Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production

Quasi-phase-matching of resonance-enhanced high-order harmonics in laser plasmas

The resonance-enhanced harmonics in laser-induced arsenic and selenium plasmas are studied at the quasi-phase-matching (QPM) conditions. We demonstrate that the enhancement of these harmonics was significantly smaller than the one of the neighboring harmonics. Though the enhancement factors of the harmonics in the vicinity of resonance-enhanced harmonics were in the range of 5× to 18×, the resonance-enhanced harmonics were almost unenhanced at QPM conditions. The most probable reason for such restriction in the enhancement of specific harmonics at the conditions of QPM was a stronger influence of free electrons on the phase-matching conditions of the resonance-enhanced single harmonic compared to the QPM-enhanced group of harmonics.

High-order harmonics enhancement in laser-induced plasma

The methods of enhancement of the strong high-order harmonics of femtosecond pulses in laser-induced plasma are demonstrated. It comprises the application of the four techniques allowing the enhancement of harmonics in different spectral ranges. Among them are the selection of targets for ablation to create the conditions for resonance enhancement of single harmonic, formation of the quasi-phase-matching of a spectrally tunable group of harmonics, application of the two-color pump of plasma, and the formation of nanoparticles-contained plasmas. The number of generated coherent XUV photons increased in the region of single resonantly enhanced harmonic (62 nm) and the shorter-wavelength region (30-50 nm). The above techniques of harmonics enhancement allowed a significant (up to 50 times) growth in a whole harmonic yield in the case of indium plasma. We discuss the reasons preventing the joint implementation of the four methods of harmonics enhancement in the same spectral region.

Extension of high-order harmonic generation cutoff from laser-ablated tin plasma plumes

The high-order harmonic spectra from laser-ablated tin plasma plumes are investigated experimentally and theoretically at different laser wavelengths. It is found that the harmonic cutoff is extended to ∼84 eV and the harmonic yield is greatly improved by decreasing the driving laser wavelength from 800 nm to 400 nm. Appling the Perelomov-Popov-Terent'ev theory with the semiclassical cutoff law and one-dimensional time-dependent Schrödinger equation, the contribution of the Sn³⁺ ion to harmonic generation accounts for the cutoff extension at 400 nm. With the qualitative analysis of the phase mismatching effect, we reveal the phase matching caused by the dispersion of free electrons is greatly optimized in the 400 nm driving field relative to the 800 nm driving field. The high-order harmonic generated from laser-ablated tin plasma plumes driven by the short laser wavelength provides a promising way to extend cutoff energy and generate intensely coherent extreme ultraviolet radiation.

High-Order Harmonics Generation in MoS2 Transition Metal Dichalcogenides: Effect of Nickel and Carbon Nanotube Dopants

The transition metal dichalcogenides have instigated a lot of interest as harmonic generators due to their exceptional nonlinear optical properties. Here, the molybdenum disulfide (MoS2) molecular structures with dopants being in a plasma state are used to demonstrate the generation of intense high-order harmonics. The MoS2 nanoflakes and nickel-doped MoS2 nanoflakes produced stronger harmonics with higher cut-offs compared with Mo bulk and MoS2 bulk. Conversely, the MoS2 with nickel nanoparticles and carbon nanotubes (MoS2-NiCNT) produced weaker coherent XUV emissions than other materials, which is attributed to the influence of phase mismatch. The influence of heating and driving pulse intensities on the harmonic yield and cut-off energies are investigated in MoS2 molecular structures. The enhanced coherent extreme ultraviolet emission at ~32 nm (38 eV) due to the 4p-4d resonant transitions is obtained from all aforementioned molecular structures, except for MoS2-NiCNT.

Ultrafast Resonant State Formation by the Coupling of Rydberg and Dark Autoionizing States

Studying the dynamics of dark states is challenging due to their inability to undergo single-photon emission or absorption. This challenge is made even more difficult for dark autoionizing states owing to their ultrashort lifetime of a few femtoseconds. High-order harmonic spectroscopy recently appeared as a novel method to probe the ultrafast dynamics of a single atomic or molecular state. Here, we demonstrate the emergence of a new type of ultrafast resonance state as a manifestation of coupling between Rydberg and a dark autoionizing state dressed by a laser photon. Through high-order harmonic generation, this resonance results in extreme ultraviolet light emission that is more than one order of magnitude stronger than for the off-resonance case. The induced resonance can be leveraged to study the dynamics of a single dark autoionizing state and the transient changes in the dynamics of real states due to their overlap with the virtual laser-dressed states. In addition, the present results allow the generation of coherent ultrafast extreme ultraviolet light for advanced ultrafast science applications.

