Session J6: Short Pulse (e.g., Attosecond, Femtosecond Processes) I

Evidence of H$_2^+$ dynamical alignment in short laser pulses

We will present theoretical results for H$_2^+$ dissociation in 10-135 fs laser pulses from calculations including nuclear vibration, rotation, and electronic excitation. Nuclear rotation has commonly been neglected for dissociation in short pulses with the nuclei usually considered to be fixed along laser polarization. We will show that the comparison of the total dissociation probability between calculations with nuclear rotation and without it proves to be a good way to quantify dynamical alignment. For example, we find a large difference in the total dissociation probabilities from the two calculations, indicating that there is significant dynamical alignment of H$_2^+$ for 135 fs pulses and even for 45 fs pulses. For 10 fs pulses, though, the difference is small, hence there is little dynamical alignment. Our results indicate, however, that the angular distribution of the dissociating fragments can not be obtained correctly --- even for very short pulses like 10 fs --- when nuclear rotation is neglected. It is therefore important to include nuclear in calculations to obtain results directly comparable with the experiments.   

Numerical simulations of double optical gating for controlling attosecond pulse generation

Our simulations revealed that by adding a second harmonic field to a laser field with a time-dependent ellipticity, single isolated attosecond pulses can be generated as a result of the combined power of the two-color gating and the polarization gating. The duration of the pump laser applicable to this double optical gating scheme is a factor of two longer than that for the conventional polarization gating. Pulses with less than 100 attosecond duration can be generated from helium gas even with 10 fs pump lasers. It was discovered that the number of attosecond pulses and their intensities could be controlled by either the relative phase between the two color laser fields or the carrier-envelope phase. Techniquely, 10 fs pulses are much easier to generate, propagate and manipulate than the 5 fs pulses used in the past for generating attosecond pulses.   

Controlled stopping of nuclear vibrational wave packets in $D_2^+$

Ionization of neutral $D_2$ molecules by a short pump laser pulse may create a vibrational wave packet on the lowest ($1s\sigma_g^+$) adiabatic potential curve of the $D_2^+$ molecular ion. We investigated the possibility of manipulating the bound motion, dissociation, and vibrational--state composition of $D_2^+$ nuclear wave packets with a sequence of ultra--short, intense, near infrared control laser pulses. Our numerical results show that a single control pulse with an appropriate time delay can quench the vibrational state distribution of the nuclear wave packet by increasing the contribution of a selected stationary vibrational state of $D_2^+$ to more than 50\%. We also demonstrate that a second control pulse with a carefully adjusted delay can further squeeze the vibrational-state distribution, suggesting a multi--pulse control protocol for preparing stationary excited nuclear wave functions. With the subsequent fragmentation of the molecular ion with a probe pulse, we suggest a scheme for experimentally assessing the degree at which the nuclear motion in small molecules can be controlled, cf., Phys. Rev. {\bf 77}, 013407 (2008).   

Accurate retrieval of atomic and molecular structure from high-order harmonic spectra

We show that high-order harmonic generation (HHG) yield can be expressed as the product of a returning electron wave-packet and photo-recombination cross section, and the shape of the returning wave-packet is largely independent of the target. By comparing the harmonic spectra generated from different targets, accurate structural information, including the phase of recombination amplitude, can be retrieved. The model can readily be extended to molecules where theoretical calculation of HHG spectra itself is still a challenge. We show on the example of molecular ion H$_{2}^{+}$ that HHG spectra, including positions of interference minima, are quite accurately reproduced by using the wave-packet from the Lewenstein model. This result opens up the possibility of studying the target structure of complex systems and their time evolution, from the HHG spectra generated by short laser pulses.   

Effect of Nuclear Motion on Molecular High Order Harmonic Generation

Exact (non-BornOppenheimer) solutions of the Time-dependent Schroedinger Equation for 1-D H2+,D2+,H2,D2 are used to investigate the effect of nuclear motion on the electron recombination process in the presence of ultrashort (few cycles) intense laser pulses, which process leads to MHOHG, molecular high order harmonic gemeration. Time series analysis methods allow for obtaining from the MHOHG spectrum the recombination times of the ionized electron during the nuclear motion.The results show that the emission process of MHOHG is controlled by the motion of the nuclear wave packets on ``bond-softened'' or Laser Induced Molecular Potentials, LIMPS in both the ionized and ground state. MHOHG is thus limited to a short time and not during the whole pulse duration.   

Scaling of high harmonic generation efficiency with wavelength

We present experimental measurements of the efficiency of high harmonic generation in noble gases as function of wavelength in the range of 800nm to 2000nm. The efficiency is calculated as the integral of the XUV yield from 16eV to 45eV. We report measurements at different ionization regimes. These different stages of ionization are measured at the same time as the harmonics by means of an ion detector. The dependence of the harmonic yield is also measured for different phase matching conditions by changing the focusing geometry in the gas. We find that the harmonic generation scales like $\propto \lambda^{-\alpha}$ with $\alpha \approx$ 4 to 5 depending on the ionization regime and phase matching condition.   

