Two-photon finite-pulse model for resonant transitions in attosecond experiments

We present an analytical model capable of describing two-photon ionization of atoms with attosecond pulses in the presence of intermediate and final isolated autoionizing states. The model is based on the finite-pulse formulation of second-order time-dependent perturbation theory. It approximates the intermediate and final states with Fano's theory for resonant continua, and it depends on a small set of atomic parameters that can either be obtained from separate \emph{ab initio} calculations, or be extracted from few selected experiments. We use the model to compute the two-photon resonant photoelectron spectrum of helium below the N=2 threshold for the RABITT (Reconstruction of Attosecond Beating by Interference of Two-photon Transitions) pump-probe scheme, in which an XUV attosecond pulse train is used in association to a weak IR probe, obtaining results in quantitative agreement with those from accurate \emph{ab initio} simulations. In particular, we show that: i) Use of finite pulses results in a homogeneous red shift of the RABITT beating frequency, as well as a resonant modulation of the beating frequency in proximity of intermediate autoionizing states; ii) The phase of resonant two-photon amplitudes generally experiences a continuous excursion as a function of the intermediate detuning, with either zero or $2\pi$ overall variation.Comment: 23 pages, 13 figure

Attosecond spectroscopy of autoionizing states

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Química. Fecha de lectura: 15-12-2015In this PhD Thesis we report a theoretical time-resolved study of the effects of electron correlation in the single photoionization spectrum of atomic systems, with particular focus on multi-photon transitions occurring in the presence of autoionizing states. For this task, we take two complementary approaches. On the one hand, we solve ab initio the time dependent Schrödinger equation in a virtually exact way for the helium atom. Helium is a hallmark system for electron correlation studies, and will be our target in the majority of this work. The results obtained, however, are general and apply to many-electron systems. On the other hand, we derive simplified models, which allow to gain physical insight on the phenomenology observed and to extend our theoretical predictions on helium to larger systems. The models are benchmarked against the ab initio solution yielding results in excellent agreement. We explore electron dynamics by means of two novel attosecond pump-probe techniques: reconstruction of attosecond beating by interference of two-photon transitions and attosecond transient absorption spectroscopy. First, by using a weak probe field, we study two-photon transitions resonant with the doubly-excited autoionizing states embedded in the single-channel single-ionization continuum of helium. Using the reconstruction of attosecond beating by interference of two-photon transitions technique, we access both the amplitude and phase of the transitions, which permits us to extract the dynamical properties of the doubly-excited wave packet. Excellent agreement is found by comparing an experimentally reconstructed meta-stable wave packet with that reconstructed from theory. The predictions of our model are then applied to experiments performed in the multi-channel continuum of the argon atom, confirming that the extension of the model to larger systems works. Second, we investigate the effects of varying the probe field intensity on the phases and positions of doubly-excited states in helium. By looking at the intensity-dependent phase of doubly-excited states in the attosecond transient absorption spectrum, we show that the ac-Stark shift higher terms in the doublyexcited series exceeds the ponderomotive energy. This circumstance indicates that the concurrent motion of the two correlated electrons plays a crucial role in the response of the electron wave packet to the driving laser field at relatively high intensities. By photoionizing selected doubly-excited states, we see that the shift of the photoelectron signal depends on both the final ionization channel and the series to which the doubly-excited state belongs. Finally, in the non-resonant region, we explore angularly-resolved two-photon transitions. We discuss quantitatively that, when measuring photo-ejection time delays, the measurement process induces a universal anisotropy. At variance with hydrogen, in helium the polarizable parent ion has a noticeable effect on the observed time delay anisotropy, which points out the potential of angularlyresolved time delay measurements to investigate multi-electron effectsEn esta Tesis presentamos un estudio teórico de los efectos de correlación electrónica resueltos temporalmente en el espectro de ionización simple de sistemas atómicos, con particular atención a las transiciones multifotónicas que ocurren en presencia de estados autoionizantes. Para ello, hemos tomado dos enfoques complementarios. Por un lado, resolvemos de manera ab initio la ecuación de Schrödinger dependiente del tiempo de manera virtualmente exacta para el átomo de helio. El átomo de helio es un candidato perfecto para estudios de correlación electrónica, y lo usaremos como principal objeto de nuestro estudio. Los resultados obtenidos, no obstante, son generales y aplicables a átomos de más electrones. Por otro lado, hemos derivado modelos analíticos, que permiten obtener una comprensión más profunda de la fenomenología observada y extender las predicciones teóricas para el átomo de helio a sistemas más grandes. Los modelos son comparados con la solución ab initio obteniéndose un acuerdo excelente. Exploramos la dinámica electrónica por medio de dos técnicas pump-probe: reconstrucción de la oscilación de attosegundos por medio de la interferencia de transiciones a dos fotones (RABITT , por sus siglas en inglés) y espectroscopía de absorción transitoria de attosegundos (ATAS, por sus siglas en inglés). Primero, usando un láser de intensidad débil, estudiamos transiciones de dos fotones resonantes con los estados doblemente excitados que se encuentran contenidos en el continuo de ionización simple del helio. Usando la técnica de RABITT , accedemos a las amplitudes y las fases de las transiciones, lo que nos permite extraer las propiedades dinámicas del paquete de ondas doblemente excitado. Comparando el paquete de ondas metaestable reconstruido experimentalmente con el predicho por la teoría, encontramos un acuerdo excelente. Posteriormente aplicamos las predicciones de nuestro modelo a experimentos realizados en el continuo multi-canal del átomo de argon, confirmando que la extensión de nuestro modelo a sistemas más grandes funciona. Segundo, investigamos los efectos que produce la variación de la intensidad del láser en las fases y posiciones de los estados doblemente excitados del helio. Mirando a la fase de los estados doblemente excitados en el espectro de ATAS, mostramos que el desplazamiento ac-Stark para los órdenes más altos de la serie de estados doblemente excitados excede la energía ponderomotriz. Esta circunstancia indica que el movimiento correlacionado de dos electrones juega un papel crucial en la respuesta del paquete de ondas electrónico al campo láser para intensidades relativamente altas. Mediante la fotoionización a partir estados doblemente excitados, encontramos que el desplazamiento de la señal fotoelectrónica depende tanto del canal del continuo final de ionización como de la serie autoionizante a la que el estado doblemente excitado pertenece. vii Por último, en la región no resonante, exploramos transiciones a dos fotones resueltas angularmente. Mostramos de manera cuantitativa que en el proceso de medición de los tiempos de fotoemisión, se induce una anisotropía universal. A diferencia del átomo de hidrógeno, en el helio la polarizabilidad del ión padre tiene un efecto notable en la anisotropía observada, lo que pone de manifiesto el potencial de usar mediciones del tiempo de fotoemisión resueltas angularmente para investigar efectos multi-electrónico