Recent Advances in the Study of Negative-Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

The transient resonances are a challenge to bound state quantum mechanics. These states lie in the continuum part of the spectrum of the Hamiltonian. For this, one has to treat a continuum problem due to electron-molecule scattering and the many-electron correlation problem simultaneously. Moreover, the description of a resonance requires a wavefunction that bridges the part that resembles a bound state with another that resembles a continuum state such that the continuity of the wavefunction and its first derivative with respect to the distance between the incoming projectile and the target is maintained. A review of the recent advances in the theoretical investigation of the negative-ion resonances (NIR) is presented. The NIRs are ubiquitous in nature. They result from the scattering of electrons off of an atomic or molecular target. They are important for numerous chemical processes in upper atmosphere, space and even biological systems. A contextual background of the existing theoretical methods as well as the newly-developed multiconfigurational propagator tools based on a complex absorbing potential are discussed.

High-order harmonics generation in nanosecond-pulses-induced plasma containing Ni-doped CsPbBr3perovskite nanocrystals using chirp-free and chirped femtosecond pulses

We demonstrate high-order harmonic generation in Ni-doped CsPbBr₃perovskite nanocrystals ablated by nanosecond pulses using chirp-free 35 fs, and chirped 135 fs pulses in the case of single-color pump (800 nm) and a two-color pump (800 and 400 nm). We analyzed the spectral shift, cut-off, and intensity distribution of harmonics in the case of chirped drving pulses compared to chirp-free pulses. It is shown that the presence of Ni dopants and CsPbBr₃plasma components improves the harmonics emission. Also, we measured the third-order nonlinear optical (NLO) properties of these nanocrystals using 800 nm, 60 fs, 1 kHz pulses. The variations of measured NLO parameters of CsPbBr₃perovskite nanocrystals containing different concentrations of nickel correlate with variations of generated high-order harmonics from laser induced plasmas of studied nanocrystals in terms of harmonics intensity, cut-off, and spectral shift (in case of chirped driving pulses). The spectral shift of the harmonics generated from the Ni-doped CsPbBr₃perovskite nanocrystals can be used to form tunable extreme ultraviolet sources.

Application of Box and Voronoi CAPs for Metastable Electronic States in Molecular Clusters

The complex absorbing potential (CAP) approach offers a practical tool for characterization of energies and lifetimes of metastable electronic states, such as temporary anions and core ionized states. Here, we present an implementation of the smooth Voronoi CAP combined with the equation-of-motion coupled cluster with single and double substitutions method for metastable states. The performances of the smooth Voronoi CAP and box CAP are compared for different classes of systems: resonances in isolated molecules and localized and delocalized resonances in molecular clusters. The benchmark calculations show that the Voronoi CAP is generally more robust when applied to molecular clusters, but box CAPs are equally reliable for localized resonances or in the cases when the resonance does not exhibit significant electron density delocalization into the intramolecular region. As such, the choice of the CAP shape and onset should be guided by the character of the metastable states.

Investigation of high-harmonic cutoff of metal ions driven by near-infrared laser

The cutoff-energies of high-harmonic generation in the laser-ablated plumes of various metal targets (Ca, Mg, Fe, Zn, Ta, Mo, Al, W, In, Cu, Au, Ti, Ag) driven by near-infrared (0.8-µm) femtosecond laser are investigated and compared. Due to the low ionization potentials of metal atoms, it is believed that the observed high-harmonic cutoffs are contributed by the singly charged or even doubly charged ions. Ionization calculations using Perelomov-Popov-Terent'ev theory are performed to estimate the laser intensities at which saturation of ionization occur for different ions. Treating the calculated values as the effective driving laser intensities, the observed cutoffs from most of the targets are in reasonable agreement with the predictions of the semi-classical cutoff law.

Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

Distinguishing monomer and nanoparticle contributions to high-harmonic emission from laser-ablated plumes

Nano-clusters and nano-particles (NPs) are attractive media for high-harmonic generation (HHG) since they combine the advantages of using atomic media (for the low average density) and bulk solid media (for the high local density). Recently, laser ablated plumes from metal nano-powders have been used as HHG media and it has been often assumed that the harmonics mainly come from the NPs in the plumes but not by the isolated atoms/ions. However, this assumption is yet to be fully justified. Here, we show that in fact both NPs and isolated monomers could dominate the harmonic spectrum, depending on which part of the plume is interacting with the driving laser. From the ablated plume of indium NPs, it is found that the harmonic spectra from the region where monomers dominate are distinctively different from the region where NPs dominate. Our results demonstrate that accurately capturing the contribution of NPs in HHG processes requires precise selection of the laser-plasma interaction region, a factor that had not been carefully considered in previous studies.

Resonance-enhanced high harmonic in metal ions driven by elliptically polarized laser pulses

Resonance enhancement of a single order harmonic has been a main attractive feature in high-harmonic generation from laser ablated plumes of metals. Although it has been extensively investigated experimentally and theoretically, studies so far have focused only on linearly polarized driving fields. In this Letter, we study the dependence of the resonant harmonic yield in tin ions on the driving laser ellipticity. We find that the resonance leads to a less rapid decay of the harmonic yield as a function of driving ellipticity, and it is qualitatively reproduced by quantum mechanical simulations. To the best of our knowledge, our findings provide a new type of evidence for supporting previously proposed mechanisms for enhancement.

Revealing Molecular Strong Field Autoionization Dynamics

The novel strong field autoionization (SFAI) dynamics is identified and investigated by channel-resolved angular streaking measurements of two electrons and two ions for the double-ionized CO. Comparing with the laser-assisted autoionization calculations, we demonstrate the electrons from SFAI are generated from the field-induced decay of the autoionizing state with a following acceleration in the laser fields. The energy-dependent photoelectron angular distributions further reveal that the subcycle ac-Stark effect modulates the lifetime of the autoionizing state and controls the emission of SFAI electrons in molecular frame. Our results pave the way to control the emission of resonant high-harmonic generation and trace the electron-electron correlation and electron-nuclear coupling by strong laser fields. The lifetime modulation of quantum systems in the strong laser field has great potential for quantum manipulation of chemical reactions and beyond.

Reexamining Different Factors of the Resonance-Enhanced High-Order Harmonic Generation in Atomic and Nanoparticle Laser-Induced Tin Plasmas

We reexamine the resonance enhancement of a single harmonic emission during the propagation of ultrafast pulses through atomic and nanoparticle tin-containing laser-induced plasma (LIP). We compare the single atomic Sn and Sn nanoparticle plasmas to demonstrate a distinction in the enhancement factor of the single harmonic in the case of fixed and tunable near-infrared pulses. The analysis of the dynamics of Sn LIP shows the range of optimal delays between heating and driving pulses (130–180 ns), at which the maximal harmonic yield can be achieved. The enhancements of the 17th and 18th harmonics of 806 nm pulses were analyzed in the case of single-color and two-color pumps of LIP, showing up to a 12-fold enhancement of even harmonics in the two-color pump case. We show the enhancement of a single harmonic in the vicinity of the 4d105s25p2P3/2→4d95s25p2 transitions of Sn II ions and demonstrate how this process depends on the constituency of the plasma components at different conditions of target ablation. The application of tunable (1280–1440 nm) radiation allows for demonstrating the variations of single harmonic enhancement using a two-color pump of Sn-containing LIP.

High-Order Harmonics Generation in Atomic and Molecular Zinc Plasmas

We demonstrate the variations of single harmonic resonance enhancement during high-order harmonics generation in zinc-containing atomic and molecular species at the conditions of single-color and two-color pumps of laser-induced plasmas by applying different laser sources. We show how selenides of this metal notably modify the enhancement of single (9th, 15th or 16th) harmonic compared with purely atomic zinc plasmas. The variations of single harmonic enhancement are demonstrated using fixed (806 nm) and tunable (1280–1440 nm) radiation.

