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We investigate the ultrafast electron dynamics of a model of a wide-bandgap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are employed to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our TDDFT and SBE-based results allows us to interpret the ab-initio TDDFT simulations in terms of SBEs' interband couplings, validating our SBE-based model and corroborating its conclusions., Comment: 21 pages, 8 figures

The chaotic nature of x-ray free-electron-laser pulses is a major bottleneck that has limited the joint temporal and spectral resolution of spectroscopic measurements. We show how to use the stochastic x-ray field statistics to overcome this difficulty by correlation signals averaged over independent pulse realizations. No control is required over the spectral phase of the pulse, enabling immediate application with existing, noisy x-ray free-electron-laser pulses. The proposed stimulated Raman technique provides the broad observation bandwidth and high time-frequency resolution needed for the observation of elementary molecular events. A model is used to simulate chaotic free-electron-laser pulses and calculate their correlation properties. The resulting joint temporal/spectral resolution is exemplified for a molecular model system with time-dependent frequencies and for the RNA base Uracil passing through a conical intersection. Ultrafast coherences, which represent a direct signature of the nonadiabatic dynamics, are resolved. The detail and depth of physical information accessed by the proposed stochastic signal are virtually identical to those obtained by phase-controlled pulses., Comment: 24 pages, 13 figures

A scheme to infer the temporal coherence of EUV frequency combs generated from intra-cavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, interacting with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at time scales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to $\delta\omega/\omega\sim10^{-17}$., Comment: 6 pages, 3 figures and 1 table

We demonstrate time-resolved nonlinear extreme-ultraviolet absorption spectroscopy on multiply charged ions, here applied to the doubly charged neon ion, driven by a phase-locked sequence of two intense free-electron laser pulses. Absorption signatures of resonance lines due to 2$p$--3$d$ bound--bound transitions between the spin-orbit multiplets $^3$P$_{0,1,2}$ and $^3$D$_{1,2,3}$ of the transiently produced doubly charged Ne$^{2+}$ ion are revealed, with time-dependent spectral changes over a time-delay range of $(2.4\pm0.3)\,\text{fs}$. Furthermore, we observe 10-meV-scale spectral shifts of these resonances owing to the AC Stark effect. We use a time-dependent quantum model to explain the observations by an enhanced coupling of the ionic quantum states with the partially coherent free-electron-laser radiation when the phase-locked pump and probe pulses precisely overlap in time.

The transient-absorption spectrum of a $V$-type three-level system is investigated, when this is periodically excited by a train of equally spaced, $\delta$-like pump pulses as, e.g., from an optical-frequency-comb laser. We show that, even though the probe pulse is not assumed to be much shorter than the pump pulses, light-induced states appear in the absorption spectrum. The frequency- and time-delay-dependent features of the absorption spectra are investigated as a function of several laser control parameters, such as the number of pump pulses used, their pulse area, and the pulse-to-pulse phase shift. We show that the frequencies of the light-induced states and the time-delay-dependent features of the spectra contain information on the action of the intense pulses exciting the system, which can thus complement the information on light-imposed amplitude and phase changes encoded in the absorption line shapes., Comment: 26 pages, 8 figures

Since the advent of x-ray free-electron lasers (XFELs), considerable efforts have been devoted to achieve x-ray pulses with better temporal coherence. Here, we put forward a scheme to generate fully coherent x-ray lasers (XRLs) based on population inversion in highly charged ions (HCIs), created by fast inner-shell photoionization using XFEL pulses in a laser-produced plasma. Numerical simulations show that one can obtain high-intensity, femtosecond x-ray pulses of relative bandwidths $\Delta\omega/\omega=10^{-5}$ - $10^{-7}$ by orders of magnitude narrower than in XFEL pulses for wavelengths down to the sub-\aa{}ngstr\"om regime. Such XRLs may be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopy studies in laboratory astrophysics., Comment: 5 pages, 3 figures, 1 table

Causality implies that by measuring an absorption spectrum, the time-dependent linear response function can be retrieved. Recent experiments suggest a link between the shape of spectral lines observed in absorption spectroscopy with the amplitude and phase of the systems response function. This has even been observed in the presence of strong, nonlinear interactions, which promote the observed system out of equilibrium, making it explicitly time dependent. Thus far, however, only the special case of a sudden modification of the response function was understood analytically, leaving the general case of the dynamical response to arbitrary interactions open to interpretation. Here, we demonstrate that even for the case of a strongly driven, time-dependent system, one can reconstruct the full temporal response information from a single spectrum if a sufficiently short signal is used to trigger the absorption process. This finding is directly applied to a time-domain observation of Rabi cycling between doubly-excited atomic states in the few-femtosecond regime. This general approach unlocks single-shot real-time-resolved signal reconstruction across time scales down to attoseconds for non-equilibrium states of matter. In contrast to available pump-probe schemes, there is no need for scanning time delays in order to access real-time information. The scientific applications of this technique range from testing fundamental quantum dynamics, to measuring and controlling ultrafast, chemical and biological reaction processes., Comment: 5 pages, 4 figures

