Theory of laser-driven double-ionization of atoms at Ti : sapphire laser wavelengths

Progress in the theoretical understanding of non-sequential double-ionization of atoms is reviewed from its beginnings with Kuchiev's work in the late 1980s and Corkum's work in the early 1990s to the present day. The crucial role of laboratory experiment as a persistent stimulus to theoretical endeavour is underlined but the predictive roles of simple, yet fundamental, theory and also of a full quantum mechanical description are not forgotten. A theoretical forward look is provided.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Density-potential mapping in time-dependent density-functional theory

The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.

Thermal and quantum fluctuations in chains of ultracold polar molecules

Ultracold polar molecules, in highly anisotropic traps and interacting via a repulsive dipolar potential, may form one-dimensional chains at high densities. According to classical theory, at low temperatures there exists a critical value of the density at which a second-order phase transition from a linear to a zigzag chain occurs. We study the effect of thermal and quantum fluctuations on these self-organized structures using classical and quantum Monte Carlo methods, by means of which we evaluate the pair correlation function and the static structure factor. Depending on the parameters, these functions exhibit properties typical of a crystalline or of a liquid system. We compare the thermal and the quantum results, identifying analogies and differences. Finally, we discuss experimental parameter regimes where the effects of quantum fluctuations on the linear-zigzag transition can be observed.

Ultra-fast spin dynamics in the 2s2p^2 configuration of C^+ studied by time-dependent R-matrix theory

We employ time-dependent R-matrix theory to study ultra-fast dynamics in the doublet 2s2p(2) configuration of C+ for a total magnetic quantum number M = 1. In contrast to the dynamics observed for M = 0, ultra-fast dynamics for M = 1 is governed by spin dynamics in which the 2s electron acts as a flag rather than a spectator electron. Under the assumption that m(S) = 1/2, m(2s) = 1/2 allows spin dynamics involving the two 2p electrons, whereas m(2s) = -1/2 prevents spin dynamics of the two 2p electrons. For a pump-probe pulse scheme with (h) over bar omega(pump) = 10.9 eV and (h) over bar omega(probe) = 16.3 eV and both pulses six cycles long, little sign of spin dynamics is observed in the total ionization probability. Signs of spin dynamics can be observed, however, in the ejected-electron momentum distributions. We demonstrate that the ejected-electron momentum distributions can be used for unaligned targets to separate the contributions of initial M = 0 and M = 1 levels. This would, in principle, allow unaligned target ions to be used to obtain information on the different dynamics in the 2s2p(2) configuration for the M = 0 and M = 1 levels from a single experime

Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Almost all quantum states have nonclassical correlations

Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Quantum Discord Bounds the Amount of Distributed Entanglement

The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.

Qubit-assisted thermometry of a quantum harmonic oscillator

We use the theory of quantum estimation in two different qubit-boson coupling models to demonstrate that the temperature of a quantum harmonic oscillator can be estimated with high precision by quantum-limited measurements on the qubit. The two models that we address embody situations of current physical interest due to their connection with ongoing experimental efforts on the control of mesoscopic dynamics. We show that population measurements performed over the qubit probe are near optimal for a broad range of temperatures of the harmonic oscillator.

Universal tight binding model for chemical reactions in solution and at surfaces. II. Water

A revised water model intended for use in condensed phase simulations in the framework of the self consistent polarizable ion tight binding theory is constructed. The model is applied to water monomer, dimer, hexamers, ice, and liquid, where it demonstrates good agreement with theoretical results obtained by more accurate methods, such as DFT and CCSD(T), and with experiment. In particular, the temperature dependence of the self diffusion coefficient in liquid water predicted by the model, closely reproduces experimental curves in the temperature interval between 230 K and 350 K. In addition, and in contrast to standard DFT, the model properly orders the relative densities of liquid water and ice. A notable, but inevitable, shortcoming of the model is underestimation of the static dielectric constant by a factor of two. We demonstrate that the description of inter and intramolecular forces embodied in the tight binding approximation in quantum mechanics leads to a number of valuable insights which can be missing from ab initio quantum chemistry and classical force fields. These include a discussion of the origin of the enhanced molecular electric dipole moment in the condensed phases, and a detailed explanation for the increase of coordination number in liquid water as a function of temperature and compared with ice-leading to insights into the anomalous expansion on freezing. The theory holds out the prospect of an understanding of the currently unexplained density maximum of water near the freezing point. 

