X. M. Tong

Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime

We propose an empirical formula for the static field ionization rates of atoms and molecules by extending the well-known analytical tunnelling ionization rates to the barrier-suppression regime. The validity of this formula is checked against ionization rates calculated from solving the Schrodinger equation for a number of atoms and ions. The empirical formula retains the simplicity of the original tunnelling ionization rate expression but can be used to calculate the ionization rates of atoms and molecules by lasers at high intensities.

Post ionization alignment of the fragmentation of molecules in an ultrashort intense laser field

We studied the angular distributions of the fragmented ions of diatomic molecules in an intense linearly polarized short laser pulse. In addition to the well-known dynamic alignment of the neutral molecules before ionization, we identified a more important post ionization alignment effect of the molecular ions. The latter is modelled quantum mechanically as resulting from the breakup of a rotating linear rotor. We showed that only for very short pulses are the two alignment mechanisms not important. In this case the angular distributions of the fragmented ions mimic the shape of the electronic density of the outermost molecular orbital.

Correlation dynamics between electrons and ions in the fragmentation ofD2molecules by short laser pulses

We studied the recollision dynamics between the electrons and D{sub 2}{sup +} ions following the tunneling ionization of D{sub 2} molecules in an intense short pulse laser field. The returning electron collisionally excites the D{sub 2}{sup +} ion to excited electronic states; from there D{sub 2}{sup +} can dissociate or be further ionized by the laser field, resulting in D{sup +}+D or D{sup +}+D{sup +}, respectively. We modeled the fragmentation dynamics and calculated the resulting kinetic-energy spectrum of D{sup +} to compare with recent experiments. Since the recollision time is locked to the tunneling ionization time which occurs only within a fraction of an optical cycle, the peaks in the D{sup +} kinetic-energy spectra provide a measure of the time when the recollision occurs. This collision dynamics forms the basis of the molecular clock where the clock can be read with attosecond precision, as first proposed by Corkum and co-workers. By analyzing each of the elementary processes leading to the fragmentation quantitatively, we identified how the molecular clock is to be read from the measured kinetic-energy spectra of D{sup +} and what laser parameters are to be used to measure the clock more accurately.

Ionization suppression of Cl 2 molecules in intense laser fields

The strong field ionization of Cl{sub 2} molecules is investigated by using an ultrashort pulse Ti:sapphire laser. A spatial imaging technique is used in such measurements to reduce the effect of spatial integration. Cl{sub 2} shows strong ionization suppression as do other diatomic molecules having valence orbitals with antibonding symmetry (O{sub 2},S{sub 2}) when compared with the field ionization of atoms with nearly identical ionization potential. A more general molecular tunneling ionization model is proposed, and the calculations are in reasonable agreement with the measurements. Our results support that antibonding leads to ionization suppression, a trend that only F{sub 2} goes against and that needs to be further investigated.

Effects of orbital symmetries on the ionization rates of aligned molecules by short intense laser pulses

It is shown that by measuring the angular distributions of fragmented ions of simple molecules by sub-10 fs laser pulses at intensities in the non-sequential double ionization regime the electron density of the highest occupied molecular orbital can be probed directly. For pulses of a few tens of femtoseconds or longer, it is shown that the angular distributions of the ions are dominated by post-ionization alignment which results from the additional rotation of the molecular axis during the breakup process. These models are used to explain recent experiments.

Circularly-polarized laser-assisted photoionization spectra of argon for attosecond pulse measurements

Angle-resolved photoelectron spectra of argon atoms by XUV attosecond pulses in the presence of a circularly polarized laser field are calculated to examine their dependence on the duration and the chirp of the attosecond pulses. From the calculated electron spectra, we show how to retrieve the duration and the chirp of the attosecond pulse using genetic algorithm. The method is expected to be used for characterizing the attosecond pulses which are produced by polarization gating of few-cycle left- and right-circularly polarized infrared laser pulses.