Investigation of Resonance-Enhanced High-Order Harmonics by Two-Component Laser-Produced Plasmas

Resonance-enhanced harmonics from laser-produced plasma plumes are an interesting phenomenon, whose underlying mechanism is still under debate. In particular, it is unclear whether the macroscopic dispersion properties of the plasma are the key factors for the formation of the enhancement. To shed light on this problem, we perform experiments with two-component plasmas, in which one of the components (tin) is known to be able to generate enhanced harmonics and the other component (lead) is known for altering the overall dispersion properties of the plasma medium. We compare the harmonics spectra from the plasma of pure tin and the plasma of tin/lead alloy. Depending on the driving wavelength, we observe enhanced harmonics at around 47 or 44 nm in both types of plasmas. The two enhanced regions could be attributed to resonances in singly-charged and doubly-charged tin ions, respectively. Our results indicate that the co-existence of lead plasma does not destroy the presence of the enhanced harmonics of tin plasma, and it seems to suggest that the macroscopic properties of the plasma are not the origin of the resonance-enhanced harmonics in tin.

Negative Ion Resonance States: The Fock-Space Coupled-Cluster Way

The negative ion resonance states, which are electron-molecule metastable compound states, play the most important role in free-electron controlled molecular reactions and low-energy free-electron-induced DNA damage. Their electronic structure is often only poorly described but crucial to an understanding of their reaction dynamics. One of the most important challenges to current electronic structure theory is the computation of negative ion resonance states. As a major step forward, coupled-cluster theories, which are well-known for their ability to produce the best approximate bound state electronic eigen solutions, are upgraded to offer the most accurate and effective approximations for negative ion resonance states. The existing Fock-space coupled-cluster (FSCC) and the equation-of-motion coupled-cluster (EOM-CC) approaches that compute bound states are redesigned for the direct and simultaneous determination of both the kinetic energy of the free electron at which the electron-molecule compound states are resonantly formed and the corresponding autodetachment decay rate of the electron from the metastable compound state. This Feature Article reviews the computation of negative ion resonances using the FSCC approach and, in passing, provides the highlights of the equivalent EOM-CC approach.

Application of 150 kHz Laser for High-Order Harmonic Generation in Different Plasmas

Application of high pulse repetition rate lasers opens the way for increasing the average flux of the high-order harmonics generating in the ions- and nanoparticles-containing plasmas ablated on the surfaces of various metal targets. We demonstrate the harmonic generation of 37 fs, 150 kHz, 1030 nm, 0.5 mJ pulses in different plasmas. The formation of plasma plumes on the surfaces of carbon, titanium, boron, zinc, and manganese targets was performed during laser ablation, using 250 fs pulses from the same laser. The ablation of the mixed powder of boron nanoparticles and silver microparticles was used for generation of harmonics with high yield. Harmonics up to the fortieth orders from the carbon plasma were obtained. The estimated conversion efficiencies in laser-produced plasmas were ≤10−5. The photon flux for a single harmonic generating in carbon plasma was estimated to be 8 × 1013 photons/s.

Ab Initio Complex Transition Dipoles between Autoionizing Resonance States from Real Stabilization Graphs

Electronic transition dipoles are crucial for investigating light-matter interactions. Transition dipoles between metastable (autoionizing resonance) states become complex within non-Hermitian formalism, analogous to the resonance energies. Herein, we put forward a robust method for evaluating complex transition dipoles based on real ab initio stabilization calculations. The complex transition dipoles are obtained by analytical continuation via the Padé approximant and are identified as stationary solutions in the complex plane. The capability of the new approach is demonstrated for several transition dipoles of the doubly excited helium resonance states, for which exact values are available for comparison. Nevertheless, the method presented here has no inherent limitation and is suitable for polyatomic systems.

Laser Control of Resonance Tunneling via an Exceptional Point

According to the familiar Breit-Wigner formula, tunneling through a potential barrier is strongly enhanced when the energy of the projectile is equal to the resonance energy. Here we show how a weak continuous wave laser can qualitatively change the character of resonance tunneling, and enforce a sudden and total suppression of the transmission by inducing an exceptional point (EP, special non-Hermitian degeneracy). Our findings are relevant not only for laser control of transmission in the resonance tunneling diodes, but also in the context of electron scattering through any type of metastable (e.g., autoionization, Auger, intermolecular Coulombic decay) atomic or molecular states, and even in the case of transmission of light or sound waves in active systems with gain and loss.

