Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy.

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 high harmonic generation (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 a negligible contribution from the ionization step.

Characterizing Anomalous High-Harmonic Generation in Solids.

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, originating from a Berry-curvature-induced perpendicular anomalous current. The observation of pure anomalous harmonics is, however, often prohibited by contamination from harmonics stemming from interband coherences. Here, we fully 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 unique properties of the anomalous harmonic yields: an overall yield increase with laser wavelength; and pronounced minima at certain laser wavelengths and laser intensities around which the spectral phases drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from competing HHG mechanisms, and thus pave the way for the experimental identification and time-domain control of pure anomalous harmonics, as well as reconstruction of Berry curvatures.

Attochemistry Regulation of Charge Migration.

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-C6H4-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 → C6H4 delocalized → 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 σ 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.

Investigation of Interferences in Carbon Dioxide through Multidimensional Molecular-Frame High-Harmonic Spectroscopy.

We present molecular-frame high-harmonic spectroscopic measurements of the spectral intensity and group delay of carbon dioxide. Using four different driving wavelengths and a range of intensities at each wavelength for high-harmonic generation, we observe a well-characterized minimum in the harmonic emission that exhibits both a wavelength and intensity dependence. Using the intensity dependence at each driving wavelength, we classify the minimum as due to either a structural two-center interference or dynamic multichannel interference, consistent with previous literature. By additionally measuring the group delay at each driving wavelength and intensity, we find that the sign of the group delay excursion across the interference is an acute probe of the interference mechanism. The experimental results are confirmed by ab initio time-dependent density functional theory calculations of both the spectral intensity and the phase of the harmonic emission.

4D spatio-temporal electric field characterization of ultrashort light pulses undergoing filamentation.

We present an experimental method capable of capturing the complete spatio-temporal dynamics of filamenting ultrashort laser pulses. By employing spatially resolved Fourier transform spectrometry in combination with the capability to terminate the filament at any length, we can follow the nonlinear dynamics in four dimensions, i.e. the transverse domain, time and filament length. Our method thus not only enables the full characterization of the filamentation process throughout its evolution, but also allows to identify and select laser pulses with desired parameters.

Signatures of Multiband Effects in High-Harmonic Generation in Monolayer MoS_{2}.

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 multiband recombination dipoles.

Resonant Perfect Absorption Yielded by Zero-Area Pulses.

We propose and study the manipulation of the macroscopic transient absorption of an ensemble of open two-level systems via temporal engineering. The key idea is to impose an ultrashort temporal gate on the polarization decay of the system by transient absorption spectroscopy, thus confining its free evolution and the natural reshaping of the excitation pulse. The numerical and analytical results demonstrate that even at moderate optical depths, the resonant absorption of light can be reduced or significantly enhanced by more than 5 orders of magnitude relative to that without laser manipulation. The achievement of the quasicomplete extinction of light at the resonant frequency, here referred to as resonant perfect absorption, arises from the full destructive interference between the excitation pulse and its subpulses developed and tailored during propagation, and is revealed to be connected with the formation of zero-area pulses in the time domain.

Molecular Modes of Attosecond Charge Migration.

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes (∼1 eV) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed (∼4 Å/fs) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

Noncollinear Enhancement Cavity for Record-High Out-Coupling Efficiency of an Extreme-UV Frequency Comb.

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 µW, 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.

Attosecond Time-Domain Measurement of Core-Level-Exciton Decay in Magnesium Oxide.

Excitation of ionic solids with extreme ultraviolet pulses creates localized core-level excitons, which in some cases couple strongly to the lattice. Here, core-level-exciton states of magnesium oxide are studied in the time domain at the Mg 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 pulses. Combined with a few-state theoretical model, this reveals that the infrared pulse shifts the energy of bright (dipole-allowed) core-level-exciton states as well as induces features arising from dark core-level excitons. We report coherence lifetimes for the two lowest core-level excitons of 2.3±0.2 and 1.6±0.5 fs and show that these are primarily a consequence of strong exciton-phonon coupling, disclosing the drastic influence of structural effects in this ultrafast relaxation process.

Imperfect Recollisions in High-Harmonic Generation in Solids.

We theoretically investigate high-harmonic generation in hexagonal boron nitride with linearly polarized laser pulses. We show that imperfect recollisions between electron-hole pairs in the crystal give rise to an electron-hole-pair polarization energy that leads to a double-peak structure in the subcycle emission profiles. An extended recollision model (ERM) is developed that allows for such imperfect recollisions, as well as effects related to Berry connections, Berry curvatures, and transition-dipole phases. The ERM illuminates the distinct spectrotemporal characteristics of harmonics emitted parallel and perpendicularly to the laser polarization direction. Imperfect recollisions are a general phenomenon and a manifestation of the spatially delocalized nature of the real-space wave packet; they arise naturally in systems with large Berry curvatures, or in any system driven by elliptically polarized light.

Angle-dependent strong-field ionization of halomethanes.