The soft-photon approximation in infrared-laser-assisted atomic ionization by extreme-ultraviolet attosecond-pulse trains

We use the soft-photon approximation, formulated for finite pulses, to investigate the effects of the dressing pulse duration and intensity on simulated attosecond pump–probe experiments employing trains of attosecond extremeultraviolet pulses in conjunction with an IR probe pulse.We illustrate the validity of the approximation by comparing the modelled photoelectron distributions for the helium atom, in the photon energy region close to the N = 2 threshold, to the results from the direct solution of the time-dependent Schr¨odinger equation for two active electrons. Even in the presence of autoionizing states, the model accurately reproduces most of the background features of the ab initio photoelectron spectrum in the 1s channel. A splitting of the photoelectron harmonic signal along the polarization axis, in particular, is attributed to the finite duration of the probe pulse. Furthermore, we study the dependence of the sideband integrated signal on the pump–probe time delay for increasing IR field strengths. Starting at IR intensities of the order of 1TWcm−2, overtones in the sideband oscillations due to the exchange of three or more IR photons start to appear. We derive an analytical expression in the frequency-comb limit of the soft-photon model for the amplitude of all the sideband frequency components and show that these amplitudes oscillate as a function of the intensity of the IR field. In particular, we predict that the amplitude of the fundamental component with frequency 2!IR, on which the rabitt optical reconstruction technique is based, changes sign periodicallyWe thank Mare Nostrum BSC and CCC-UAM (Centro de Computación Científica, Universidad Autónoma de Madrid) for allocation of computer time. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 290853, the European COST Actions CM0702 and CM1204, the ERA-Chemistry project number PIM2010EEC-00751, the Marie Curie ITN CORINF and the MICINN projects numbers FIS2010-15127 and CSD 2007-00010 (Spain

