Strong-Field Interference of Quantum Trajectories with Coulomb Distortion and Electron Correlation

This thesis explores quantum interference patterns present in the strong-field phenomena of above-threshold ionisation and non-sequential double ionisation, which correspond to one and two ionisation processes, respectively. For above-threshold ionisation a new model is explored that uses Coulomb-distorted quantum trajectories to produce the transition amplitude of the process. This method is one of only a few semi-analytic models to account for the Coulomb potential for electrons in the continuum. The quantum trajectories utilised in this model lead to a myriad of interference patterns, some of which have never been identified before and the signature of most can be found in experimental results or \textit{ab-initio} solutions of the time dependent Schrödinger equation. Given the recent interest in using such interferences for holographic imaging of atoms and molecules, conditions and an analytic model are formulated to better understand the potential of this new imaging process. The role of recollision is also investigated and how trajectories in this new model relate to well known direct and rescattered trajectories from above-threshold ionisation models employing the strong field approximation. Subsequently, interference is examined for the case of non-sequential double ionisation for the recollision with subsequent ionisation mechanism using the strong field approximation. Many types of interference patterns are found, where previously it was expected that interference would not play a role. These patterns are investigated in detail and conditions formulated for them. The model is extended to different lengths of laser pulses by incorporating a particular superposition of intermediate excited states in the process in order to replicated experimental data, opening up the possibility of using experimental data to reconstruct the intermediate excited state of the second electron in the non-sequential double ionisation process

Assessing the Life Average Daily Dose (Ladd) due to Heavy Metal Contents in Water Samples from Covenant University, Canaanland, Ota, South West Nigeria

The consumption of water with elevated concentration of lead (Pb) can prevent Hemoglobin Synthesis (Anemia) and results in Kidney diseases. A cross sectional study was conducted in to estimate the risk of exposure to lead via groundwater and bottled water ingestion pathway for the population of Covenant University, Canaanland, Ota, Ogun Sate using Perkin Elmer Optima 8000 ICP-OES. The concentration of Pb, Cr, Cd and As varies from water sample to another with the highest value of .7.07 ¹gL¡1 was noted in borehole water sample (BH1) behind John Hall. Comparing the value with the International recommended level by USEPA and WHO respectively, 7.07gL¡1is less than 15¹gL¡1 and 10 ¹gL¡1. The Life Average Daily Dose (LADD) estimated in this present study reported higher in BH1 for lead (Pb) and could pose health hazard if accumulated for a long time. This work suggest measures to employ quality water treatment plant to reduce the level of heavy metals in the selected water samples and also more research on radioisotopes in the same water sample

Exact synthesis of multiqubit Clifford-cyclotomic circuits

Let $n\geq 8$ be an integer divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive $n$-th root of unity. In this note, we show that, when $n$ is a power of 2, a multiqubit unitary matrix $U$ can be exactly represented by a circuit over $\mathcal{G}_n$ if and only if the entries of $U$ belong to the ring $\mathbb{Z}[1/2,\zeta_n]$. We moreover show that $\log(n)-2$ ancillas are always sufficient to construct a circuit for $U$. Our results generalize prior work to an infinite family of gate sets and show that the limitations that apply to single-qubit unitaries, for which the correspondence between Clifford-cyclotomic operators and matrices over $\mathbb{Z}[1/2,\zeta_n]$ fails for all but finitely many values of $n$, can be overcome through the use of ancillas

Principal frequency of an ultrashort laser pulse

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain.Comment: 11 pages, 6 figures, accepted in PR

Dissecting Sub-Cycle Interference in Photoelectron Holography

Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory and experimental analysis: unit-cell averaging and time-filtering data and simulations. Together these suppress ATI rings and enable an unprecedented highly-detailed quantitative match between strong-field ionization experiments in argon and the Coulomb-quantum orbit strong-field approximation (CQSFA) theory. Velocity map images reveal fine modulations on the holographic spider-like interference fringes that form near the polarization axis. CQSFA theory traces this to the interference of three types of electron pathways. The level of agreement between experiment and theory allows sensitive determination of quantum phase differences and symmetries, providing an important tool for quantitative dynamical imaging in quantum systems.Comment: 13 Pages, 8 figure

