Controlling Below-Threshold Nonsequential Double Ionization via Quantum Interference

We show through simulation that quantum interference in nonsequential double ionization can be used to control the recollision excitation with subsequent ionization (RESI) mechanism. This includes the shape, localization, and symmetry of RESI electron-momentum distributions, which may be shifted from a correlated to an anticorrelated distribution or vice versa, far below the direct ionization threshold intensity. As a testing ground, we reproduce recent experimental results by employing specific coherent superpositions of excitation channels. We examine two types of interference, from electron indistinguishability and intracycle events, and from different excitation channels. These effects survive focal averaging and transverse-momentum integration

Quantum estimation in strong fields: In situ ponderomotive sensing

We develop a theoretical framework to optimize and understand uncertainty from in situ strong-field measurements of laser field parameters. We present a derivation of quantum and classical Fisher information in attoscience for an electron undergoing strong-field ionization. This is used for parameter estimation and to characterize the uncertainty of the ponderomotive energy, directly proportional to laser intensity. In particular, the quantum and classical Fisher information for the momentum basis displays quadratic scaling over time. This can be linked to above-threshold ionization interference rings for measurements in the momentum basis and to a "ponderomotive phase"for the optimal quantum measurements. Preferential scaling in uncertainty is found for increasing laser pulse length and intensity. We use this to demonstrate for in situ measurements of laser intensity that high-resolution momentum spectroscopy has the capacity to reduce the uncertainty by more than 25 times compared to measurements employing the ionization rate, while using the optimal quantum measurement would reduce it by a further factor of 2.6. A minimum uncertainty of the order 2.8×10-3% is theorized for this framework. Finally, we examine previous in situ measurements, formulating a measurement that matches the experimental procedure, and suggest alterations to the measurement scheme that could reduce the laser intensity uncertainty

Coulomb-free and Coulomb-distorted recolliding quantum orbits in photoelectron holography

We perform a detailed analysis of the different types of orbits in the Coulomb quantum orbit strong-field approximation (CQSFA), ranging from direct to those undergoing hard collisions. We show that some of them exhibit clear counterparts in the standard formulations of the strong-field approximation for direct and rescattered above-threshold ionization, and show that the standard orbit classification commonly used in Coulomb-corrected models is over-simplified. We identify several types of rescattered orbits, such as those responsible for the low-energy structures reported in the literature, and determine the momentum regions in which they occur. We also find formerly overlooked interference patterns caused by backscattered Coulomb-corrected orbits and assess their effect on photoelectron angular distributions. These orbits improve the agreement of photoelectron angular distributions computed with the CQSFA with the outcome of ab initio methods for high energy phtotoelectrons perpendicular to the field polarization axis

Probing two-path electron quantum interference in strong-field ionization with time-correlation filtering

Attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions. These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfering pairs of electron orbits by performing a differential Fourier analysis on the measured momentum spectrum. We identify electron holograms formed by trajectory pairs whose ionization times are separated by less than a single quarter cycle, between a quarter cycle and half cycle, between a half cycle and three fourths of a cycle, and a full cycle apart. We compare our experimental results to the predictions of the Coulomb quantum orbit strong-field approximation (CQSFA) with significant success. We also time-filter the CQSFA trajectory calculations to demonstrate the validity of the technique on spectra with known time correlations. As a general analysis technique, the filter can be applied to all energy- and angularly resolved data sets to recover time correlations between interfering electron pathways, providing an important tool to analyze any strong-field ionization spectra. Moreover, it is independent of theory and can be applied directly to experiments, without the need of a direct comparison with orbit-based theoretical methods

Treating branch cuts in quantum trajectory models for photoelectron holography

Most implementations of Coulomb-distorted strong-field approaches that contain features such as tunneling and quantum interference use real trajectories in continuum propagation, while a fully consistent approach must use complex trajectories throughout. A key difficulty in the latter case are singularities of the Coulomb potential in the complex time plane. These singularities have the form of branch points which generate corresponding branch cuts. We present a method for treating branch cuts in quantum-trajectory models, which is subsequently applied to photoelectron holography. Our method is not numerically intensive and is applicable to Coulomb-free and Coulomb-distorted trajectories. We show that the presence of branch cuts leads to discontinuities and caustics in the holographic fringes in above-threshold ionization (ATI) photoelectron momentum distributions. These artifacts are removed with our method, provided no hard recollision takes place during the interaction. A comparison with the full solution of the time-dependent Schrödinger equation is also performed, and a discussion of the applicability range of the present approach is provided

