Attosecond Imaging of Electron Dynamics

Ongoing progress in laser technology presents the atomic, molecular and optical sciences with the opportunity to explore new laser intensity, frequency and time domain regimes. Theoretical research of the interaction of strong electromagnetic radiation with matter is closely related to, as well as stimulated by the development of intense laser systems and ultrashort light pulses. Nowadays laser frequencies range from the far-infrared through the optical up to the vacuum-ultraviolet and the soft x-ray region, whereas available focused laser intensities increased to the order of 1020 Wcm-2 and above.

Groundbreaking achievements in laser technology over the recent years allow for design of novel sources of coherent radiation  such as for example high intensity infrared femtosecond sources and attosecond XUV/x-ray sources of both linear and elliptical polarization.

Attosecond coherent  control of electron dynmics  in atoms and molecules

In recent years, it has become possible to change phases, amplitudes and polarization of different frequency components of large-bandwidth laser pulses. Such developments open up new venues for studying coherent control of atomic and molecular processes. In this context, recently in a project on coherent control of a nonresonant two-photon excitation and ionization for hydrogen atom, hydrogen molecular ion  and for the single electron system modeled to resemble nitrogen molecule electronic properties, we have discovered that depending on the temporal and spectral shapes of the laser pulses one can control the population distribution of vibrational states in mid-infrared regime and for example very efficiently enhance or suppress vibrational excitations of a molecule. In particular we have found that in the mid-infrared regime  two photon resonant vibrational excitation results in surprising enhancement by many orders of magnitude of the ionization and dissociation yields. Furthermore our results show that with a designed chirped pulse  one can achieve 99.89% controlled population transfer between vibrational states for nonpolar molecules. In the future I plan to study this effect for other molecules.

Attosecond measurement techniques

The development of attosecond extreme ultraviolet (XUV) laser technology in recent years has offered the opportunity to observe and control directly the dynamics of electrons and the coupling to nuclear dynamics in atoms and molecules on their natural time scale. In particular, the capability to lock XUV pulses to a near-infrared (near-IR) pulse has initiated the development of techniques in which the dynamics is triggered by the attosecond pulse and observed as a function of the delay between the XUV and the near-IR pulses.

Our efforts in this direction have been devoted to analysis of the streaking experiments for non-resonant and resonant ionization. One of our calculations show how the time dependent multielectron wavefunction can be used to obtain the time delays in photoionization. In additional we have been working using alternative time-dependent approaches and modification of both quantum and classical theories. We have applied a fundamental quantum mechanical definition of time delay as the difference between the time a particle spends within a finite region of a potential and the time a free particle spends in the same region, to time-dependent numerical simulations on the grid using a back-propagation technique.  The method expands the options for a theoretical analysis of ultrashort time-dependent processes and can be %more easily applied also to molecules. We have s also hown that the time delay in numerical streaking simulations arises from the electron dynamics in the coupled potential of the Coulomb and the streaking fields and therefore strongly depends on the duration and polarization direction of the streaking field. Based on our numerical streaking simulations we have shown that the observed time delays with respect to the instant of ionization are related to the finite range in space, which the emitted electron probes along the polarization direction of the streaking pulse after its emission until the streaking pulse ceases. We have further explored the possibility of the remote imaging of the moving objects using the streaking technique. Finally we have proposed to use streaking technique for  two-photon ionization of the helium atom. The temporal shifts in the streaking traces are found to consist of two contributions, namely a time delay acquired during the absorption of the two photons from the extreme ultraviolet field and a time delay accumulated by the photoelectron after photoabsorption. From our results we find that in the case of a non-resonant transition the absorption of the two photons occurs without time delay. In contrast, for a resonant transition a substantial absorption time delay is found, which scales linearly with the duration of the ionizing pulse.

1.Time delays in two photon resonant ionization
Our numerical simulations of time delays in two-photon resonant and nonresonant ionization of helium using the attosecond streaking technique confirm that the temporal shifts in the streaking traces consist of two contributions, namely a time delay acquired during the absorption of the two photons from the extreme ultraviolet field and a time delay accumulated by the photoelectron after photoabsorption. From our results we find that in the case of a nonresonant transition the absorption of the two photons occurs without time delay. In contrast, for a resonant transition a substantial absorption time delay is found, which scales linearly with the duration of the ionizing pulse. The two-photon absorption time delay can be related to the phase acquired during the transition of the electron from the initial ground state to the continuum and the influence of the streaking field on the resonant structure of the atom.

2. Efficient calculations of streaking time delays using cut off Coulomb potential
Based on our numerical streaking simulations we have shown previously that the observed time delays with respect to the instant of ionization are related to the finite range in space, which the emitted electron probes along the polarization direction of the streaking pulse after its emission until the streaking pulse ceases. We have further explored the finite range aspect and  used cutoff Coulomb potential. The calculations for the Wigner-Smith time delays for the cut off Coulomb potential can be performed analytically. These time delays can be used in the formula derived by us, in which the time delay measured in a streaking experiment can be represented as a sum of piecewise field-free time delays over a finite-range weighted by the instantaneous field strength. The calculations performed in this way are very efficient and agree well with ab initio numerical simulations. One of the advantages is that it can be easily extended to calculations for three dimensional case and for multielectron systems within 'single active approximation' model potentials.

3.Time Delays in Two-Photon Ionization: effect of attochirp
Measurements invoking the use of attosecond pulses can be incorrectly interpreted if the chirp of such pulses is not taken into account. We use a physically intuitive analytical model to understand the effect  a chirp in the extreme ultraviolet (XUV) attosecond pulse will have upon the delay observed in streaking experiments. It is known that both the photoionization cross-section of the system and the spectral and temporal characteristics of the attosecond pulse used will determine the relative time-dependent probability of absorbing a particular photon energy. We developed an analytical method to calculate the streaking delay as a function of the absorbed photon energy and the time delay between the XUV and streaking pulses. We have determined the expected value of the streaking delay observed when a chirped attosecond XUV pulse is used to initiate streaking experiments. We then demonstrate that depending on the chirp, the streaking delay can be changed by several attoseconds, which is on the order of the delays usually observed in such experiments.