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The ability to control absorption by modifying the polarization of light presents an exciting opportunity to experimentally determine the orbital alignment of absorption features. Here, attosecond extreme ultraviolet (XUV) transient absorption spectroscopy is used to investigate the polarization dependence of core exciton dynamics in LiF thin films at the Li+ K edge. XUV pulses excite electrons from the Li 1s core level into the conduction band, allowing for the formation of a p-orbital-like core exciton, aligned along the XUV light polarization axis. A sub-5 fs near-infrared (NIR) probe pulse then arrives at variable time delays, perturbing the XUV-excited states and allowing the coherence decay of the core exciton to be mapped. The coherence lifetimes are found to be ~2.4 +- 0.4 fs, which is attributed to a phonon-mediated dephasing mechanism as in previous core exciton studies. The differential absorption features are also shown to be sensitive to the relative polarization of the XUV and NIR fields. The parallel NIR probe induces couplings between the initial XUV-excited p-like bright exciton and s-like dark excitons. When crossed pump and probe polarizations are used, the coupling between the bright and dark states is no longer dipole-allowed, and the transient absorption signal associated with the coupling is suppressed by approximately 90%. This interpretation is supported by simulations of a few-level model system, as well as analysis of the calculated band structure. The results indicate that laser polarization can serve as a powerful experimental tool for exploring the orbital alignment of core excitonic states in solid-state materials., Comment: 18 pages, 14 figures

We compare the high-harmonic-generation (HHG) yield driven by a mid-infrared laser in three organic ring-shaped molecules, calculated using time-dependent density-functional theory (TDDFT). We average the yield over the relative orientation of the molecules and the linearly-polarized, 1825 nm driving laser pulse in order to compare to experimental spectra obtained by Alharbi et al., Phys. Rev. A 92, 041801 (2015). We find that the raw TDDFT-calculated HHG yield in cyclohexane (CHA) is strongly overestimated compared to those of benzene and cyclohexene, and that this can be attributed to unphysically large contributions from CHA orbitals lying well below the highest-occupied molecular orbital. We show that implementing a simple orbital-resolved scaling factor, which corrects the yield of the tunneling ionization contribution to the first step in the HHG process, leads to much better comparisons with experimental results. Our results are encouraging for the use of TDDFT in systematic computations of HHG in large molecules., Comment: 11 pages, 8 figures

We show that applying a few-femtosecond mid-infrared laser pulse parallel to the backbone of a halogenated, conjugated organic molecule induces localized ionization followed by long-lasting field-free charge migration (CM). Through time-dependent density-functional theory calculations, we find that this CM is robust with respect to the parameters of the applied laser pulse. We document the spatial and temporal origin of the localized hole, which is initiated via strong-field tunnel ionization in the halogen end of the molecule, and near the peak of the laser electric field. In bromobutadiyne we find a range of wavelengths around $1500~\text{nm}$ that consistently leads to the initiation of high-contrast CM. In addition, we show that the inclusion of Ehrenfest nuclear dynamics does not disrupt the creation of the localized hole, nor the subsequent CM motion, in bromobutadiyne or \emph{para}-bromoaniline., Comment: 6 pages, 4 figures

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density-functional theory. CM+FMSS is a pump-probe scheme that uses a frequency-matched HHG-driving laser as an independent probe step following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process, in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with negligible contribution from the ionization step.

