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We show that the complete photoemission dynamics in situations of electron-ion entanglement can be retrieved from photoelectron spectral measurements without information on the ion. To this end, we develop an energy-time analysis of the photoelectron's reduced density matrix based on first principles. We test and assess our approach with numerical simulations on a low dimensional model molecule in interaction with broadband composite pulses occulting the vibrational resolution. Our method is directly applicable to recent experimental schemes measuring the photoelectron reduced density matrices in atomic and molecular photoemission. Therefore, it opens a new window on the dynamics of decoherence and entanglement at the attosecond timescale., Comment: 7 pages, 2 figures

We photoionize nitrogen molecules with a train of extreme ultraviolet attosecond pulses together with a weak infrared field. We measure the phase of the two-color two-photon ionization transition (molecular phase) for different states of the ion. We observe a 0.76 $\pi$ shift for the electrons produced in the ionization channels leading to the X$^2 \Sigma_g^+$, $v'=1$ and $v'=2$ states. We relate this phase shift to the presence of a complex resonance in the continuum. By providing both a high spectral and temporal resolution, this general approach gives access to the evolution of extremely short lived states, which is hardly accessible otherwise.

Quantum coherence plays a fundamental role in the study and control of ultrafast dynamics in matter. In the case of photoionization, entanglement of the photoelectron with the ion is a well known source of decoherence when only one of the particles is measured. Here we investigate decoherence due to entanglement of the radial and angular degrees of freedom of the photoelectron. We study two-photon ionization via the 2s2p autoionizing state in He using high spectral resolution photoelectron interferometry. Combining experiment and theory, we show that the strong dipole coupling of the 2s2p and 2p$^2$ states results in the entanglement of the angular and radial degrees of freedom. This translates, in angle integrated measurements, into a dynamic loss of coherence during autoionization.

Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach due to the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by twophoton transitions through intermediate bound states. Using spectrally- and angularly-resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude towards the photoelectron quantum state. This allows reconstructing in space, time and energy the complete formation of the photoionized wavepacket., Comment: 7 pages, 4 figures

We characterize the temporal profile of the high-order harmonic emission from ablation plasma plumes using cross-correlations with the infrared (IR) laser beam provided by 2-photon harmonic+IR ionization of rare gas atoms. We study both non-resonant plasmas (lead, gold and chrome) and resonant plasmas (indium and tin), i.e. plasmas presenting in the singly-charged ions a strong radiative transition coinciding with an harmonic order. The cross-correlation traces are found very similar for all harmonic orders and all plasma targets. The recovered harmonic pulse durations are very similar to the driving laser, with a tendency towards being shorter, demonstrating that the emission is a \stef{directly} laser-driven process even in the case of resonant harmonics. This provides valuable input for theories describing resonant harmonic emission and opens the perspective of a very-high-flux tabletop \textsc{xuv} source for applications.

This tutorial presents the most important aspects of the molecular self-probing paradigm, which views the process of high harmonic generation as "a molecule being probed by one of its own electrons". Since the properties of the electron wavepacket acting as a probe allow a combination of attosecond and \AA ngstr\"om resolutions in measurements, this idea bears great potential for the observation, and possibly control, of ultrafast quantum dynamics in molecules at the electronic level. Theoretical as well as experimental methods and concepts at the basis of self-probing measurements are introduced. Many of these are discussed on the example of molecular orbital tomography., Comment: A PhD Tutorial

Using a spectrally resolved electron interferometry technique, we measure photoionization time delays between the $3s$ and $3p$ subshells of argon over a large 34-eV energy range covering the Cooper minima in both subshells. The observed strong variations of the $3s-3p$ delay difference, including a sign change, are well reproduced by theoretical calculations using the Two-Photon Two-Color Random Phase Approximation with Exchange. Strong shake-up channels lead to photoelectrons spectrally overlapping with those emitted from the $3s$ subshell. These channels need to be included in our analysis to reproduce the experimental data. Our measurements provide a stringent test for multielectronic theoretical models aiming at an accurate description of inter-channel correlation.

Amplitude and phase of wavepackets encode the dynamics of quantum systems. However, the rapidity of electron dynamics on the attosecond timescale has precluded their complete measurement in the time domain. Here, we demonstrate that spectrally-resolved electron interferometry reveals the amplitude and phase of a photoelectron wavepacket created through a Fano autoionizing resonance in helium. Replicas obtained by two-photon transitions interfere with reference wavepackets formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wavepacket released in the continuum. This in turn resolves the buildup of the autoionizing resonance on attosecond timescale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for both detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave-packets.

One of the most ubiquitous techniques within attosecond science is the so-called Reconstruction of Attosecond Bursts by Interference of Two-Photon Transitions (RABBITT). Originally proposed for the characterization of attosecond pulses, it has been successfully applied to accurate determinations of time delays in photoemission. Here, we examine in detail, using numerical simulations, the effect of the spatial and temporal properties of the light fields and of the experimental procedure on the accuracy of the method. This allows us to identify the necessary conditions to achieve the best temporal resolution in RABBITT measurements.

