42
A. Palacios et al.
lation of the intermediate states is depleted, and, consequently, the (1 + 1)-REMPI
probability exhibits a relative minimum around 3.5 fs. After 4 fs, two-photon ionization becomes the dominant process over one-photon excitation.
Furthermore, the ground state is completely depleted for the laser parameters
here considered, so the ionization saturates. The population of the ground state is
shown for various laser intensities and as a function of photon energy in Fig. 2.7(b).
For the higher intensities, the ground state is completely depopulated in the (1 + 1)REMPI energy region. Besides, the higher the intensity, the larger the shift of the
absolute minimum to lower photon energies, which would be expected from the AT
effect. As the energy splitting becomes larger (the higher the intensity, the larger
Ω), the (1 + 1)-REMPI becomes accessible at lower photon energies. The other
minima in the population of the ground state correspond to (2 + 1)-REMPI. At
those photon energies, ∼ 6 and ∼ 7.5 eV, extremely high laser intensities would
be required to saturate ionization. The reason lies in the character of the electronic
states involved, the singly excited states of Σ +
g symmetry. They present doublewell potential energy curves that diminish the efficiency of the transitions among
their vibronic states.
At this point we have the time scales at which these phenomena are restricted.
Two conditions must be fulfilled to observe the step-ladder mechanism: (i) T >
1/Ω, i.e. the pulse is long enough to accommodate a complete Rabi oscillation,
which is determined by the laser intensity, and (ii) T < 1//E v , i.e. the pulse is
short enough to populate manifolds of vibrational states. The step-ladder mechanism, which allows for higher protons to be ejected, is thus observed if the pulse
duration lies between those limits (1/Ω < T < 1//E v ), i.e., the electronic structure (dipole moment) and the field intensity set the lower limit, while the vibronic
structure, i.e. the nuclear motion, imposes the upper one. In the H 2 molecule, the
vibrational energy spacing fixes an effective upper limit of ∼ 15 fs. And, for instance, the use of intensities around 10 14 W/cm 2 impose pulse lengths above 5 fs
in order to observe step-ladder Rabi oscillations in H 2 [80]. It should be noticed
that, in contrast with the step-ladder mechanism, the AT effect will be observed as
long as the fist condition, T > 1/Ω, is satisfied. In conclusion, the manipulation of
laser intensities in a range of values 10 12 –10 15 W/cm 2 with UV and XUV sources
in the fs time scale allows for the control of ionization channels, either by modifying the relative importance of non-dissociative (NDI) or dissociative (DI) ionization
processes or by suppressing and/or favoring the emission of faster electrons.
It is clear that a complete characterization of vibronic wave packets involving the
intermediate singly excited states is mandatory to elucidate and design new strategies to control the above explained mechanisms. To explore the dynamics of these
states, the most straightforward and experimentally affordable technique is the use
of pump-probe schemes with two identical pulses. In the next section, we will use
the same central frequencies employed through this work with (i) photon energies
around 12 eV, where (1 + 1)-REMPI probability reaches its maximum, (ii) short
pulses, to create vibronic wave packets containing an appreciable number of vibrational states, and (iii) low intensities, to avoid non-linear effects that, in principle,
complicate the patterns in the probing of vibronic wave packets involving the singly
A. Palacios et al.
lation of the intermediate states is depleted, and, consequently, the (1 + 1)-REMPI
probability exhibits a relative minimum around 3.5 fs. After 4 fs, two-photon ionization becomes the dominant process over one-photon excitation.
Furthermore, the ground state is completely depleted for the laser parameters
here considered, so the ionization saturates. The population of the ground state is
shown for various laser intensities and as a function of photon energy in Fig. 2.7(b).
For the higher intensities, the ground state is completely depopulated in the (1 + 1)REMPI energy region. Besides, the higher the intensity, the larger the shift of the
absolute minimum to lower photon energies, which would be expected from the AT
effect. As the energy splitting becomes larger (the higher the intensity, the larger
Ω), the (1 + 1)-REMPI becomes accessible at lower photon energies. The other
minima in the population of the ground state correspond to (2 + 1)-REMPI. At
those photon energies, ∼ 6 and ∼ 7.5 eV, extremely high laser intensities would
be required to saturate ionization. The reason lies in the character of the electronic
states involved, the singly excited states of Σ +
g symmetry. They present doublewell potential energy curves that diminish the efficiency of the transitions among
their vibronic states.
At this point we have the time scales at which these phenomena are restricted.
Two conditions must be fulfilled to observe the step-ladder mechanism: (i) T >
1/Ω, i.e. the pulse is long enough to accommodate a complete Rabi oscillation,
which is determined by the laser intensity, and (ii) T < 1//E v , i.e. the pulse is
short enough to populate manifolds of vibrational states. The step-ladder mechanism, which allows for higher protons to be ejected, is thus observed if the pulse
duration lies between those limits (1/Ω < T < 1//E v ), i.e., the electronic structure (dipole moment) and the field intensity set the lower limit, while the vibronic
structure, i.e. the nuclear motion, imposes the upper one. In the H 2 molecule, the
vibrational energy spacing fixes an effective upper limit of ∼ 15 fs. And, for instance, the use of intensities around 10 14 W/cm 2 impose pulse lengths above 5 fs
in order to observe step-ladder Rabi oscillations in H 2 [80]. It should be noticed
that, in contrast with the step-ladder mechanism, the AT effect will be observed as
long as the fist condition, T > 1/Ω, is satisfied. In conclusion, the manipulation of
laser intensities in a range of values 10 12 –10 15 W/cm 2 with UV and XUV sources
in the fs time scale allows for the control of ionization channels, either by modifying the relative importance of non-dissociative (NDI) or dissociative (DI) ionization
processes or by suppressing and/or favoring the emission of faster electrons.
It is clear that a complete characterization of vibronic wave packets involving the
intermediate singly excited states is mandatory to elucidate and design new strategies to control the above explained mechanisms. To explore the dynamics of these
states, the most straightforward and experimentally affordable technique is the use
of pump-probe schemes with two identical pulses. In the next section, we will use
the same central frequencies employed through this work with (i) photon energies
around 12 eV, where (1 + 1)-REMPI probability reaches its maximum, (ii) short
pulses, to create vibronic wave packets containing an appreciable number of vibrational states, and (iii) low intensities, to avoid non-linear effects that, in principle,
complicate the patterns in the probing of vibronic wave packets involving the singly