Probing ultrafast dynamics of chiral molecules using time-resolved photoelectron circular dichroism

Measuring the ultrafast dynamics of chiral molecules in the gas phase has been a long standing and challenging quest of molecular physics. The main limitation to reach that goal has been the lack of highly sensitive chiroptical measurement. By enabling chiral discrimination with up to several 10% of sensitivity, photoelectron circular dichroism (PECD) offers a solution to this issue. However, tracking ultrafast processes requires measuring PECD with ultrashort light pulses. Here we compare the PECD obtained with different light sources, from the extreme ultraviolet to the mid-infrared range, leading to different ionization regimes: single-photon, resonance-enhanced multiphoton, above-threshold and tunnel ionization. We use single and multiphoton ionization to probe the ultrafast relaxation of fenchone molecules photoexcited in their first Rydberg states. We show that time-resolved PECD enables revealing dynamics much faster than the population decay of the Rydberg states, demonstrating the high sensitivity of this technique to vibronic relaxation.

Harmonic Generation from Neutral Manganese Atoms in the Vicinity of the Giant Autoionization Resonance

High harmonics from laser-ablated plumes are mostly generated from ionic species. We demonstrate that with ultrashort infrared (∼1.82  μm) driving lasers, high harmonics from laser-ablated manganese are predominantly generated from neutral atoms, a transition metal atom with an ionization potential of 7.4 eV. Our results open the possibility to advance laser-ablation technique to study the dynamics of neutral atoms of low ionization potential. Moreover, as manganese contains giant autoionizing resonance, intense and broadband high harmonics have been demonstrated from this resonance at energies from 49 to 53 eV. This opens the possibility to generate intense attosecond pulses directly from the giant resonances, as well as to study these resonances using high-harmonic spectroscopy.

Chirp-control of resonant high-order harmonic generation in indium ablation plumes driven by intense few-cycle laser pulses

We have studied high-order harmonic generation (HHG) in an indium ablation plume driven by intense few-cycle laser pulses centered at 775 nm as a function of the frequency chirp of the laser pulse. We found experimentally that resonant emission lines between 19.7 eV and 22.3 eV (close to the 13th and 15th harmonic of the laser) exhibit a strong, asymmetric chirp dependence, with pronounced intensity modulations. The chirp dependence is reproduced by our numerical time-dependent Schrödinger equation simulations of a resonant HHG by the model indium ion. As demonstrated with our separate simulations of HHG within the strong field approximation, the resonance can be understood in terms of the chirp-dependent HHG photon energy coinciding with the energy of an autoionizing state to ground state transition with high oscillator strength. This supports the validity of the general theory of resonant four-step HHG in the few-cycle limit.

Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.

High-order harmonic generation from the dressed autoionizing states

In high-order harmonic generation, resonant harmonics (RH) are sources of intense, coherent extreme-ultraviolet radiation. However, intensity enhancement of RH only occurs for a single harmonic order, making it challenging to generate short attosecond pulses. Moreover, the mechanism involved behind such RH was circumstantial, because of the lack of direct experimental proofs. Here, we demonstrate the exact quantum paths that electron follows for RH generation using tin, showing that it involves not only the autoionizing state, but also a harmonic generation from dressed-AIS that appears as two coherent satellite harmonics at frequencies ±2Ω from the RH (Ω represents laser frequency). Our observations of harmonic emission from dressed states open the possibilities of generating intense and broadband attosecond pulses, thus contributing to future applications in attosecond science, as well as the perspective of studying the femtosecond and attosecond dynamics of autoionizing states.

High-energy photons in XUV range and attosecond pulses are generated from infrared laser pulses through high harmonic generation in gases and solids. Here, the authors demonstrate the microscopic origin of resonant harmonic generation involving the autoionizing states of Sn in plasma plumes.

Sub-cycle ionization dynamics revealed by trajectory resolved, elliptically-driven high-order harmonic generation

The sub-cycle dynamics of electrons driven by strong laser fields is central to the emerging field of attosecond science. We demonstrate how the dynamics can be probed through high-order harmonic generation, where different trajectories leading to the same harmonic order are initiated at different times, thereby probing different field strengths. We find large differences between the trajectories with respect to both their sensitivity to driving field ellipticity and resonant enhancement. To accurately describe the ellipticity dependence of the long trajectory harmonics we must include a sub-cycle change of the initial velocity distribution of the electron and its excursion time. The resonant enhancement is observed only for the long trajectory contribution of a particular harmonic when a window resonance in argon, which is off-resonant in the field-free case, is shifted into resonance due to a large dynamic Stark shift.

