Search

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

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation and strong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFAT relied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation in Gaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integral representation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating its implementation in standard quantum chemistry packages. The integral reformulation introduced here is therefore much more robust when applied to molecules with arbitrary geometry. We present several case studies, among which is the CO molecule where some earlier theories disagree with experiments. Here, we find that ME-WFAT produces the largest ionization probability when the field points from C to O, as experiments suggest. An attractive feature of ME-WFAT is that it can be used with various types of multielectron methods whether of density functional [Phys. Rev. A 106, 052211 (2022)] or multiconfiguration types, this in turn facilitates tunnel ionization calculation in systems exhibiting a strong multireference character., Comment: 20 pages and 6 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

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

Attosecond pulses are fundamental for the investigation of valence and core-electron dynamics on their natural timescale. At present the reproducible generation and characterisation of attosecond waveforms has been demonstrated only through the process of high-order harmonic generation. Several methods for the shaping of attosecond waveforms have been proposed, including metallic filters, multilayer mirrors and manipulation of the driving field. However, none of these approaches allow for the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free Electron Lasers, on the contrary, deliver femtosecond, extreme ultraviolet and X-ray pulses with energies ranging from tens of $\mathrm{\mu}$J to a few mJ. Recent experiments have shown that they can generate sub-fs spikes, but with temporal characteristics that change shot-to-shot. Here we show the first demonstration of reproducible generation of high energy ($\mathrm{\mu}$J level) attosecond waveforms using a seeded Free Electron Laser. We demonstrate amplitude and phase manipulation of the harmonic components of an attosecond pulse train in combination with a novel approach for its temporal reconstruction. The results presented here open the way to perform attosecond time-resolved experiments with Free Electron Lasers.

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.

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

Ionization with ultrashort pulses in the extreme ultraviolet (XUV) regime can be used to prepare an ion in a superposition of spin--orbit substates. In this work, we study the coherence properties of such a superposition, created by ionizing xenon atoms using two phase-locked XUV pulses at different frequencies. In general, if the duration of the driving pulse exceeds the quantum beat period, dephasing will occur. If however, the frequency difference of the two pulses matches the spin--orbit splitting, the coherence can be efficiently increased and dephasing does not occur.

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

Strong-field phenomena driven by an intense infrared (IR) laser depend on during what part of the field cycle they are initiated. By changing the sub-cycle character of the laser electric field it is possible to control such phenomena. For long pulses, sub-cycle shaping of the field can be done by adding a relatively weak, second harmonic of the driving field to the pulse. Through constructive and destructive interference, the combination of strong and weak fields can be used to change the probability of a strong-field process being initiated at any given part of the cycle. In order to control sub-cycle phenomena with optimal accuracy, it is necessary to know the phase difference of the strong and the weak fields precisely. If the weaker field is an even harmonic of the driving field, electrons ionized by the field will be asymmetrically distributed between the positive and negative directions of the combined fields. Information about the asymmetry can yield information about the phase difference. A technique to measure asymmetry for few-cycle pulses, called Stereo-ATI (Above Threshold Ionization), has been developed by [Paulus G G, et al 2003 Phys. Rev. Lett. 91]. This paper outlines an extension of this method to measure the phase difference between a strong IR and its second harmonic.

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 study theoretically the quantum dynamics of nitrogen molecules (N$_2$) exposed to intense and ultrafast x-rays at a wavelength of 1.1 nm (1100 eV photon energy) from the Linac Coherent Light Source (LCLS) free electron laser. Molecular rate equations are derived to describe the intertwined photoionization, decay, and dissociation processes occurring for N$_2$. This model complements our earlier phenomenological approaches, the single-atom, symmetric-sharing, and fragmentation-matrix models of J. Chem. Phys. $\mathbf{136}$, 214310 (2012). Our rate-equations are used to obtain the effective pulse energy at the sample and the time scale for the dissociation of the metastable dication N$_2^{2+}$. This leads to a very good agreement between the theoretically and experimentally obtained ion yields and, consequently, the average charge states. The effective pulse energy is found to decrease with shortening pulse duration. This variation together with a change in the molecular fragmentation pattern and frustrated absorption---an effect that reduces absorption of x-rays due to (double) core hole formation---are the causes for the drop of the average charge state with shortening LCLS pulse duration discovered previously., Comment: 23 pages, 4 figures, 1 table, LaTeX

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 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

We examine the archetype of an interference experiment for Auger electrons: two electron wave packets are launched by inner-shell ionizing a krypton atom using two attosecond light pulses with a variable time delay. This setting is an attosecond realization of the Ramsey method of separated oscillatory fields. Interference of the two ejected Auger-electron wave packets is predicted, indicating that the coherence between the two pulses is passed to the Auger electrons. For the detection of the interference pattern an accurate coincidence measurement of photo- and Auger electrons is necessary. The method allows one to control inner-shell electron dynamics on an attosecond timescale and represents a sensitive indicator for decoherence., Comment: 5 pages, 5 figures, RevTeX4.1, revised

We devise an ab initio formalism for the quantum dynamics of Auger decay by laser-dressed atoms which are inner-shell ionized by extreme ultraviolet (XUV) light. The optical dressing laser is assumed to be sufficiently weak such that ground-state electrons are neither excited nor ionized by it. However, the laser has a strong effect on continuum electrons which we describe in strong-field approximation with Volkov waves. The XUV light pulse has a low peak intensity and its interaction is treated as a one-photon process. The quantum dynamics of the inner-shell hole creation with subsequent Auger decay is given by equations of motion (EOMs). For this paper, the EOMs are simplified in terms of an essential-states model which is solved analytically and averaged over magnetic subshells. We apply our theory to the M_4,5 N_1 N_2,3 Auger decay of a 3d hole in a krypton atom. The orbitals are approximated by scaled hydrogenic wave functions. A single attosecond pulse produces 3d vacancies which Auger decay in the presence of an 800nm laser with an intensity of 10^13 W / cm^2. We compute the Auger electron spectrum and assess the convergence of the various quantities involved., Comment: 19 pages, 7 figures, 1 table, RevTeX4

Using attoscience, we study the electron correlations responsible for Auger decay in krypton atoms. The Auger decay is induced by a pulse train or a twin pulse composed of subpulses of attosecond duration. During the Auger decay an optical dressing laser may be present. Interference effects between the ejected Auger electron wave packets are predicted., Comment: 1 page, 1 figure, OOXML, accepted by Journal of Physics B

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