Even harmonic generation in isotropic media of dissociating homonuclear molecules

Isotropic gases irradiated by long pulses of intense IR light can generate very high harmonics of the incident field. It is generally accepted that, due to the symmetry of the generating medium, be it an atomic or an isotropic molecular gas, only odd harmonics of the driving field can be produced. Here we show how the interplay of electronic and nuclear dynamics can lead to a marked breakdown of this standard picture: a substantial part of the harmonic spectrum can consist of even rather than odd harmonics. We demonstrate the effect using ab-initio solutions of the time-dependent Schr\"odinger equation for $H$$_2$$^+$ and its isotopes in full dimensionality. By means of a simple analytical model, we identify its physical origin, which is the appearance of a permanent dipole moment in dissociating homonuclear molecules, caused by light-induced localization of the electric charge during dissociation. The effect arises for sufficiently long laser pulses and the region of the spectrum where even harmonics are produced is controlled by pulse duration. Our results (i) show how the interplay of femtosecond nuclear and attosecond electronic dynamics, which affects the charge flow inside the dissociating molecule, is reflected in the nonlinear response, and (ii) force one to augment standard selection rules found in nonlinear optics textbooks by considering light-induced modifications of the medium during the generation process.Comment: 7 pages, 6 figure

Autoionizing decay of H 2 doubly excited states by using xuv-pump-infrared-probe schemes with trains of attosecond pulses

We present a theoretical study of H2 ionization by a pump-probe scheme consisting on an attosecond pulse train (APT) and a near-infrared (IR) pulse.We focus on the autoionization dynamics of the first series of resonant states of the molecule, the Q1 doubly excited states. The APT central frequency is tuned to populate the 1∑ + u resonant states. The trace of autoionization is clearly visible in the two-dimensional (2D) proton-electron coincidence spectra and in the proton kinetic energy spectra. The dynamics of the autoionization process is clearly visible in the movie obtained by plotting the 2D spectrum as a function of the time delay between the APT and IR pulses. An analysis of the final symmetries ∑g and ∑u allows us to track the origin of the different structuresThis work was partially supported by the MICINN Projects No. FIS2010- 15127, No. ACI2008-0777, and No. CSD 2007-00010, the ERA-Chemistry Project No. PIM2010EEC-00751, the European grants MC-ITN CORINF and MC-RG ATTOTREND, the European COST Action CM0702, and the Advanced Grant of the European Research Council XCHEM 29085

\epsilon-regularity for systems involving non-local, antisymmetric operators

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations

Correlated electron and nuclear dynamics in strong field photoionization of H2+

We present a theoretical study of H2+ ionization under strong IR femtosecond pulses by using a method designed to extract correlated (2D) photoelectron and proton kinetic energy spectra. The results show two distinct ionization mechanisms—tunnel and multiphoton ionization—in which electrons and nuclei do not share the energy from the field in the same way. Electrons produced in multiphoton ionization share part of their energy with the nuclei, an effect that shows up in the 2D spectra in the form of energy-conservation fringes similar to those observed in weak-field ionization of diatomic molecules. In contrast, tunneling electrons lead to fringes whose position does not depend on the proton kinetic energy. At high intensity, the two processes coexist and the 2D plots show a very rich behavior, suggesting that the correlation between electron and nuclear dynamics in strong field ionization is more complex than one would have anticipatedThis work was accomplished with an allocation of computer time from Mare Nostrum BSC and CCC-UAM, and was partially supported by the MICINN Projects No. FIS2010-15127, No. ACI2008-0777, and No. CSD 2007-00010, the ERA-Chemistry Project No. PIM2010EEC-00751, the European Grants No. MCITN CORINF and No. MC-RG ATTOTREND, the European COST Action CM0702, and the Advanced Grant of the European Research Council, Grant No. XCHEM 290853. R. E. F. S. acknowledges a Ph.D. contract from ITN CORINF. P. R. acknowledges a Juan de la Cierva contract grant from MICIN

Molecular resolvent-operator method: Electronic and nuclear dynamics in strong-field ionization

