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Strong-field quantum-state control is investigated, taking advantage of the full---amplitude and phase---characterization of the interaction between matter and intense ultrashort pulses via transient-absorption spectroscopy. A sequence of intense delayed pulses is used, whose parameters are tailored to steer the system into a desired quantum state. We show how to experimentally enable this optimization by retrieving all quantum features of the light-matter interaction from observable spectra. This provides a full characterization of the action of strong fields on the atomic system, including the dependence upon possibly unknown pulse properties and atomic structures. Precision and robustness of the scheme are tested, in the presence of surrounding atomic levels influencing the system's dynamics., Comment: 6 pages, 4 figures

Attosecond transient absorption spectroscopy has thus far been lacking the capability to simultaneously characterize the intense laser pulses at work within a time-resolved quantum-dynamics experiment. However, precise knowledge of these pulses is key to extracting quantitative information in strong-field highly nonlinear light-matter interactions. Here, we introduce and experimentally demonstrate an ultrafast metrology tool based on the time-delay-dependent phase shift imprinted on a strong-field driven resonance. Since we analyze the signature of the laser pulse interacting with the absorbing spectroscopy target, the laser pulse duration and intensity are determined in situ. As we also show, this approach allows for the quantification of time-dependent bound-state dynamics in one and the same experiment. In the future, such experimental data will facilitate more precise tests of strong-field dynamics theories.

Obtaining a detailed understanding of strong-field double ionisation of many-electron systems (heavy atoms and molecules) remains a challenging task. By comparing experimental and theoretical results in the mid-IR regime, we have unambiguously identified the transition from non-sequential (e,2e) to sequential double ionisation in Xe and shown that it occurs at an intensity below $10^{14}$ Wcm$^{-2}$. In addition, our data demonstrate that ionisation from the Xe 5s orbital is decisive at low intensities. Moreover, using the acetylene molecule, we propose how sequential double ionisation in the mid-IR can be used to study molecular dynamics and fragmentation on unprecedented few-femtosecond timescales., Comment: 12 pages overall, 5 pages of main text, 3 figures

Non-collinear four-wave mixing (FWM) techniques at near-infrared (NIR), visible, and ultraviolet frequencies have been widely used to map vibrational and electronic couplings, typically in complex molecules. However, correlations between spatially localized inner-valence transitions among different sites of a molecule in the extreme ultraviolet (XUV) spectral range have not been observed yet. As an experimental step towards this goal we perform time-resolved FWM spectroscopy with femtosecond NIR and attosecond XUV pulses. The first two pulses (XUV-NIR) coincide in time and act as coherent excitation fields, while the third pulse (NIR) acts as a probe. As a first application we show how coupling dynamics between odd- and even-parity inner-valence excited states of neon can be revealed using a two-dimensional spectral representation. Experimentally obtained results are found to be in good agreement with ab initio time-dependent R-matrix calculations providing the full description of multi-electron interactions, as well as few-level model simulations. Future applications of this method also include site-specific probing of electronic processes in molecules., Comment: 5 pages, 3 figures

In any atomic species, the spherically symmetric potential originating from the charged nucleus results in fundamental symmetry properties governing the structure of atomic states and transition rules between them. If atoms are exposed to external electric fields, these properties are modified giving rise to energy shifts such as the AC Stark-effect in varying fields and, contrary to this in a constant (DC) electric field for high enough field strengths, the breaking of the atomic symmetry which causes fundamental changes in the atom's properties. This has already been observed for atomic Rydberg states with high principal quantum numbers. Here, we report on the observation of effects linked to symmetry breaking in helium within the optical cycle of the utilized strong visible laser fields for states with principal quantum number n=2. These findings were enabled by temporally resolving the dynamics better than the sub-optical cycle of the applied laser field, utilizing the method of attosecond transient absorption spectroscopy (ATAS). We identify the spectroscopic fingerprint of instantaneous polarization and breaking of the symmetry of the atom in the intense visible femtosecond pulse used in an ATAS experiment and develop a time domain picture describing the dipole response that leads to these signatures. In the future, this general experimental approach can be used to measure strong-field induced symmetry-breaking effects in other atomic or molecular systems also consisting of two or more active electrons and thus to examine new routes to their bound-state and transition-state control by laser fields., Comment: 6 pages, 4 figures

Understanding and controlling the electronic as well as ro-vibrational motion and, thus, the entire chemical dynamics in molecules is the ultimate goal of ultrafast laser and imaging science. In photochemistry, laser-induced dissociation has become a valuable tool for modification and control of reaction pathways and kinetics. Here, we present a pump-probe study of the dissociation dynamics of H$_2^+$ using ultrashort extreme-ultraviolet (XUV) and near-infrared (IR) laser pulses. The reaction kinematics can be controlled by varying the pump-probe delay. We demonstrate that the nuclear motion through the transition state can be reduced to isolated pairs of initial vibrational states. The dynamics is well reproduced by intuitive semi-classical trajectories on a time-dependent potential curve. From this most fundamental scenario we gain insight in the underlying mechanisms which can be applied as design principles for molecular quantum control, particularly for ultrafast reactions involving protons., Comment: 7 pages and 3 figures. Supplementary materials: 6 pages and 3 figures

