense, the required CPU minituarization makes the design of structures at atomic levels inevitable, as foreseen by Moore's law.
From these perspectives, it is necessary to concentrate further research efforts into controlling and manipulating quantum mechanical systems. This enables for example to encode quantum superposition states to tackle problems which are computationally NP hard and which therefore cannot be solved efficiently by classical computers. The only limitation affecting these solutions is the low scalability of existing quantum systems. Similarly, quantum communication schemes are devised to certify the secure transmission of quantum information, but are still limited by a low transmission bandwidth.
This thesis follows the guideline defined by these research projects and aims to further increase the scalability of the quantum mechanical systems required to perform these tasks. The method used here is to encode quantum states into photons generated by spontaneous parametric down-conversion (SPDC). An intrinsic limitation of photons is that the scalability of quantum information schemes employing them is limited by the low detection efficiency of commercial single photon detectors. This is addressed by encoding higher dimensional quantum states into two photons, increasing the scalability of the scheme in comparison to multi-photon states. Further on, the encoding of quantum information into the emission-time degree of freedom improves its applicability to long distance quantum communication schemes. By doing that, the intrinsic limitations of other schemes based on the encoding into the momentum and polarization degree of freedom are overcome.
This work presents results on a scalable experimental implementation of time-energy encoded higher dimensional states, demonstrating the feasibility of the scheme. Further tools are defined and used to characterize the properties of the prepared quantum states, such as their entanglement, their dimension and their preparation fidelity. Finally, the method of quantum state tomography is used to fully determine the underlying quantum states at the cost of an increased measurement effort and thus operation time. It is at this point that results obtained from the research field of compressed sensing help to decrease the necessary number of measurements. This scheme is compared with an adaptive tomography scheme designed to offer an additional reconstruction speedup. These results display the scalability of the scheme to bipartite dimensions higher than 2x8, equivalent to the encoding of quantum information into more than 6 qubits.Es ist in den letzten Jahren immer deutlicher geworden, dass weitere Forschung zur Untersuchung von quantenmechanischen Systemen durchgeführt werden muss um die wachsenden Probleme in der heutigen Informationstechnologie zu adressieren. Insbesondere sticht hier die exponentiell wachsende Nachfrage nach Computerressourcen und nach sicheren Kommunikationsprotokollen mit hoher Bandbreite hervor, um der weiter wachsenden Datengenerationsrate standzuhalten. Dies stösst auf fundamentale Grenzen, wie die erforderliche Miniaturisierung von Prozessorstrukturen (CPUs) auf atomare Dimensionen demonstriert.
Von dieser Perspektive her ist es erforderlich weitere Forschung zur Kontrolle und Manipulation von Quantenzuständen durchzuführen, wie sie zum Beispiel im Feld der Quanteninformation erfolgt ist. Diese Strategie ermöglicht es von weiteren Eigenschaften der Quantenmechanik, wie zum Beispiel der Präparation von Superpositionszuständen, Gebrauch zu machen. Dies ist insbesondere relevant, da es ermöglicht NP harte Probleme zu lösen, die durch klassische Computer nicht effizient gelöst werden können. Allerdings sind bisher experimentell realisierte quantenmechanische Systeme noch nicht skalierbar genug um den Anforderungen der klassischen Technologie gerecht zu werden. Ähnlichen Argumenten folgend sind Quantenkommunikationssysteme, die die Sicherheit von Kommunikationsprotokolle zertifizieren können, noch nicht in der Lage angemessene Bandbreiten zu gewährleisten.
Diese Doktorarbeit gliedert sich diesen Forschungsprojekten an, mit dem Ziel die Skalierbarkeit von quantenmechanischen Systemen zu vergrössern und entsprechend den genannten Anforderungen gerecht zu machen. Die Strategie die hier verfolgt wird basiert auf die Kodierung von Quantenzuständen in Photonenpaare, die durch den Prozess der Spontanen Parametrischen Down-conversion (SPDC) erzeugt werden. Dieses Verfahren bringt allerdings eine limitierte Skalierbarkeit der Quantensysteme mit sich, da die Detektionseffizienz von kommerziell erhältlichen Einzelphotonendetektoren limitiert ist. Dieses Problem wird in dieser Arbeit umgangen indem die Quantenzustände in höher dimensionale Hilberträume eines Zweiphotonenzustands kodiert werden, was einen deutlichen Vorteil gegenüber der Kodierung in einen Mehrphotonenzustand darstellt. Darüber hinaus ermöglicht die Kodierung der Quantenzustände in den Emissionszeit Freiheitsgrad der Photonen intrinsische Vorteile bei ihrer Anwendung auf die Quantenkommunikation. Hier ist insbesondere der Vorteil gegenüber der Kodierung in den Impuls- und Polarisationsfreiheitsgrad gemeint, die durch deutliche Einschränkungen bei der Transmission über lange Strecken gekennzeichnet sind.
Mit einem Augenmerk auf diese Ziele wird in dieser Arbeit die experimentelle Umsetzbarkeit des beschriebenen Schemas gezeigt. Dies wurde durch die Anwendung von geeigneten Maßen wie die Verschränkung, Dimension und Präparationsfidelity auf die generierten Zustände quantifiziert. Insbesondere bei der Abschätzung der Fidelity wurde von Forschungsergebnissen rund um Compressed Sensing Gebrauch gemacht und weiter mit einem adaptiven Messschema kombiniert, um die effektive Betriebszeit dieser Systeme zu verringern. Dies ist für die weitere skalierbare Anwendung zur Quanteninformationsverarbeitung von Vorteil. Die Ergebnisse verdeutlichen, dass eine Skalierbarkeit der Dimension des Systems auf grösser als 2x8 Dimensionen, äquivalent zur Dimension eines 6-Qubit Zustands, in der Reichweite einer experimentellen Umsetzung liegt
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Reactive Flow and Transport Through Complex Systems
The meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods
Connected Attribute Filtering Based on Contour Smoothness
A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform
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