We present an extension of the resolvent-operator method (ROM), originally designed for atomic systems, to extract differential photoelectron spectra (in photoelectron- and nuclear-kinetic energy) for diatomic molecules interacting with strong, ultrashort laser fields in the single active electron approximation. The method is applied to the study of H2+ photodissociation and photoionization by femtosecond laser pulses in the XUV-IR frequency range. In particular, the method is tested (i) in the perturbative regime, for few-photon absorption and bound-bound electronic transitions, and (ii) in the strong-field regime, in which multiphoton absorption and tunneling are present. In the latter case, we show how the differential ROM allows one to track the transition between both regimes. We also analyze isotopic effects by comparing the dynamics of H2+ and D2+ ionization for different pulses. © 2014 American Physical Society.This work was accomplished with an allocation of computer time from Mare Nostrum BSC and CCC-UAM and was partially supported by the MICINN Projects No. FIS2010- 15127 and No. CSD 2007-00010, ERA-Chemistry Project No. PIM2010EEC-00751, the European grants No. MC-ITN CORINF and No. MC-RG ATTOTREND, the European COST Action No. CM0702, and European Research Council Advanced Grant No. XCHEM 290853. R.E.F.S. acknowledges a Ph.D. contract from ITN CORINF and Grant No. SFRH/BD/84053/2012 from the Portuguese government. P.R. acknowledges a Juan de la Cierva contract grant from the Spanish MICIN

Delocalization of slowly damped eigenmodes on Anosov manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a "strip" of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two reference

Enhancing high-order harmonic generation in light molecules by using chirped pulses

One of the current challenges in high-harmonic generation is to extend the harmonic cutoff to increasingly high energies while maintaining or even increasing the efficiency of the high-harmonic emission. Here we show that the combined effect of down-chirped pulses and nuclear dynamics in light molecules allows one to achieve this goal, provided that long enough IR pulses are used to allow the nuclei to move well outside the Franck-Condon region. We also show that, by varying the duration of the chirped pulse or by performing isotopic substitution while keeping the pulse duration constant, one can control the extension of the harmonic plateauWe gratefully acknowledge fruitful discussions with Y.Mairesse. This work has been accomplished with a generous allocation of computer time from Mare Nostrum BSC and CCC-UAM and has been partially supported by the European Research Council Advanced Grant No. XCHEM 290853, MINECO Project No. FIS2013-42002-R, ERA-Chemistry Project No. PIM2010EEC-00751, European Grant No. MC-ITN CORINF, European COST Action XLIC CM1204, and the CAM project NANOFRONTMAG. R. E. F. S. acknowledges FCT—Fundação para a Ciência e Tecnologia, Portugal, Grant No. SFRH/BD/84053/201

Energy- and angle-resolved ionization of H2+ interacting with xuv subfemtosecond laser pulses

We present an extension of the resolvent operator method to extract fully differential ionization probabilities resulting from the interaction of ultrashort laser pulses with H2+ by including all electronic and vibrational (dissociative) degrees of freedom. The wave function from which ionization probabilities are extracted is obtained by solving the time-dependent Schrödinger equation in a grid for the case of H2+ oriented parallel to the polarization direction of the field. The performance of the method is illustrated by using pulses in the xuv domain. Correlated kinetic-energy (CKE) and correlated angular and nuclear kinetic-energy (CAKN) spectra have been evaluated and used to analyze the underlying mechanisms of the photoionization process. In particular, for pulses with a central frequency ω=0.8 a.u., which is smaller than the vertical ionization potential of H2+, we show the opening of the one-photon ionization channel by decreasing the pulse duration down to less than 1 fs. An analysis of the CKE and CAKN spectra allows us to visualize individual contributions from one- and two-photon ionization processes, as well as to study the variation of these contributions with pulse duration. The latter information is difficult to extract when only the kinetic energy release (KER) spectrum is measured. This points out the importance of performing multiple-coincidence measurements for better elucidation of competing ionization mechanisms, such as those arising when ultrashort pulses are usedWe gratefully acknowledge fruitful discussions with Dr. A. Palacios. This work was accomplished with an allocation of computer time from Mare Nostrum BSC and CCCUAM and was partially supported by European Research Council Advanced Grant No. XCHEM 290853, MINECO Project No. FIS2013-42002-R, ERA-Chemistry Project No. PIM2010EEC-00751, European Grant No. MC-ITN CORINF, European COST Action XLIC CM1204, and the CAM project NANOFRONTMAG. H.B. acknowledges support for mobility from ITN CORINF and is grateful for the hospitality of the Universidad Autónoma de Madrid. R.E.F.S. acknowledges FCT - Fundacao para a Ciencia e Tecnologia, Portugal, Grant No. SFRH/BD/84053/201