This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational purposes, it has been used to explain and control the dynamics in various physical systems. In order to use the quantum walk to its fullest potential, it is important to know and optimize the properties purely due to quantum dynamics and in presence of noise. Various studies of its dynamics in the absence and presence of noise have been reported. We propose new approaches to optimize the dynamics, discuss symmetries and effect of noise on the quantum walk. Making use of its properties, we propose the use of quantum walk as an efficient new tool for various applications in physical systems and quantum information processing. In the first and second part of this dissertation, we discuss evolution process of the quantum walks, propose and demonstrate the optimization of discrete-time quantum walk using quantum coin operation from SU(2) group and discuss some of its properties. We investigate symmetry operations and environmental effects on dynamics of the walk on a line and an $n-$cycle highlighting the interplay between noise and topology. Using the properties and behavior of quantum walk discussed in part two, in part three we propose the application of quantum walk to realize quantum phase transition in optical lattice, that is to efficiently control and redistribute ultracold atoms in optical lattice. We also discuss the implementation scheme. Another application we consider is creation of spatial entanglement using quantum walk on a quantum many body system.

Photoionization cross section calculations are performed for the ground ([Ne]3s23p63d 2D ) and the first two excited ([Ne]3s23p63d 2D and [Ne]3s23p64s 2S ) states of potassium-like transition metal ions (Sc+2, Ti+3, V+4, Cr+5, Mn+6, Fe+7), along with photoionization calculations for K-like Ca+ ions in the ground ([Ne]3s23p64s 2S ) state and the first two excited ([Ne]3s23p63d 2D and [Ne]3s23p63d 2D ) states. The discrete N-electron final state ion system orbitals are generated using the computer program AUTOSTRUCTURE; 24 configurations are included in the configuration-interaction (CI) calculation for transition metal ions, and 30 configurations for the case of Ca+ ions. The initial and final (N+1)-electron wavefunctions are generated using R-matrix along with photoionization cross sections. In addition to the non-relativistic (LS-coupling) R-matrix, we have used the relativistic (Breit-Pauli) R -matrix method to carry out these calculations to focus on relativistic effects. Relativistic and non-relativistic results are compared to demonstrate the influence of relativistic effects. The prominent 3p → 3d giant resonances are analyzed and identified, and our calculated positions and widths are compared with experimental results for K-like ions such as Ca+, Sc+2 and Ti+3. In the case of lower Z (22  Z  20) ions (Ca+, Sc+2 and Ti+3), the photoionization cross section spectra are dominated by the giant (3p  3d excitation) resonances, while in cases of higher Z (26  Z  23) ions (V+4, Cr+5, Mn+6 and Fe+7), the 3p  3d resonances lie below the ionization threshold, and the cross sections are dominated by 3p53d nd and 3p53d n’s Rydberg series of resonances. Comparison of the Ca+, Sc+2 and Ti3+ results with available theoretical and experimental data shows good agreement.

This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational purposes, it has been used to explain and control the dynamics in various physical systems. In order to use the quantum walk to its fullest potential, it is important to know and optimize the properties purely due to quantum dynamics and in presence of noise. Various studies of its dynamics in the absence and presence of noise have been reported. We propose new approaches to optimize the dynamics, discuss symmetries and effect of noise on the quantum walk. Making use of its properties, we propose the use of quantum walk as an efficient new tool for various applications in physical systems and quantum information processing. In the first and second part of this dissertation, we discuss evolution process of the quantum walks, propose and demonstrate the optimization of discrete-time quantum walk using quantum coin operation from SU(2) group and discuss some of its properties. We investigate symmetry operations and environmental effects on dynamics of the walk on a line and an $n-$cycle highlighting the interplay between noise and topology. Using the properties and behavior of quantum walk discussed in part two, in part three we propose the application of quantum walk to realize quantum phase transition in optical lattice, that is to efficiently control and redistribute ultracold atoms in optical lattice. We also discuss the implementation scheme. Another application we consider is creation of spatial entanglement using quantum walk on a quantum many body system.