Temperature dependence of the mid-infrared dielectric function of YBCO in the ab plane

We have excited mid-infrared surface plasmons in two YBCO thin films of contrasting properties using attenuated total reflection of light and found that the imaginary part of the dielectric function decreases linearly with reduction in temperature. This result is in contrast with the commonly reported conclusion of infrared normal reflectance studies. If sustained it may clarify the problem of understanding the normal state properties of YBCO and the other cuprates. The dielectric function of the films, epsilon = epsilon(1) + i epsilon(2), was determined between room temperature and 80K: epsilon(1) was found to be only slightly temperature dependent but somewhat sample dependent, probably as a result of surface and grain boundary contamination. The imaginary part, epsilon(2), (and the real part of the conductivity, sigma(1),) decreased linearly with reduction in temperature in both films. Results obtained were: for film 1: epsilon(1) = - 14.05 - 0.0024T and epsilon(2) - 4.11 + 0.086T and for film 2: epsilon(1) = - 24.09 + 0.0013T and epsilon(2) = 7.66 + 0.067T where T is the temperature in Kelvin. An understanding of the results is offered in terms of temperature-dependent intrinsic intragrain inelastic scattering and temperature-independent contributions: elastic and inelastic grain boundary scattering and optical interband (or localised charge) absorption. The relative contribution of each is estimated. A key conclusion is that the interband (or localised charge) absorption is only similar to 10%. Most importantly, the intrinsic scattering rate, 1/tau, decreases linearly with fall in temperature, T, in a regime where current theory predicts dependence on frequency, omega, to dominate. The coupling constant, lambda, between the charge carriers and the thermal excitations has a value of 1.7, some fivefold greater than the far infrared value. These results imply a need to restate the phenomenology of the normal state of high temperature superconductors and seek a corresponding theoretical understanding.

A quantum measurement paradigm for educational predicates: Implications for validity in educational measurement

The outcomes of educational assessments undoubtedly have real implications for students, teachers, schools and education in the widest sense. Assessment results are, for example, used to award qualifications that determine future educational or vocational pathways of students. The results obtained by students in assessments are also used to gauge individual teacher quality, to hold schools to account for the standards achieved by their students, and to compare international education systems. Given the current high-stakes nature of educational assessment, it is imperative that the measurement practices involved have stable philosophical foundations. However, this paper casts doubt on the theoretical underpinnings of contemporary educational measurement models. Aspects of Wittgenstein’s later philosophy and Bohr’s philosophy of quantum theory are used to argue that a quantum theoretical rather than a Newtonian model is appropriate for educational measurement, and the associated implications for the concept of validity are elucidated. Whilst it is acknowledged that the transition to a quantum theoretical framework would not lead to the demise of educational assessment, it is argued that, where practical, current high-stakes assessments should be reformed to become as ‘low-stakes’ as possible. The paper also undermines some of the pro high-stakes testing rhetoric that has a tendency to afflict education.

Density functional theory study of the interaction between CO and on a Pt surface:CO/Pt(111), O/Pt(111), and CO/O/Pt(111)

Ab initio total energy calculations within the Density Functional Theory framework were carried out for Pt(111), Pt(111)-p(2x2)-CO, Pt(111)-p(2x2)-O, and Pt(111)-p(2x2)-(CO+O) to provide an insight into the interaction between CO and O on metal surfaces, an important issue in CO oxidation, and also in promotion and poisoning effects of catalysis. The geometrical structures of these systems were optimized with respect to the total energy, the results of which agree with existing experimental values very well. It is found that (i) the local structures of Pt(111)-p(2x2)-(CO+O), such as the bond lengths of C-O, C-Pt, and O-Pt (chemisorbed O atom with Pt), are almost the same as that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively, (ii) the total valence charge density distributions in Pt(111)-p(2x2)-(CO+O) are very similar to that in Pt(111)-p(2x2)-CO, except in the region of the chemisorbed oxygen atom, and also nearly identical to that in Pt(111)-p(2x2)-O, apart from in the region of the chemisorbed CO, and (iii) the chemisorption energy of CO on a precovered Pt(111)-p(2x2)-O and the chemisorption energy of O on a precovered Pt(111)-p(2x2)CO are almost equal to that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively. These results indicate that the interaction between CO and chemisorbed oxygen on a metal surface is mainly shore range in nature. The discussions of Pt-CO and Pt-O bonding and the interaction between CO and the chemisorbed oxygen atom on Pt(111) are augmented by local densities of states and real space distributions of quantum states.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyse the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

Contributions to the theory of maximum entropy estimation for ill-posed models

As técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.