We revisit Kohn-Sham time-dependent density-functional theory (TDDFT) equations and show that they derive from a canonical Hamiltonian formalism. We use this geometric description of the TDDFT dynamics to define families of symplectic split-operator schemes that accurately and efficiently simulate the time propagation for certain classes of DFT functionals. We illustrate these with numerical simulations of the far-from-equilibrium electronic dynamics of a one-dimensional carbon chain. In these examples, we find that an optimized 4th order scheme provides a good compromise between the numerical complexity of each time step and the accuracy of the scheme. We also discuss how the Hamiltonian structure changes when using a basis set to discretize TDDFT and the challenges this raises for using symplectic split-operator propagation schemes., Comment: 20 pages, 4 figures

We develop and test a method that integrates many-electron weak-field asymptotic theory (ME-WFAT) [Phys. Rev. A 89, 013421 (2014)] in the integral representation (IR) into the density functional theory (DFT) framework. In particular, we present modifications of the integral formula in the IR ME-WFAT to incorporate the potential terms unique to DFT. By solving an adiabatic rate equation for the angle-resolved ionization yield in our DFT-based ME-WFAT method, we show that the results are in excellent agreement with those of real-time time-dependent density functional theory (RT-TDDFT) simulations for NO, OCS, CH$_3$Br, and CH$_3$Cl interacting with one- and two- color laser fields with a fundamental wavelength of $800$ nm. This agreement is significant because the WFAT calculations take only a small fraction of the time of full TDDFT calculations. These results suggest that in the wavelength region commonly used in strong-field experiments ($800$ nm and longer), our DFT-based WFAT treatment can be used to rapidly screen for the ionization properties of a large number of molecules as a function of alignment or orientation between the molecule and the strong field.

Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. To determine the relationship between a molecule's structure and the CM dynamics it exhibits, we perform systematic studies of para-functionalized bromobenzene molecules (X-C$_6$H$_4$-R) using real-time time-dependent density functional theory. We initiate valence-electron dynamics by emulating rapid strong-field ionization leading to a localized hole on the bromine atom. The resulting CM, which takes on the order of 1 fs, occurs via an X localized to C$_6$H$_4$ delocalized to R localized mechanism. Interestingly, the hole contrast on the acceptor functional group increases with increasing electron donating strength. This trend is well-described by the Hammett sigma value of the group, which is a commonly used metric for quantifying the effect of functionalization on the chemical reactivity of benzene derivatives. These results suggest that simple attochemistry principles and a density-based picture can be used to predict and understand CM., Comment: 5 pages, 3 figures

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, as the result of a nonlinear perpendicular current akin to a Hall current. Here, we theoretically characterize the anomalous HHG mechanism, via development of an ab-initio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two key characteristics of the anomalous harmonic yields: an overall increase with laser wavelength; and pronounced minima at certain intensities or wavelengths around which the emission time profiles drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from the competing interband harmonics, and thus pave way for the experimental identification and time-domain control of pure anomalous harmonics., Comment: 7 pages, 4 figures

We introduce high-harmonic sideband spectroscopy (HHSS) and show that it can be a robust probe of attosecond charge migration (CM) in a halogenated carbon-chain molecule. We simulate both the CM and harmonic-generation (HHG) dynamics using ab initio time-dependent density-functional theory. We find that CM dynamics initiated along the molecular backbone induces sidebands in the HHG spectrum driven by a delayed laser pulse that is polarized perpendicular to the molecular axis. Monitoring the spectrum as either the HHG laser frequency or the relative delay is scanned allows for the extraction of detailed information about the time-domain characteristics of the CM process., Comment: 8 pages, 7 figures

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS$_2$, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. This observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multi-band recombination dipoles.

High-harmonic generation (HHG) in solids has emerged in recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter and the atomic, molecular, and optics communities. It has exciting prospects for the engineering of new light sources and the probing of ultrafast carrier dynamics in solids, and the theoretical understanding of this process is of fundamental importance. This tutorial provides a hands-on introduction to the theoretical description of the strong-field laser-matter interactions in a condensed-phase system that give rise to HHG. We provide an overview ranging from a detailed description of different approaches to calculating the microscopic dynamics and how these are intricately connected to the description of the crystal structure, through the conceptual understanding of HHG in solids as supported by the semiclassical recollision model, and finally a brief description of how to calculate the macroscopic response. We also give a general introduction to the Berry phase, and we discuss important subtleties in the modelling of HHG, such as the choice of structure and laser gauges, and the construction of a smooth and periodic structure gauge for both nondegenerate and degenerate bands. The advantages and drawback of different structure and laser-gauge choices are discussed, both in terms of their ability to address specific questions and in terms of their numerical feasibility., Comment: 34 pages, 5 figures