Simulation of High Harmonic Generation in Solids

To overcome fundamental limitations in high harmonic generation (HHG) from single atoms, solid targets have moved into the focus of interest. For single atoms the increase of the high-energy cut-off with increasing wavelength, Ecut ∝ λ 2, goes hand in hand with the dramatic decrease of the harmonic intensity, I ∝ λ−5.5. In principle, solids promise to overcome this intensity limitation due to the large density of target atoms. Indeed, HHG from dielectrics has already been observed with well-pronounced harmonics up to very high orders. In parallel, theoretical methods are sought for to identify the source of the emitted radiation and to help optimizing the emission process. We use a real-space real-time implementation of time-dependent density functional theory (TDDFT) employing periodic boundary conditions to model the interaction of ultrashort laser pulses with solids [1]. However, when applied to a realistic 3D solid for one fixed intensity I of the IR pulse (in this case for diamond) only very few harmonics on top of a broad background above the band-gap energy are recognizable (top panel). This is in contrast to the clean highharmonic spectrum observed in experiment (starting with [2]). We show that a realistic description of solidstate harmonics requires the treatment of the average over the inhomogeneous intensity distribution as well as decoherent processes. Forming a coherent average over the ensemble of harmonic spectra generated by the inhomogeneous intensity distribution in the laser spot clearly “cleans” the spectrum by amplifying the harmonics while damping other frequencies (bottom panel). Moreover, electron-phonon and electron-electron scattering not accounted for in standard TDDFT further purifies the spectrum and dampens the post-pulse ringing. We have developed an open-system TDDFT which accounts for decoherence without changing the time-depending density of the system [3]. We find an almost noiseless HHG spectrum (decoherence time τ = 2 fs, center panel). Open-system TDDFT in combination with intensity averaging promises to allow for a realistic simulation of HHG in dielectrics.

IR-assisted ionization of He by attosecond XUV radiation

In this work we characterize the underlying processes behind the IR-assisted ionization of helium by extreme ultra violet (XUV) attosecond radiation. We show that, if used in the form of an attosecond pulse train, the XUV radiation can have a good spectral resolution as well as good temporal resolution. Our experimental data and associated theoretical calculations show how to use the properties of attosecond XUV radiation to induce a desired excited state of helium, and how to tune the IR laser electric field to control the ionization pathways.

PROBING ORBITAL SYMMETRIES AND IONIZATION DYNAMICS OF SIMPLE MOLECULES WITH FEMTOSECOND LASER PULSES

It is shown that by measuring the angular distributions of fragmented ions of simple molecules by sub-10 fs laser pulses at intensities in the non-sequential double ionization regime the electron density of the highest occupied molecular orbital can be probed directly. It is also shown that using a single laser pulse, from the kinetic energy release of the fragmented ions following the double ionization of H2, the time interval between the two ionizations can be controlled and determined to sub-fs accuracy by varying the pulse duration and laser intensity. Furthermore, using a pump-probe scheme the time evolution of the vibrational wave packet on two potential surfaces can be mapped directly using two sub-10 fs lasers. Theoretical models are used to explain these recent experiments.

Photon-ion collisions and molecular clocks

The timing of molecular rearrangements can be followed in the time domain on a femtosecond scale by using momentum imaging techniques. Three examples are discussed in this paper: first, the diffraction of electrons ejected from the K-shell of one of the atomic constituents of the molecule takes a ‘picture’ of the molecule, and the correlation between the momentum vector of the photoelectron and the subsequent fragmentation pattern is used to estimate the time delay which accompanies the latter process. Second, the kinetic energy release of proton pairs from the double ionization of hydrogen by fast laser pulses is timed using the optical cycle as a clock. The mechanisms of rescattering, sequential and enhanced ionization are clearly identified in the momentum spectra. Third, the operation of rescattering double ionization in the case of nitrogen and oxygen molecules is discussed.