<p>Collective behavior in many-body systems, where the dynamics of an individual element depend on the state of the entire ensemble, play an important role in both basic science research and applied technologies. Over the last twenty years, studies of such effects in cold atomic vapors have lead to breakthroughs in areas such as quantum information science and atomic and condensed matter physics. Nevertheless, in order to generate photon-mediated atom-atom coupling strengths that are large enough to produce collective behavior, these studies employ techniques that intrinsically limit their applicability. In this thesis, I describe a novel nonlinear optical process that enables me to overcome these limitations and realize a new regime of collective light-matter interaction.</p><p>My experiment involves an anisotropic cloud of cold rubidium atoms illuminated by a pair of counterpropagating optical (pump) fields propagating at an angle to the trap's long axis. When the pump beam intensities exceed a threshold value, a collective instability occurs in which new beams of light are generated spontaneously and counterpropagate along the trap's long axis. In order to understand the physical mechanism responsible for this behavior, I study first the system's nonlinear optical response when driven below the instability threshold. I find that the incident optical fields produce an optical lattice that causes the atoms to become spatially organized on the sub-wavelength length scale. This organization corresponds to the formation of an atomic density grating, which effectively couples the involved fields to one another and enables the transfer of energy between them. The loading of atoms into this grating is enhanced by my choice of field polarizations, which simultaneously results in cooling of the atoms from T~30 &mu;K to T~3 &mu;K via the Sisyphus effect. As a result, I observe a fifth-order nonlinear susceptibility &chi;^{(5)}=1.9x10^-12 (m/V)^4 that is 7 orders of magnitude larger than previously observed. In addition, because of the unique scaling of the resulting nonlinear response with material parameters, the magnitude of the nonlinearity can be large for small pump intensities (\ie, below the resonant electronic saturation intensity 1.6 mW/cm^2) while simultaneously suffering little linear absorption. I confirm my interpretation of the nonlinearity by developing a theoretical model that agrees quantitatively with my experimental observations with no free parameters.</p><p>The collective instability therefore corresponds to the situation where the cold vapor transitions spontaneously from a spatially-homogeneous state to an ordered one. This emergent organization leads to the simultaneous emission of new optical fields in a process that one can interpret either in terms of mirrorless parametric self-oscillation or superradiance. By mapping out the phase diagram for this transition, I find that the instability can occur for pump intensities as low as 1 mW/cm^2, which is approximately 50 times smaller than previous observations of similar phenomena. The intensity of the emitted light can be up to 20% of the pump beam intensity and depends superlinearly on the number of atoms, which is a clear signature of collective behavior. In addition, the generated light demonstrates temporal correlations between the counterpropagating modes of up to 0.987 and is nearly coherent over several hundred &mu;s. The most significant attributes of the light, though, are that it consists of multiple transverse spatial modes and persists in steady-state. This result represents the first observation of such dynamics, which have been shown theoretically to lead to a rich array of new phenomena and possible applications.</p> / Dissertation

Die Arbeit beschäftigt sich mit der Dynamik von Gasen aus hoch angeregten Atomen. Es wird sowohl die Erzeugung von Rydberggasen, als auch ihre Dynamik nach der Laser-Anregung betrachtet. Zur Beschreibung des Anregungsprozesses wird ein quasi-klassischer Zugang verwendet. Er basiert auf der adiabatischen Eliminierung von Kohärenzen aus der vollen Quanten-Beschreibung und führt auf eine klassische Mastergleichung. Diese Näherung ist gerade für typische experimentelle Situationen durchführbar. Die klassische Mastergleichung kann durch ein simples Monte-Carlo-Verfahren für Systeme aus zehntausenden von Teilchen unter voller Berücksichtigung der Rydberg-Rydberg-Wechselwirkung gelöst werden. Mit Hilfe des Monte-Carlo-Verfahrens wird die Anregung von Rydbergatomen in einem ultrakalten Gas untersucht. Die in Experimenten gefundene Anregungsblockade wird durch die Methode gut beschrieben. Bei der Anregung von Rydbergatomen aus einem optischen Gitter wird sogar eine Anregungsverstärkung - eine Antiblockade - vorhergesagt. Die Antiblockade in einem Gitter erlaubt eine Charakterisierung räumlicher Korrelationen der Rydbergatome allein durch die Messung ihrer Dichte. Sie ist robust gegenüber Gitterfehlstellen und sollte mit heutigen experimentellen Techniken nachweisbar sein. Für die Anregung im ungeordneten Gas wird gezeigt, dass sich die räumlichen Korrelationen der Rydbergatome indirekt in den Momenten der Häufigkeitsverteilung angeregter Atome widerspiegeln. Durch die Untersuchung der Fluktuationen in der Zahl angeregter Atome lassen sich die Unterschiede in den Paarkorrelationsfunktionen bei Blockade und Antiblockade im Gas messen. Ein Vergleich mit experimentellen Daten zeigt eine qualitativ gute Übereinstimmung. Für die Dynamik des Rydberggases nach dem Abschalten der Anregungslaser ist der Fall besonders interessant, dass Atome in unterschiedlichen Rydbergzuständen resonant ihre Anregungsenergie austauschen können. In der Arbeit wird argumentiert, dass sich der räumliche Transfer von Anregungsenergie in Rydbergsystemen ohne störende Umgebungseinflüsse gezielt untersuchen lässt. Mit Hilfe der Frenkelschen Exziton-Theorie wird der Energietransfer entlang einer eindimensionalen Anordnung von Rydbergatomen untersucht. Zusätzlich wird dargelegt, dass die exzitonische Anregung auch mechanische Kräfte auf die Rydbergatome induziert. Diese werden mit Hilfe einer quanten-klassischen Methode analysiert. Der Zusammenhang der auftretenden Kräfte mit den Symmetrien der exzitonischen Eigenfunktionen wird aufgezeigt. In einer eindimensionalen Anordnung von Rydbergatomen wird ein adiabatischer Energietransfer vorhergesagt, der an die Bewegung der Atome gebunden ist. Er läuft vollständig auf einer einzigen adiabatischen Potentialfläche ab. Dieser Transport ist langsam genug, um mit heutigen experimentellen Methoden im Prinzip orts- und zeitaufgelöst abgebildet zu werden.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 86-97).