Role of Excited States In High-order Harmonic Generation

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 extreme ultraviolet 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.

Mollow sidebands in high order harmonic spectra of molecules

Novel feature of high order harmonic generation process for molecules is presented for several molecules at their equilibrium geometries. The high order harmonic spectra reveal additional sidebands for each odd harmonic, which are a consequence of the resonant coupling of two valence orbitals, a mechanism analogous to Mollow triplets known from quantum optics. Strong modification of the high order harmonic generation process is illustrated with time frequency analysis in which there appear additional minima dependent on the Rabi frequency for the corresponding transition. The orbital coupling further leads to the modification of the electron dynamics which is presented using total electron density difference maps.

Discriminating between the Role of Phase Matching and that of the Single-Atom Response in Resonance Plasma-Plume High-Order Harmonic Generation

Resonance enhancement of high-order harmonic generation has recently been found in the interaction of intense ultrashort laser pulses with laser ablated plasma plumes. It is a promising route towards the production of an intense and coherent extreme ultraviolet radiation source. However, the mechanism of this resonance enhancement is still not clear. There are two possible explanations; one relies on a better recombination cross section through an autoionization state in the single-atom response. The other relies on improved phase matching conditions around the resonance. Here, we try to discriminate between these two conjectures by measuring coherence lengths of the harmonics, both on resonance and off resonance. Our findings support the single-atom response hypothesis.

Multi-channel electronic and vibrational dynamics in polyatomic resonant high-order harmonic generation

High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF6 as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20-26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected.

Enhancing the macroscopic yield of narrow-band high-order harmonic generation by Fano resonances

Resonances in the photoabsorption spectrum of the generating medium can modify the spectrum of high-order harmonics. In particular, window-type Fano resonances can reduce photoabsorption within a narrow spectral region and, consequently, lead to an enhanced emission of high-order harmonics in absorption-limited generation conditions. For high harmonic generation in argon it is shown that the 3s3p(6)np(1)P(1) window resonances (n = 4, 5, 6) give rise to enhanced photon yield. In particular, the 3s3p(6)4p(1)P(1) resonance at 26.6 eV allows a relative enhancement up to a factor of 30 in a 100 meV bandwidth compared to the characteristic photon emission of the neighboring harmonic order. This enhanced, spectrally isolated, and coherent photon emission line has a relative energy bandwidth of only ΔE/E = 3 × 10(-3). Therefore, it might be very useful for applications such as precision spectroscopy or coherent diffractive imaging. The presented mechanism can be employed for tailoring and controlling the high harmonic emission of manifold target materials.

Mechanisms of below-threshold harmonic generation in atoms

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

Enhancement of high harmonics from plasmas using two-color pump and chirp variation of 1 kHz Ti:sapphire laser pulses

We have investigated resonance effects in high-order harmonic generation (HHG) within laser-produced plasmas. We demonstrate a significantly improved harmonic yield by using two-color pump-induced enhancement and a 1 kHz pulse repetition rate. Together with an increased HHG output, the even harmonics in the cutoff region were enhanced with respect to odd harmonics. We report the observation of a resonance-induced growth in intensity of 20th harmonic in silver plasma (2×), 26th harmonic in vanadium plasma (4×), and 28th harmonic in chromium plasma (5×).

Density functional resonance theory of unbound electronic systems

Density functional resonance theory (DFRT) is a complex-scaled version of ground-state density functional theory (DFT) that allows one to calculate the in-principle exact resonance energies and lifetimes of metastable anions. In this formalism, the energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation, just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N-electron interacting system to a Kohn-Sham system of N noninteracting particles. This mapping facilitates self-consistent calculations with an initial guess for the complex density, as illustrated with an exactly solvable model system.

Multichannel molecular high-order harmonic generation from asymmetric diatomic molecules

Multichannel molecular high-order harmonic generation (MHOHG) from a single electron asymmetric molecular ion HeH2+ is investigated numerically. It is found that considerable resonant excitation occurs by laser induced electron transfer (LIET) to neighboring ions and multiple frequency (fractional-order) harmonics are observed from the excited states shifted by some energy Δ from the main Nω energy harmonics. A time series analysis is used to confirm this MHOHG channel which is created by initial ionization from the excited state prepared by LIET and recombination to the neighboring ion at specific field phases, resulting in interference between recombination pathways from ground and excited states.