We theoretically investigate electron-hole recollisions in high-harmonic generation (HHG) in band-gap solids irradiated by linearly and elliptically polarized drivers. We find that in many cases the emitted harmonics do not originate in electron-hole pairs created at the minimum band gap, where the tunneling probability is maximized, but rather in pairs created across an extended region of the Brillouin zone (BZ). In these situations, the analogy to gas-phase HHG in terms of the short- and long-trajectory categorizations is inadequate. Our analysis methodology comprises three complementary levels of theory: the numerical solutions to the semiconductor Bloch equations, an extended semiclassical recollision model, and a quantum wave packet approach. We apply this methodology to two general material types with representative band structures: a bulk system and a hexagonal monolayer system. In the bulk, the interband harmonics generated using elliptically-polarized drivers are found to originate not from tunneling at the minimum band gap $\Gamma$, but from regions away from it. In the monolayer system driven by linearly-polarized pulses, tunneling regions near different symmetry points in the BZ lead to distinct harmonic energies and emission profiles. We show that the imperfect recollisions, where an electron-hole pair recollide while being spatially separated, are important in both bulk and monolayer materials. The excellent agreement between our three levels of theory highlights and characterizes the complexity behind the HHG emission dynamics in solids, and expands on the notion of interband HHG as always originating in trajectories tunnelled at the minimum band gap. Our work furthers the fundamental understanding of HHG in periodic systems and will benefit the future design of experiments., Comment: 18 pages, 13 figures

We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a 3D time-dependent Schr\"odinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level 1s-3p transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states $1s^{-1}3p$ and $2p^{-1}3p$ occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar $1s^{-1}-2p^{-1}$ response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources., Comment: 14 pages, 11 figures

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges, and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: an 1D model of ZnO and the 2D monolayer hexagonal boron nitride (h-BN). The omittance of Berry connections or TDPs in the SBEs for h-BN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process, and are applicable to all strong-field matter simulations with SBEs.

We demonstrate a femtosecond enhancement cavity with a crossed-beam geometry for efficient generation and extraction of extreme-ultraviolet (XUV) frequency combs at a 154 MHz repetition rate. We achieve a record-high out-coupled power of 600 {\mu}W, directly usable for spectroscopy, at a wavelength of 97 nm. This corresponds to a >60% out-coupling efficiency. The XUV power scaling and generation efficiency are similar to that achieved with a single Gaussian-mode fundamental beam inside a collinear enhancement cavity. The noncollinear geometry also opens the door for the generation of isolated attosecond pulses at >100 MHz repetition rate., Comment: 13 pages, 5 figures

The interaction of strong near-infrared (NIR) laser pulses with wide-bandgap dielectrics produces high harmonics in the extreme ultraviolet (XUV) wavelength range. These observations have opened up the possibility of attosecond metrology in solids, which would benefit from a precise measurement of the emission times of individual harmonics with respect to the NIR laser field. Here we show that, when high-harmonics are detected from the input surface of a magnesium oxide crystal, a bichromatic probing of the XUV emission shows a clear synchronization largely consistent with a semiclassical model of electron-hole recollisions in bulk solids. On the other hand, the bichromatic spectrogram of harmonics originating from the exit surface of the 200 $\mu$m-thick crystal is strongly modified, indicating the influence of laser field distortions during propagation. Our tracking of sub-cycle electron and hole re-collisions at XUV energies is relevant to the development of solid-state sources of attosecond pulses.