We demonstrate a two-dimensional time-domain spectroscopy method to extract amplitude and phase modifications of excited atomic states caused by the interaction with ultrashort laser pulses. The technique is based on Fourier analysis of the absorption spectrum of perturbed polarization decay. An analytical description of the method reveals how amplitude and phase information can be directly obtained from measurements. We apply the method experimentally to the helium atom, which is excited by attosecond-pulsed extreme ultraviolet light, to characterize laser-induced couplings of doubly-excited states., Comment: 8 pages, 5 figures

Optical frequency combs have had a remarkable impact on precision spectroscopy. Enabling this technology in the x-ray domain is expected to result in wide-ranging applications, such as stringent tests of astrophysical models and quantum electrodynamics, a more sensitive search for the variability of fundamental constants, and precision studies of nuclear structure. Ultraprecise x-ray atomic clocks may also be envisaged. In this work, an x-ray pulse-shaping method is put forward to generate a comb in the absorption spectrum of an ultrashort high-frequency pulse. The method employs an optical-frequency-comb laser, manipulating the system's dipole response to imprint a comb on an excited transition with a high photon energy. The described scheme provides higher comb frequencies and requires lower optical-comb peak intensities than currently explored methods, preserves the overall width of the optical comb, and may be implemented by presently available x-ray technology.

A general mechanism for the generation of frequency combs referenced to atomic resonances is put forward. The mechanism is based on the periodic phase control of a quantum system's dipole response. We develop an analytic description of the comb spectral structure, depending on both the atomic and the phase-control properties. We further suggest an experimental implementation of our scheme: Generating a frequency comb in the soft-x-ray spectral region, which can be realized with currently available techniques and radiation sources. The universality of this mechanism allows the generalization of frequency-comb technology to arbitrary frequencies, including the hard-x-ray regime by using reference transitions in highly charged ions.

Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase {\phi} of the time-dependent dipole-response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also prove the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism amplifies resonantly interacting extreme-ultraviolet light by quantum-phase control. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with scientific applications in many branches of spectroscopy., Comment: 11 pages, 4 figures

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum of helium dressed by a few-cycle visible pulse [Ott et al., arXiv:1205.0519[physics.atom-ph] ] provide evidence of novel ultrafast resonant phenomena, namely, two-photon Rabi oscillations between doubly-excited states and the inversion of Fano profiles. Here we present the results of accurate \emph{ab-initio} calculations that agree with these observations and in addition predict that (i) inversion of Fano profiles is actually periodic in the coupling laser intensity and (ii) the supposedly dark $2p^2$ {$^1$S} state also appears in the spectrum. Closer inspection of the experimental data confirms the latter prediction., Comment: 5 pages, 4 figures

The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes and chemical reactions. It is thus a long-standing scientific dream to measure the dynamics of two bound correlated electrons in the quantum regime. Quantum wave packets were previously observed for single-active electrons on their natural attosecond timescales. However, at least two active electrons and a nucleus are required to address the quantum three-body problem. This situation is realized in the helium atom, but direct time-resolved observation of two-electron wave-packet motion remained an unaccomplished challenge. Here, we measure a 1.2-femtosecond quantum beating among low-lying doubly-excited states in helium to evidence a correlated two-electron wave packet. Our experimental method combines attosecond transient-absorption spectroscopy at unprecedented high spectral resolution (20 meV near 60 eV) with an intensity-tuneable visible laser field to couple the quantum states from the perturbative to the strong-coupling regime. This multi-dimensional transient-coupling scheme reveals an inversion of the characteristic Fano line shapes for a range of doubly-excited states. Employing Fano-type autoionization as a natural quantum interferometer, a dynamical phase shift by laser coupling to the N=2 continuum is postulated and experimentally quantified. This phase maps a transition from effectively single-active-electron to two-electron dynamics as the electron-electron interaction increases in lower-lying quantum states. In the future, such experiments will provide benchmark data for testing dynamical few-body quantum theory. They will boost our understanding of chemically and biologically important metastable electronic transition states and their dynamics on attosecond time scales., Comment: in peer review (first reports obtained, result: scientifically sound, high quality, conclusions are robust and reliable)

In the past two decades high-harmonic generation (HHG) has become a key process in ultra-fast science due to the extremely short time-structure of the underlying electron dynamics being imprinted in the emitted harmonic light bursts. After discussing the fundamental physical picture of HHG including continuum--continuum transitions, we describe the experimental progress rendering HHG to the unique source of attosecond pulses. The development of bright photon sources with zeptosecond pulse duration and keV photon energy is underway. In this article we describe several approaches pointed toward this aim and beyond. As the main barriers for multi-keV HHG, phase-matching and relativistic drift are discussed. Routes to overcome these problems are pointed out as well as schemes to control the HHG process via alterations of the driving fields. Finally, we report on how the investigation of fundamental physical processes benefits from the continuous development of HHG sources., Comment: submitted to Advances In Atomic, Molecular, and Optical Physics