Multiscale and multimodal network dynamics underpinning working memory

Working memory (WM) allows information to be stored and manipulated over short time scales. Performance on WM tasks is thought to be supported by the frontoparietal system (FPS), the default mode system (DMS), and interactions between them. Yet little is known about how these systems and their interactions relate to individual differences in WM performance. We address this gap in knowledge using functional MRI data acquired during the performance of a 2-back WM task, as well as diffusion tensor imaging data collected in the same individuals. We show that the strength of functional interactions between the FPS and DMS during task engagement is inversely correlated with WM performance, and that this strength is modulated by the activation of FPS regions but not DMS regions. Next, we use a clustering algorithm to identify two distinct subnetworks of the FPS, and find that these subnetworks display distinguishable patterns of gene expression. Activity in one subnetwork is positively associated with the strength of FPS-DMS functional interactions, while activity in the second subnetwork is negatively associated. Further, the pattern of structural linkages of these subnetworks explains their differential capacity to influence the strength of FPS-DMS functional interactions. To determine whether these observations could provide a mechanistic account of large-scale neural underpinnings of WM, we build a computational model of the system composed of coupled oscillators. Modulating the amplitude of the subnetworks in the model causes the expected change in the strength of FPS-DMS functional interactions, thereby offering support for a mechanism in which subnetwork activity tunes functional interactions. Broadly, our study presents a holistic account of how regional activity, functional interactions, and structural linkages together support individual differences in WM in humans

Conservation laws for electron vortices in strong-field ionisation

We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation

Analog simulation of high harmonic generation in atoms

The demanding experimental access to the ultrafast dynamics of materials challenges our understanding of their electronic response to applied strong laser fields. In this work, we show that trapped ultracold atoms with highly controllable potentials can become an enabling tool to describe phenomena in a scenario where some effects are more easily accessible and twelve orders of magnitude slower. For this purpose, we characterize the mapping between the attoscience platform and atomic simulators, and propose an experimental protocol to simulate the emission yield of High Harmonic Generation, a regime that has so far been elusive to cold atom simulation. As we illustrate, the benchmark offered by these simulators can provide new insights on the conversion efficiency of extended and short nuclear potentials, as well as the response to applied elliptical polarized fields or ultrashort few-cycle pulses

Women’s experiences of receiving care for pelvic organ prolapse: a qualitative study

Background Pelvic organ prolapse is a common urogenital condition affecting 41–50% of women over the age of 40. To achieve early diagnosis and appropriate treatment, it is important that care is sensitive to and meets women’s needs, throughout their patient journey. This study explored women’s experiences of seeking diagnosis and treatment for prolapse and their needs and priorities for improving person-centred care. Methods Twenty-two women receiving prolapse care through urogynaecology services across three purposefully selected NHS UK sites took part in three focus groups and four telephone interviews. A topic guide facilitated discussions about women’s experiences of prolapse, diagnosis, treatment, follow-up, interactions with healthcare professionals, overall service delivery, and ideals for future services to meet their needs. Data were analysed thematically. Results Three themes emerged relating to women’s experiences of a) Evaluating what is normal b) Hobson’s choice of treatment decisions, and c) The trial and error of treatment and technique. Women often delayed seeking help for their symptoms due to lack of awareness, embarrassment and stigma. When presented to GPs, their symptoms were often dismissed and unaddressed until they became more severe. Women reported receiving little or no choice in treatment decisions. Choices were often influenced by health professionals’ preferences which were subtly reflected through the framing of the offer. Women’s embodied knowledge of their condition and treatment was largely unheeded, resulting in decisions that were inconsistent with women’s preferences and needs. Physiotherapy based interventions were reported as helping women regain control over their symptoms and life. A need for greater awareness of prolapse and physiotherapy interventions among women, GPs and consultants was identified alongside greater focus on prevention, early diagnosis and regular follow-up. Greater choice and involvement in treatment decision making was desired. Conclusions As prolapse treatment options expand to include more conservative choices, greater awareness and education is needed among women and professionals about these as a first line treatment and preventive measure, alongside a multi-professional team approach to treatment decision making. Women presenting with prolapse symptoms need to be listened to by the health care team, offered better information about treatment choices, and supported to make a decision that is right for them