We study the signature of two-center interferences in molecular high-order harmonic spectra, with an emphasis on the spectral phase. With the help of both ab initio computations based on the time-dependent Schr\"odinger equation and the molecular Strong-Field Approximation (SFA) as developed by Chirila et al. [Physical Review A, 73, 023410 (2006)] and Faria [Physical Review A, 76, 043407 (2007)], we observe that the phase behavior is radically different for the short and the long trajectory contributions. By means of Taylor expansions of the molecular SFA, we link this effect to the dynamics of the electron in the continuum. More precisely, we find that the value of the electric field at recombination time plays a crucial role on the shape of the destructive interference phase-jump., Comment: submitted to Phys. Rev. A

Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light-matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wavepacket. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wavepackets emitted via the sp2+ and sp3+ resonances in helium. These measurements allow us to reconstruct the corresponding temporal profiles by Fourier transform. In addition, applying various time-frequency representations, we observe the build up of the wavepackets in the continuum, monitor the instantaneous frequencies emitted at any time and disentangle the dynamics of the direct and resonant ionization channels.

We study theoretically the two-center interferences occurring in high harmonic generation from diatomic molecules. By solving the time-dependent Schroedinger equation, either numerically or with the molecular strong-field approximation, we show that the electron dynamics results in a strong spectral smoothing of the interference, depending on the value and sign of the driving laser field at recombination. Strikingly, the associated phase-jumps are in opposite directions for the short and long trajectories. In these conditions, the harmonic emission is not simply proportional to the recombination dipole any more. This has important consequences in high harmonic spectroscopy, e.g., for accessing the molecular-frame recombination dipole in amplitude and phase.

We investigate how short and long electron trajectory contributions to high harmonic emission and their interferences give access to intra-molecular dynamics. In the case of unaligned molecules, we show experimental evidences that the long trajectory signature is more dependent upon the molecule than the short one, providing a high sensitivity to cation nuclear dynamics within 100's of as to few fs. Using theoretical approaches based on Strong Field Approximation and Time Dependent Schrodinger Equation, we examine how quantum path interferences encode electronic motion whilst molecules are aligned. We show that the interferences are dependent on channels superposition and upon which ionisation channel is involved. In particular, quantum path interferences encodes electronic migration signature while coupling between channels is allowed by the laser field. Hence, molecular quantum path interferences is a promising method for Attosecond Spectroscopy, allowing the resolution of ultra-fast charge migration in molecules after ionisation in a self-referenced manner., Comment: 10 pages 9 figures 1 table

Resonant enhancement of high harmonic generation can be obtained in plasmas containing ions with strong radiative transitions resonant with harmonic orders. The mechanism for this enhancement is still debated. We perform the first temporal characterization of the attosecond emission from a tin plasma under near-resonant conditions for two different resonance detunings. We show that the resonance considerably changes the relative phase of neighbouring harmonics. For very small detunings, their phase locking may even be lost, evidencing strong phase distortions in the emission process and a modified attosecond structure. These features are well reproduced by our simulations, allowing their interpretation in terms of the phase of the recombination dipole moment.

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time-delayed attosecond pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond pulse train in a semi-analytic framework. Employing the Strong-Field Approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low-plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit., Comment: 10 pages, 7 figures (eps files). To appear in Laser Physics

We perform a detailed analysis of how high-order harmonic generation (HHG) and above-threshold ionization (ATI) can be controlled by a time-delayed attosecond-pulse train superposed to a strong, near-infrared laser field. In particular we show that the high-harmonic and photoelectron intensities, the high-harmonic plateau structure and cutoff energies, and the ATI angular distributions can be manipulated by changing this delay. This is a direct consequence of the fact that the attosecond pulse train can be employed as a tool for constraining the instant an electronic wave packet is ejected in the continuum. A change in such initial conditions strongly affects its subsequent motion in the laser field, and thus HHG and ATI. In our studies, we employ the Strong-Field Approximation and explain the features observed in terms of interference effects between various electron quantum orbits. Our results are in agreement with recent experimental findings and theoretical studies employing purely numerical methods., Comment: 10 pages revtex and 6 figures (eps files)

We apply the theory of high-order harmonic generation by low-frequency laser fields in the strong field approximation to the study of the spatial and temporal coherence properties of the harmonics. We discuss the role of dynamically induced phases of the atomic polarization in determining the optimal phase matching conditions and angular distributions of harmonics. We demonstrate that the phase matching and the spatial coherence can be controlled by changing the focusing parameters of the fundamental laser beam. Then we present a detailed study of the temporal and spectral properties of harmonics. We discuss how the focusing conditions influence the individual harmonic spectra and time profiles, and how the intensity dependence of the dynamically induced phase leads to a chirp of the harmonic frequency. This phase modulation can be used to control the temporal and spectral properties of the harmonic radiation. Temporally, the harmonic chirped pulse can be recompressed to very small durations. Spectrally, chirping of the fundamental beam may be employed to compensate for the dynamically induced chirp and to control the individual harmonic spectrum. Finally, we discuss the short pulse effects, in particular nonadiabatic phenomena and the possibility of generating attosecond pulses., Comment: Latex file with 37 pages, 25 postscript figures. to appear in Advances in Atomic, Molecular and Optical Physics