Several correlation and interference effects in strong-field physics are investigated. We show that the interference of continuum wave packets can be the dominant mechanism of high-harmonic generation (HHG) in the over-the-barrier regime. Next, we combine HHG with resonant x-ray excitation to force the recolliding continuum electron to recombine with a core hole rather than the valence hole from that it was previously tunnel ionized. The scheme opens up perspectives for nonlinear xuv physics, attosecond x-ray pulses, and spectroscopy of core orbitals. Then, a method is proposed to generate attochirp-free harmonic pulses by engineering the appropriate electron wave packet. Finally, resonant photoionization mechanisms involving two atoms are discussed which can dominate over the direct single-atom ionization channel at interatomic distances in the nanometer range., Comment: to be published in Springer Proceedings "Multiphoton Processes and Attosecond Physics"

Time-resolved measurements of quantum dynamics are based on the availability of controlled events (e.g. pump and probe pulses) that are shorter in duration than the typical evolution time scale of the dynamical processes to be observed. Here we introduce the concept of noise-enhanced pump-probe spectroscopy, allowing the measurement of dynamics significantly shorter than the average pulse duration by exploiting randomly varying, partially coherent light fields consisting of bunched colored noise. It is shown that statistically fluctuating fields can be superior by more than a factor of 10 to frequency-stabilized fields, with important implications for time-resolved pump-probe experiments at x-ray free-electron lasers (FELs) and, in general, for measurements at the frontiers of temporal resolution (e.g. attosecond spectroscopy). As an example application, the concept is used to explain the recent experimental observation of vibrational wave packet motion in a deuterium molecular ion on time scales shorter than the average pulse duration.

Two- and multi-dimensional spectroscopy is used in physics and chemistry to obtain structural and dynamical information that would otherwise be invisible by the projection into a one-dimensional data set such as a single emission or absorption spectrum. Here, we introduce a qualitatively new two-dimensional spectroscopy method by employing the carrier-envelope phase (CEP). Instead of measuring spectral vs. spectral information, the combined application of spectral interferometry and CEP control allows the measurement of otherwise inseparable temporal events on an attosecond time scale. As a specific example, we apply this general method to the case of attosecond pulse train generation, where it allows to separate contributions of three different sub-cycle electron quantum paths within one and the same laser pulse, resulting in a better physical understanding and quantification of the transition region between cutoff and plateau harmonics. The CEP-dependent separation in time between two full-cycle spaced attosecond pulses was determined to modulate by (54 +/- 16) attoseconds.

Strong-field ionization generally produces ions in a superposition of ionic eigenstates. This superposition is generally not fully coherent und must be described in terms of a density matrix. A recent experiment [E. Goulielmakis et al., Nature 466, 739 (2010)] employed attosecond transient absorption spectroscopy to determine the density matrix of strong-field-generated Kr+ ions. The experimentally observed degree of coherence of the strong-field-generated Kr+ ions is well reproduced by a recently developed multichannel strong-field-ionization theory. But there is significant disagreement between experiment and theory with respect to the degree of alignment of the Kr+ ions. In the present paper, the theory underlying attosecond transient absorption spectroscopy of strong-field-generated ions is developed. The theory is formulated in such a way that the nonperturbative nature of the strong-field-ionization process is systematically taken into account. The impact of attosecond pulse propagation effects on the interpretation of experimental data is investigated both analytically and numerically. It is shown that attosecond pulse propagation effects cannot explain why the experimentally determined degree of alignment of strong-field-generated Kr+ ions is much smaller than predicted by existing theory., Comment: 23 pages, 4 figures, to be published in Phys. Rev. A

A nonlinear interferometry scheme is described theoretically to induce and resolve electron wave- function beating on time scales shorter than the optical cycle of the time-delayed pump and probe pulses. By employing two moderately intense few-cycle laser fields with a stable carrier-envelope phase, a large range of the entire electronic level structure of a quantum system can be retrieved. In contrast to single-photon excitation schemes, the retrieved electronic states include levels that are both dipole- and non-dipole-accessible from the ground electronic state. The results show that strong-field interferometry can reveal both high-resolution and broad-band spectral information at the same time with important consequences for quantum-beat spectroscopy on attosecond or even shorter time scales., Comment: first submitted on April 19, 2010

High-order harmonic generation (HHG) is investigated theoretically in the over-the-barrier ionization (OBI) regime revealing the strong signature of interference between two separately ionized and separately propagating free wave packets of a single electron. The interference leads to the emission of coherent light at a photon energy corresponding to the kinetic-energy difference of the two recolliding electron quantum paths, thus complementary to the well-known classical three-step picture of HHG. As will be shown by time-frequency analysis of the emitted radiation, the process entirely dominates the coherent HHG emission after the atomic ground state has been depleted by a strong field. Moreover, it can be isolated from the continuum--bound harmonics via phase-matching., Comment: 5 pages, 3 figures