Excitation of ionic solids with extreme ultraviolet pulses creates localized core-excitons, which in some cases couple strongly to the lattice. Here, core-excitonic states of magnesium oxide are studied in the time domain at the Mg $\text{L}_{2,3}$ edge with attosecond transient reflectivity spectroscopy. Attosecond pulses trigger the excitation of these short-lived quasiparticles, whose decay is perturbed by time-delayed near infrared optical pulses. Combined with a few-state theoretical model, this reveals that the optical pulse shifts the energy of bright core-exciton states as well as induces features arising from dark core-excitons. We report coherence lifetimes for the first two core-excitons of $2.3 \pm 0.2$ and $1.6 \pm 0.5$ femtoseconds and show that these short lifetimes are primarily a consequence of strong exciton-phonon coupling, disclosing the drastic influence of structural effects in this ultrafast relaxation process.

The extreme ultraviolet absorption spectrum of an atom is strongly modified in the presence of a synchronized intense infrared field. In this work we demonstrate control of the absorption properties of helium atoms dressed by an infrared pulse by changing the relative polarization of the infrared and extreme ultraviolet fields. Light-induced features associated with the dressed $1s2s$, $1s3s$ and $1s3d$ states, referred to as $2s^{+}$, $3s^{\pm}$ and $3d^{\pm}$ light induced states, are shown to be strongly modified or even eliminated when the relative polarization is rotated. The experimental results agree well with calculations based on the solution of the time-dependent Schr\"{o}dinger equation using a restricted excitation model that allows efficient treatment of the three dimensional problem. We also present an analysis of the light induced states based on Floquet theory, which allows for a simple explanation of their properties. Our results open a new route to creating controllable superpositions of dipole allowed and non-dipole allowed states in atoms and molecules.

Ultrafast processes in matter can be captured and even controlled by using sequences of few-cycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semiclassical three-step model for high-order harmonic generation., Comment: 17 pages, 8 figures, published on 16 January 2018

The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme ultraviolet range and bandwidths exceeding tens of eV. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely-used approximation consisting in writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argumentation uses a simple analytical model based on Gaussian optics, numerical propagation calculations and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high quality focusing while retaining the broadband/ultrashort characteristics of the radiation.

We present first-principles calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength regime, from $1-4$ $\mu$m. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility, and with measurements for the nonlinear susceptibility up to 2.4 $\mu$m. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow accurate calculations of the long-distance propagation of intense MIR laser pulses in air.

Coherent sources of attosecond extreme ultraviolet (XUV) radiation present many challenges if their full potential is to be realized. While many applications benefit from the broadband nature of these sources, it is also desirable to produce narrow band XUV pulses, or to study autoionizing resonances in a manner that is free of the broad ionization background that accompanies above-threshold XUV excitation. Here we demonstrate a method for controlling the coherent XUV free induction decay that results from using attosecond pulses to excite a gas, yielding a fully functional modulator for XUV wavelengths. We use an infrared (IR) control pulse to manipulate both the spatial and spectral phase of the XUV emission, sending the light in a direction of our choosing at a time of our choosing. This allows us to tailor the light using opto-optical modulation, similar to devices available in the IR and visible wavelength regions.

We investigate high-order harmonic generation in a solid, modeled as a multi-level system dressed by a strong infrared laser field. We show that the cutoff energies and the relative strengths of the multiple plateaus that emerge in the harmonic spectrum can be understood both qualitatively and quantitatively by considering a combination of adiabatic and diabatic processes driven by the strong field. Such a model was recently used to interpret the multiple plateaus exhibited in harmonic spectra generated by solid argon and krypton [Ndabashimiye {\it et al.}, Nature 534, 520 (2016)]. We also show that when the multi-level system originates from the Bloch state at the $\Gamma$ point of the band structure, the laser-dressed states are equivalent to the Houston states [Krieger {\it el al.} Phys. Rev. B 33, 5494 (1986)] and will therefore map out the band structure away from the $\Gamma$ point as the laser field increases. This leads to a semi-classical three-step picture in momentum space that describes the high-order harmonic generation process in a solid., Comment: 15 pages, 8 figures