Wavelength Scaling of High-Harmonic Yield: Threshold Phenomena and Bound State Symmetry Dependence

Using our recent description of harmonic generation (HG) in terms of a system's complex quasienergy [1], we analyze the harmonic power $P_{\Delta E}(\lambda)$ (over a fixed interval, $\Delta E$, of harmonic energies) as a function of wavelength and show that it reproduces the wavelength scaling predicted recently by two groups of authors [2, 3] based on solutions of the time-dependent Schr\"{o}dinger equation: $P_{\Delta E}(\lambda)\sim \lambda^{-x}$, where $x \approx 5-6$. Furthermore, the oscillations of $P_{\Delta E}(\lambda)$ on a fine $\lambda$ scale found in Ref. [3] are then shown to have a quantum origin, involving threshold phenomena within a system of interacting ionization and HG channels. Our results are also shown to be sensitive to the bound state wave function's symmetry. [1] M.V. Frolov, A.V. Flegel, N.L. Manakov, and A.F. Starace, Phys. Rev. A {\bf 75}, 063407 (2007). [2] J. Tate, T. Auguste, H.G. Muller, P. Sali\`{e}res, P. Agostini, and L.F. DiMauro, Phys. Rev. Lett.{\bf 98}, 013901 (2007). [3] K. Schiessl, K.L. Ishikava, E. Persson, and J. Burgd\"{o}rfer, Phys. Rev. Lett.{\bf 99}, 253903 (2007).   

Molecular Recollision Interferometry in High Harmonic Generation

There has been considerable recent interest in using high-order harmonic generation to observe molecular structure and dynamics. Besides measuring the intensity of high-order harmonics, we use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned CO$_{2}$ molecules. We unambiguously observe a reversal in phase of the high order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave. Our measurements are critical for developing new approaches for molecular imaging.   

Intensity Dependent Interference Structures in High Harmonic Generation

The electronic structure of the highest occupied molecular orbital (HOMO) modulates the amplitude and phase of molecular high harmonic generation (HHG) via interferences in the HHG recombination step. Destructive interference between the recombining electron wave and the HOMO lead to reduced HHG amplitude and phase jumps at spectral positions determined by the electron de Broglie wavelength. We identify the spectral minima for the N$_{2}$ molecule. In contrast to the predictions of commonly used models, we see an intensity dependent shift of the destructive features. We present two possible interpretations of that shift that include intensity effects on the electron de Broglie wavelength and intensity dependent co-mixing of other orbitals apart from the HOMO.   

HOMO-1 Contribution in High Harmonic Generation

High harmonic generation (HHG) proceeds in three steps. First, a part of the electron wave function tunnels out of the valence orbital. Secondly, the liberated electron wave packet accelerates in the laser field and finally coherently recombines with the initially ionized orbital. In molecules the highest occupied molecular orbital (HOMO) is generally thought to be responsible for ionization and recombination. We have obtained experimental evidence that lower lying orbitals are involved in the HHG process of the N$_{2}$ molecule. Harmonic signal modulations at different molecular alignment angles display features due to a $\pi _{u}$ symmetry and have a higher spectral cut-off than the main HHG spectrum from the $\sigma _{g}$ -- symmetric HOMO. This suggests HHG from the HOMO-1 orbital.   

EUV-Driven Attosecond Processes

We have investigated the single ionization of He and double ionization of Ar on an attosecond time scale in a pump/probe geometry using an EUV attosecond pump (17-43 eV) and a femtosecond IR (800 nm) probe. The EUV photons are in the form of an attosecond pulse train (APT) generated by high-harmonic generation in Xe or Ar. We detect both ions and electrons in a COLTRIMS geometry. For both targets we found three pump-probe-delay regions of interest. When the IR precedes the APT, it has no effect on the ionization. When the IR pulse overlaps the APT, a large enhancemet of the ionization is observed, which, for the He case, oscillates with the relative phase of the IR and APT. When the IR comes after the APT but does not overlap it, a strong enhancement is observed but without oscillation. Possible explanations for this behavior will be discussed.   

Output Coupling Techniques for Intracavity High-Harmonic Generation

Cavity based high-harmonic generation has demonstrated phase-coherent frequency combs in the vacuum ultraviolet spectral domain. One outstanding issue limiting the practicality of such sources has been difficulty in finding suitable methods for coupling harmonic light out of the buildup cavity. We address the results of several novel output coupling methods and discuss the merits of each including coupling efficiency, effect on the cavity finesse and spectral filtering.