A theoretical study is presented suggesting possible photoelectron spectroscopy measurement of electron dynamics
on molecules on "attosecond" time scales. In particular, we study analytically the photoionization of
a coherent superposition of molecular electron states by an ultrashort, attosecond X-ray pulse. We show that
the broad photoelectron spectrum inherent in attosecond pulse ionization contains detailed information about
the time-dependent electron wave packet. Such ultrashort pulse photoionization leads to an asymmetry of the
photoelectron momentum distribution and this seems to measure the momentum asymmetry of the initial coherently
prepared electron bound state. We show further that universal molecular Coulomb interference effect occur in ultrashort pulse photoionization and other processes with fast momentum transfers. Thus "attosecond"
photoelectron spectra and their inherent asymmetry allow to monitor and in principle to control electron motion
on the attosecond time scale.
We examine two consequences of the unique behavior of molecular ions in intense laser fields. First, laser-induced crossings can be created with femtosecond laser pulses resulting in trapping of the molecular ion in high-field induced potential wells. We demonstrate this by numerical solutions of the time-dependent Schroedinger equation for H2+. Second we show results of numerical calculation with vibrationally excited H2+ of harmonic generation (HG), which can be enhanced by the trapping mechanism. We show next that in molecular ions, two plateaus appear in the harmonic generation spectrum, one of a molecular nature and the other atom like. Finally, we present an example of phase control of HG which can be explained in terms of a classical model.
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