We measure spectrally and spatially resolved high-order harmonics generated in argon using chirped multi-cycle laser pulses. Using a stable, high-repetition rate laser we observe detailed interference structures in the far-field. The structures are of two kinds; off-axis interference from the long trajectory only and on-axis interference including the short and long trajectories. The former is readily visible in the far-field spectrum, modulating both the spectral and spatial profile. To access the latter, we vary the chirp of the fundamental, imparting different phases on the different trajectories, thereby changing their relative phase. Using this method together with an analytical model, we are able to explain the on-axis behaviour and access the dipole phase parameters for the short (\(\alpha_s\)) and long (\(\alpha_l\)) trajectories. The extracted results compare very well with phase parameters calculated by solving the time-dependent Schr\"odinger equation. Going beyond the analytical model, we are also able to successfully reproduce the off-axis interference structure.

We investigate the role of excited states in High-order Harmonic Generation by studying the spectral, spatial and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct XUV emission through Free Induction Decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift., Comment: Accepted at Physical Review Letters

We investigate the evolution of extreme ultraviolet (XUV) spectral lineshapes in an optically-thick helium gas under near-infrared (IR) perturbation. In our experimental and theoretical work, we systematically vary the IR intensity, time-delay, gas density and IR polarization parameters to study lineshape modifications induced by collective interactions, in a regime beyond the single atom response of a thin, dilute gas. In both experiment and theory, we find that specific features in the frequency-domain absorption profile, and their evolution with propagation distance, can be attributed to the interplay between resonant attosecond pulse propagation and IR induced phase shifts. Our calculations show that this interplay also manifests itself in the time domain, with the IR pulse influencing the reshaping of the XUV pulse propagating in the resonant medium., Comment: 10 pages, 9 figures

We introduce a semi-classical wavefunction (SCWF) model for strong-field physics and attosecond science. When applied to high harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B. 43, 122001 (2010)]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.

We present a theoretical study of the influence of resonant enhancement on quantum path dynamics in the generation of harmonics above and below the ionization threshold in helium. By varying the wavelength and intensity of the driving field from 425 nm to 500 nm and from 30 TW/cm${^2}$ to 140 TW/cm${^2}$, respectively, we identify enhancements of harmonics 7, 9, and 11 that correspond to multiphoton resonances between the ground state and the Stark shifted $1s2p$, $1s3p$, and $1s4p$ excited states. A time-frequency analysis of the emission shows that both the short and long quantum path contributions to the harmonic yield are enhanced through these bound state resonances. We analyze the sub-cycle time structure of the 9th harmonic yield in the vicinity of the resonances and find that on resonance the long trajectory contribution is phase shifted by approximately $\pi/4$. Finally, we compare the single atom and the macroscopic response of a helium gas and find that while the sub-cycle time profiles are slightly distorted by propagation effects, the phase shift of the long trajectory contribution is still recognizable., Comment: 8 pages, 8 Figures

We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and subsequently to the appearance of new, narrow features in the absorption line., Comment: 5 pages, 5 figures

We study the generation of high harmonic radiation by Bloch electrons in a model transparent solid driven by a strong mid-infrared laser field. We solve the single-electron time-dependent Schr\"odinger equation (TDSE) using a velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494 (1986)], which allows us to separate inter-band and intra-band contributions to the time-dependent current. We find that the inter-band and intra-band contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under an unitary transformation but that, unlike the velocity gauge method, the Houston state treatment is numerically unstable when more than a few low lying energy bands are used.