Thesis (Ph. D. in Physics)--Vanderbilt University, May 2004. / Title from title screen. Includes bibliographical references.

This thesis describes the physics, design, and construction of an experiment to measure the electric dipole moment (EDM) of the electron. In the experiment, laser-cooled Cs atoms will be held in an optical dipole force trap in the presence of applied electric and magnetic fields. The signature of an electron EDM is a first-order electric field shift of the Zeeman resonance frequency of the Cs ground state. We present an analysis of the systematic and statistical errors of this experiment, which shows that the experiment should have a sensitivity of the order of 10⁻²⁹ e-cm. We pay particular attention to potential light-shift induced errors and to magnetic field noise. We also present the design and experimental results for a cold Cs atom source, high voltage field plates, optical trapping field in a resonant build-up cavity, noval titanim ultrahigh vacuum system, and magnetic sheilding system. These results show that a measurement of the electron edm at the level of 10⁻²⁹ e-cm. should be feasible. / text

Steps on a high index metal or semiconductor surface may play a fundamental role for electronic structure, adsorption, film growth, chemical reaction and catalysis. The surface atomic and electronic structures of stepped W(110) surfaces have been investigated by a few research groups during the past 20 years. But there is still a lot of controversy. We use high resolution core level photoemission to study several different stepped tungsten surfaces. Curve fittings of the spectra permit tests of core-level binding- energy shift models that relate local atomic coordination to binding -energy differences associated with terrace and step-edge atoms. For the first time we find a well resolved W4f₂/₇ peak associated with step edge atoms. We attribute previous failure to directly detect the step-edge effects in core level photoemission to contamination by hydrogen. The well resolved peaks for surface atoms with different coordinations can serve as a “finger print” for specific atoms. Experiments in which stepped surfaces are systematically dosed by H₂ clarify the role played by H contamination. We also grow Ag nanowires on the stepped W(110) surface and use angle resolved photoemission to study the band structure. We find distinct dispersion for the nanowires along the step edge direction while there is only little dispersion perpendicular to the wires. The second part of the research is core level photoemission study on Cesium film growth on Cu(100) surface. We study the phonon broadening effect for Cs at different temperatures. We compare our data with previous theoretical models and get good results on surface and bulk Debye temperatures and zero temperature phonon broadening. The binding energy shifts for the Cs 5p₂/₇ at different temperatures have also been investigated. The results fit the lattice expansion model very well except at temperature higher than 200 K. The higher temperature deviation is caused by thermal evaporation of Cs films. This conclusion is checked by the following coverage dependent core level peaks study on the Cs/Cu(100) system. / text

We study a system of neutral atoms trapped in a three-dimensional optical lattice suitable for the encoding, initialization and manipulation of atomic qubits. The qubits are manipulated by applied electromagnetic fields interacting with dipole moments of the atoms via light shifts, Raman transitions, Zeeman shifts, and microwave transitions. Our lattice is formed by three orthogonal one-dimensional lattices, which have different frequencies so that interference terms average to zero. This geometry allows considerable freedom in designing the component one-dimensional lattices, so that they provide not only confinement but also independent control in each dimension. Our atomic qubits are initialized from a laser-cooled atomic sample by Raman sideband cooling in individual lattice potential wells. We have demonstrated accurate and robust one-qubit manipulation using resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneities in the microwave Rabi frequency and the light shifted qubit transition frequency. Observation of qubit dynamics in near real time allows us to minimize these inhomogeneities, and therefore optimize qubit logic gates. For qubits in the lattice, we infer a fidelity of 0.990(3) for a single pi-pulse. We have also explored the use of NMR-type pulse techniques in order to further reduce the effect of errors and thus improve gate robustness in the atom/lattice system. Our schemes for two-qubit quantum logic operations are based on controlled collisional interactions. We have experimented with two schemes in order to probe these collisions. The first involves manipulation of the center-of-mass wavepackets of two qubits in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately, this scheme has proven extremely sensitive to phase errors, as the wavepackets are moved by the optical lattice. The other scheme starts with two qubits in spatially separated traps, and utilizes microwaves to drive one or both qubits into a third trap in-between the two qubits. Once the wavepackets overlap, the collisions create a large energy shift which can be probed spectroscopically.