We study, experimentally and theoretically, the ionization probability of singly halogenated methane molecules, CH3Cl and CH3Br, in intense linearly polarized 800 nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within the molecules, which are then ionized by the second, stronger pulse. The angle-dependent ionization yields are extracted from fits of the measured delay-dependent ionization signal to a superposition of moments of the rotational wave packet's angular distribution. Angle-dependent strong-field ionization (SFI) yields are also calculated using time-dependent density functional theory. Good agreement between measurements and theory is obtained. Interestingly, we find a marked difference between the angle-dependence of the ionization yields for these two halomethane species despite the similar structure of their highest occupied molecular orbitals. Calculations reveal that these differences are a result of multichannel (CH3Cl) vs single-channel (CH3Br) ionization and of increased hole localization on Br vs Cl. By adding calculations for CH3F, we can discern clear trends in the ionization dynamics with increasing halogen mass. These results are illustrative, as chemical functionalization and molecular alignment are likely to be important parameters for initiating and controlling charge migration dynamics via SFI.

High-harmonic spectroscopy of transient two-center interference calculated with time-dependent density-functional theory.

We demonstrate high-harmonic spectroscopy in many-electron molecules using time-dependent density-functional theory. We show that a weak attosecond-pulse-train ionization seed that is properly synchronized with the strong driving mid-infrared laser field can produce experimentally relevant high-harmonic generation (HHG) signals, from which we extract both the spectral amplitude and the target-specific phase (group delay). We also show that further processing of the HHG signal can be used to achieve molecular-frame resolution, i.e., to resolve the contributions from rescattering on different sides of an oriented molecule. In this framework, we investigate transient two-center interference in CO2 and OCS, and how subcycle polarization effects shape the oriented/aligned angle-resolved spectra.

Nonlinear XUV signal generation probed by transient grating spectroscopy with attosecond pulses.

Nonlinear spectroscopies are utilized extensively for selective measurements of chemical dynamics in the optical, infrared, and radio-frequency regimes. The development of these techniques for extreme ultraviolet (XUV) light sources facilitates measurements of electronic dynamics on attosecond timescales. Here, we elucidate the temporal dynamics of nonlinear signal generation by utilizing a transient grating scheme with a subfemtosecond XUV pulse train and two few-cycle near-infrared pulses in atomic helium. Simultaneous detection of multiple diffraction orders reveals delays of ≥1.5 fs in higher-order XUV signal generation, which are reproduced theoretically by solving the coupled Maxwell-Schrödinger equations and with a phase grating model. The delays result in measurable order-dependent differences in the energies of transient light induced states. As nonlinear methods are extended into the attosecond regime, the observed higher-order signal generation delays will significantly impact and aid temporal and spectral measurements of dynamic processes.

Spatiotemporal coupling of attosecond pulses.

The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme UV range and bandwidths exceeding tens of electronvolts. 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 of 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 argument 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.

Spatiotemporal filtering of high harmonics in solids.

We study the macroscopic spatial and temporal properties of harmonic radiation generated by a model solid in the interaction with an intense, focused laser beam. We show that different temporal contributions to the harmonic yield can be separated in the spatial domain because they lead to radiation with different divergences, similar to what is observed in gas-phase harmonic generation. We show that applying a spatial filter in the far field results in a temporal separation of the two contributions upon refocusing, which yields spatially collimated harmonics, a spectrum with well-resolved peaks, and a subcycle time profile of the harmonic radiation with only one burst per half-cycle.

Controlling attosecond transient absorption with tunable, non-commensurate light fields.

We demonstrate a transient absorption scheme that uses a fixed-spectrum attosecond pulse train in conjunction with a tunable probe laser to access a wide range of nonlinear light-atom interactions. We exhibit control over the time-dependent Autler-Townes splitting of the 1s4p absorption line in helium, and study its evolution from a resonant doublet to a light-induced sideband with changing probe wavelength. The non-commensurate probe also allows for the background-free study of two-infrared-photon emission processes in a collinear geometry. Using this capability, we observe two different emission pathways with non-trivial delay dependencies, one prompt and the other delayed. We identify the nonlinear processes underlying these emissions by comparing the experimental results to calculations based on the time-dependent Schrödinger equation.

Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State.

We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.

Laser waveform control of extreme ultraviolet high harmonics from solids.

Solid-state high-harmonic sources offer the possibility of compact, high-repetition-rate attosecond light emitters. However, the time structure of high harmonics must be characterized at the sub-cycle level. We use strong two-cycle laser pulses to directly control the time-dependent nonlinear current in single-crystal MgO, leading to the generation of extreme ultraviolet harmonics. We find that harmonics are delayed with respect to each other, yielding an atto-chirp, the value of which depends on the laser field strength. Our results provide the foundation for attosecond pulse metrology based on solid-state harmonics and a new approach to studying sub-cycle dynamics in solids.

Solid-state harmonics beyond the atomic limit.

Strong-field laser excitation of solids can produce extremely nonlinear electronic and optical behaviour. As recently demonstrated, this includes the generation of high harmonics extending into the vacuum-ultraviolet and extreme-ultraviolet regions of the electromagnetic spectrum. High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases. How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate. Here we report a direct comparison of high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron-hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.