The exact delay-zero calibration in an attosecond pump-probe experiment is important for the correct interpretation of experimental data. In attosecond transient absorption spectroscopy the determination of the delay-zero exclusively from the experimental results is not straightforward and may introduce significant errors. Here, we report the observation of quarter-laser-cycle (4{\omega}) oscillations in a transient absorption experiment in helium using an attosecond pulse train overlapped with a precisely synchronized, moderately strong infrared pulse. We demonstrate how to extract and calibrate the delay-zero with the help of the highly nonlinear 4{\omega} signal. A comparison with the solution of the time-dependent Schr\"odinger equation is used to confirm the accuracy and validity of the approach. Moreover, we study the mechanisms behind the quarter-laser-cycle and the better-known half-laser-cycle oscillations as a function of experimental parameters. This investigation yields an indication of the robustness of our delay-zero calibration approach., Comment: 15 pages, 10 figures

We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first involves multi photon transitions between bound states that result in interference between different excitation pathways. The other involves the modification of the bound state absorption lines by the IR field, which we find can result in a sub-cycle time dependence only when ionization limits the duration of the strong field interaction.

We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements.

We extend a model of two-center interference to include the superposition of opposite orientations in aligned polar molecules. We show that the position of the minimum in the harmonic spectrum from both aligned and oriented CO depends strongly on the relative recombination strength at different atoms, not just the relative phase. We reinterpret the minimum in aligned CO as an interference between opposite orientations, and obtain good agreement with numerical calculations. Inclusion of the first-order Stark effect shifts the position of the interference minimum in aligned CO even though aligned molecules do not posses total permanent dipoles. We explain the shift in terms of an extra phase that the continuum electron of oriented CO accumulates due to the Stark effect.

We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom response by calculating the frequency-dependent absorption cross section for XUV energies between 20 and 24 eV for several dressing wavelengths between 400 and 2000 nm and intensities up to 10^12 W/cm^2. We find that for dressing wavelengths near 1600 nm, there is an Autler-Townes splitting of the 1s ---> 2p transition that can potentially lead to transparency for absorption of XUV light tuned to this transition. We study the effect of this XUV transparency in a macroscopic helium gas by incorporating the time-frequency approach into a solution of the coupled Maxwell-Schr\"odinger equations. We find rich temporal reshaping dynamics when a 61 fs XUV pulse resonant with the 1s ---> 2p transition propagates through a helium gas dressed by an 11 fs, 1600 nm laser pulse., Comment: 13 pages, 8 figures, 1 table, RevTeX4, revised

Recent demonstrations of high-harmonic generation (HHG) at very high repetition frequencies (~100 MHz) may allow for the revolutionary transfer of frequency combs to the vacuum ultraviolet (VUV). This advance necessitates unifying optical frequency comb technology with strong-field atomic physics. While strong-field studies of HHG have often focused on above-threshold harmonic generation (photon energy above the ionization potential), for VUV frequency combs an understanding of below-threshold harmonic orders and their generation process is crucial. Here we present a new and quantitative study of the harmonics 7-13 generated below and near the ionization threshold in xenon gas. We show multiple generation pathways for these harmonics that are manifested as on-axis interference in the harmonic yield. This discovery provides a new understanding of the strong-field, below-threshold dynamics under the influence of an atomic potential and allows us to quantitatively assess the achievable coherence of a VUV frequency comb generated through below threshold harmonics. We find that under reasonable experimental conditions temporal coherence is maintained. As evidence we present the first explicit VUV frequency comb structure beyond the 3rd harmonic., Comment: 16 pages, 4 figures, 1 table

We study the temporal and spatial dynamics of the large amplitude and frequency modulation that can be induced in an intense, few cycle laser pulse as it propagates through a rapidly ionizing gas. Our calculations include both single atom and macroscopic interactions between the non-linear medium and the laser field. We analyze the harmonic generation by such pulses and show that it is spatially separated from the ionization dynamics which produce a large dynamical blue shift of the laser pulse. This means that small changes in the initial laser focusing conditions can lead to large differences in the laser frequency modulation, even though the generated harmonic spectrum remains essentially unchanged., Comment: 4 pages, 5 figures. Under revision