Reconstruction of attosecond beating by interference of two-photon transitions in bulk solids

The reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) is one of the most widely used techniques for resolving ultrafast electronic dynamics in atomic and molecular systems. As it relies on the interference of photo-electrons in vacuum, similar interference has never been contemplated in the bulk of crystals. Here we show that the interference of two-photon transitions can be recorded directly in the bulk of solids and read out with standard angle-resolved photo-emission spectroscopy. The phase of the RABBIT beating in the photoelectron spectra coming from the bulk of solids is sensitive to the relative phase of the Berry connection between bands and it experiences a shift of $\pi$ as one of the quantum paths crosses a band. For resonant interband transitions, the amplitude of the RABBIT oscillation decays as the pump and probe pulses are separated in time due to electronic decoherence, providing a simple interferometric method to extract dephasing times

All-optical valley switch and clock of electronic dephasing

2D materials with broken inversion symmetry posses an extra degree of freedom, the valley pseudospin, that labels in which of the two energy-degenerate crystal momenta, $K$ or $K'$, the conducting carriers are located. It has been shown that shining circularly-polarized light allows to achieve close to 100% of valley polarization, opening the way to valley-based transistors. Yet, switching of the valley polarization is still a key challenge for the practical implementation of such devices due to the short coherence lifetimes. Recent progress in ultrashort laser technology now allows to produce trains of attosecond pulses with controlled phase and polarization between the pulses. Taking advantage of such technology, we introduce a coherent control protocol to turn on, off and switch the valley polarization at faster timescales than electronic and valley decoherence, that is, an ultrafast optical valley switch. We theoretically demonstrate the protocol for hBN and MoS$_2$ monolayers calculated from first principles. Additionally, using two time-delayed linearly-polarized pulses with perpendicular polarization, we show that we can extract the electronic dephasing time $T_2$ from the valley Hall conductivity.Comment: 19 pages; 4 figure

Sub-cycle valleytronics: control of valley polarization using few-cycle linearly polarized pulses

So far, selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has relied on using circularly polarized fields. We theoretically demonstrate a way to induce, control, and read valley polarization in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier-envelope phase. The valley pseudospin is encoded in the helicity of the emitted high harmonics of the driving pulse, allowing one to avoid additional probe pulses and permitting one to induce, manipulate and read the valley pseudospin all-optically, in one step. High circularity of the harmonic emission offers a method to generate highly elliptic attosecond pulses with a linearly polarized driver, in an all-solid-state setup

Sub-cycle valleytronics: control of valley polarization using few-cycle linearly polarized pulses

So far, it has been assumed that selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has to rely on using circularly polarized fields. We theoretically demonstrate a way to control the valley excitation in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier–envelope phase. The valley polarization is mapped onto the strength of the perpendicular harmonic signal of a weak, linearly polarized pulse, which allows to read this information all-optically without destroying the valley state and without relying on the Berry curvature, making our approach potentially applicable to inversion-symmetric materials. We show applicability of this method to hexagonal boron nitride and MoS2

Ultrafast dephasing in solid state high harmonic generation: macroscopic origin revealed by real-space dynamics

Using a fully real-space perspective on high harmonic generation (HHG) in solids, we examine the relationship between microscopic response, macroscopic propagation of this response to the far field, and the extremely short dephasing times routinely used in the theoretical simulations of experimentally measured solid-state HHG spectra. We find that far field propagation naturally reduces the contribution to the observed HHG emission from electrons that do not return to the lattice site where they have been injected into the conduction band. We then show that extremely short dephasing times routinely used in microscopic simulations suppress many electron trajectories that contribute to the far-field spectra, leading to significant distortions of the true high harmonic response. We show that a real-space based dephasing mechanism, which preferentially suppresses trajectories which veer too far away from their original lattice site, yield HHG spectra that faithfully retain those trajectories that contribute to the far-field spectra while filtering out those which do not, already at the microscopic level. Our findings emphasize the similarities between atomic and solid-state HHG by highlighting the importance of the intensity-dependent phase of HHG emission and address the longstanding issue regarding the origin of extremely short dephasing times in solid-state HHG.Comment: 8 pages, 3 figure