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

Polarization in Strong-Field Ionization of Excited Helium

We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in helium prepared in an excited p state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using the ab initio B-spline algebraic diagrammatic construction, and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the strong-field approximation (SFA) and the Coulomb quantum-orbit strong-field approximation, we find that these specific physical mechanisms leave significant imprints in ATI spectra and photoelectron momentum distributions. Examples are changes of up to two orders of magnitude in the high-energy photoelectron region, and ramp-like structures that can be traced back to Coulomb-distorted trajectories. The present work also shows that electron exchange renders rescattering less effective, causing suppressions in the ATI plateau. Due to the long-range potential, the electron continuum dynamics are no longer confined to the polarization axis, in contrast to the predictions of traditional approaches. Thus, one may in principle probe excited-state configurations perpendicular to the driving-field polarization without the need for orthogonally polarized fields

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

Forward and hybrid path-integral methods in photoelectron holography: Sub-barrier corrections, initial sampling, and momentum mapping

We construct two strong-field path integral methods with full Coulomb distortion, in which the quantum pathways are mimicked by interfering electron orbits: the rate-based CQSFA (R-CQSFA) and the hybrid forward-boundary CQSFA (H-CQSFA). The methods have the same starting point as the standard Coulomb quantum-orbit strong-field approximation (CQSFA), but their implementation does not require preknowledge of the orbits' dynamics. These methods are applied to ultrafast photoelectron holography. In the rate-based method, electron orbits are forward propagated and we derive a nonadiabatic ionization rate from the CQSFA, which includes sub-barrier Coulomb corrections and is used to weight the initial orbit ensemble. In the H-CQSFA, the initial ensemble provides initial guesses for a subsequent boundary problem and serves to include or exclude specific momentum regions, but the ionization probabilities associated with individual trajectories are computed from sub-barrier complex integrals. We perform comparisons with the standard CQSFA and ab initio methods, which show that the standard, purely boundary-type implementation of the CQSFA leaves out whole sets of trajectories. We show that the sub-barrier Coulomb corrections broaden the resulting photoelectron momentum distributions (PMDs) and improve the agreement of the R-CQSFA with the H-CQSFA and other approaches. We probe different initial sampling distributions, uniform and otherwise, and their influence on the PMDs. We find that initial biased sampling emphasizes rescattering ridges and interference patterns in high-energy ranges, while an initial uniform sampling guarantees accurate modeling of the holographic patterns near the ionization threshold or polarization axis. Our results are explained using the initial to final momentum mapping for different types of interfering trajectories

Investigation of associations between retinal microvascular parameters and albuminuria in UK Biobank: a cross-sectional case-control study

BACKGROUND: Associations between microvascular variation and chronic kidney disease (CKD) have been reported previously. Non-invasive retinal fundus imaging enables evaluation of the microvascular network and may offer insight to systemic risk associated with CKD. METHODS: Retinal microvascular parameters (fractal dimension [FD] - a measure of the complexity of the vascular network, tortuosity, and retinal arteriolar and venular calibre) were quantified from macula-centred fundus images using the Vessel Assessment and Measurement Platform for Images of the REtina (VAMPIRE) version 3.1 (VAMPIRE group, Universities of Dundee and Edinburgh, Scotland) and assessed for associations with renal damage in a case-control study nested within the multi-centre UK Biobank cohort study. Participants were designated cases or controls based on urinary albumin to creatinine ratio (ACR) thresholds. Participants with ACR ≥ 3 mg/mmol (ACR stages A2-A3) were characterised as cases, and those with an ACR < 3 mg/mmol (ACR stage A1) were categorised as controls. Participants were matched on age, sex and ethnic background. RESULTS: Lower FD (less extensive microvascular branching) was associated with a small increase in odds of albuminuria independent of blood pressure, diabetes and other potential confounding variables (odds ratio [OR] 1.18, 95% confidence interval [CI] 1.03-1.34 for arterioles and OR 1.24, CI 1.05-1.47 for venules). Measures of tortuosity or retinal arteriolar and venular calibre were not significantly associated with ACR. CONCLUSIONS: This study supports previously reported associations between retinal microvascular FD and other metabolic disturbances affecting the systemic vasculature. The association between retinal microvascular FD and albuminuria, independent of diabetes and blood pressure, may represent a useful indicator of systemic vascular damage associated with albuminuria