Numerous few-electron atomic systems are considered which can be used effectively for observing a potential variation of the fine-structure constant $\alpha$ and the electron-proton mass ratio $m_e/m_p$. We examine optical magnetic dipole transitions between hyperfine-structure components in heavy highly charged H-like and Li-like ions with observably high sensitivity to a variation of $\alpha$ and $m_e/m_p$. The experimental spectra of the proposed systems consist of a strong single line, which simplifies significantly the data analysis and shortens the necessary measurement time. Furthermore, we propose systems for an experimental test of the variation of quark masses and discuss the expected level of accuracy in assessing its limitations. Finally, we establish which constraints on the variation of these fundamental constants could be provided by measurements with a hyperfine-structure highly-charged-ion clock and some reference clock, showing that a significant improvement of the current limitations can be reached.

The quantum dynamics of a system of Rb atoms, modeled by a V-type three-level system interacting with intense probe and pump pulses, are studied. The time-delay-dependent transient-absorption spectrum of an intense probe pulse is thus predicted, when this is preceded or followed by a strong pump pulse. Numerical results are interpreted in terms of an analytical model, which allows us to quantify the oscillating features of the resulting transient-absorption spectra in terms of the atomic populations and phases generated by the intense pulses. Strong-field-induced phases and their influence on the resulting transient-absorption spectra are thereby investigated for different values of pump and probe intensities and frequencies, focusing on the atomic properties which are encoded in the absorption line shapes for positive and negative time delays., Comment: 15 pages, 12 figures

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

The influence of nonlinear dynamical effects is analyzed on the observed spectra of controversial 3C and 3D astrophysically relevant x-ray lines in neonlike Fe${}^{16+}$ and the A, B, C lines in natriumlike Fe${}^{15+}$ ions. First, a large-scale configuration-interaction calculation of oscillator strengths is performed with the inclusion of higher-order electron-correlation effects. Also, quantum-electrodynamic corrections to the transition energies are calculated. Further considered dynamical effects provide a possible resolution of the discrepancy between theory and experiment found by recent x-ray free-electron-laser measurements of these controversial lines. We find that, for strong x-ray sources, the modeling of the spectral lines by a peak with an area proportional to the oscillator strength is not sufficient and nonlinear dynamical effects have to be taken into account. Thus, we advocate the use of light-matter-interaction models also valid for strong light fields in the analysis and interpretation of the associated astrophysical and laboratory spectra. We investigate line-strength ratios distinguishing between the coherent and incoherent parts of the emission spectrum. In addition, the spectrum of Fe${}^{15+}$, an autoionizing ion which was also present in the recent laboratory experiment, is also analized., Comment: 16 pages, 10 figures

Line intensities and oscillator strengths for the controversial 3C and 3D astrophysically relevant lines in neonlike Fe${}^{16+}$ ions are calculated. We show that, for strong x-ray sources, the modeling of the spectral lines by a peak with an area proportional to the oscillator strength is not sufficient and non-linear dynamical effects have to be taken into account. Furthermore, a large-scale configuration-interaction calculation of oscillator strengths is performed with the inclusion of higher-order electron-correlation effects. The dynamical effects give a possible resolution of discrepancies of theory and experiment found by recent measurements, which motivates the use of light-matter interaction models also valid for strong light fields in the analysis and interpretation of astrophysical and laboratory spectra., Comment: 5 pages, 3 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.

An x-ray pulse-shaping scheme is put forward for imprinting an optical frequency comb onto the radiation emitted on a driven x-ray transition, thus producing an x-ray frequency comb. A four-level system is used to describe the level structure of N ions driven by narrow-bandwidth x rays, an optical auxiliary laser, and an optical frequency comb. By including many-particle enhancement of the emitted resonance fluorescence, a spectrum is predicted consisting of equally spaced narrow lines which are centered on an x-ray transition energy and separated by the same tooth spacing as the driving optical frequency comb. Given a known x-ray reference frequency, our comb could be employed to determine an unknown x-ray frequency. While relying on the quality of the light fields used to drive the ensemble of ions, the model has validity at energies from the 100 eV to the keV range., Comment: 11 pages, 2 figures