2 XUV Lasers for Ultrafast Electronic Control in H 2
39
Fig. 2.5 where the variation of DI and NDI probabilities are plotted as a function
of the pulse duration for a fixed photon energy of 13.3 eV and a moderate intensity
of 10 12 W/cm 2 . Both contributions vary monotonously with the pulse length, but
the DI probability increases by more than two orders of magnitude when the pulse
duration varies from 2 to 12 fs. Consequently, the ratio between DI and NDI can be
controlled by varying the pulse duration.
The analogous behavior and control can be achieved by varying the laser intensity. It is illustrated in panel (c) of Fig. 2.5 for the same photon energy, 13.3 eV, and
for a 10 fs pulse. For intensities below 10 14 W/cm 2 , DI becomes the major ionization
channel. The increase of the field intensity is qualitatively equivalent to shortening
the pulse duration. Increasing intensity, i.e. the amplitude of the field, ionization
takes place progressively faster, making the effective pulse duration decrease. Thus,
when using high intensities one loses the vibrational selectivity through the intermediate states that favors the DI channel. However, although an equivalent behavior is
qualitatively achieved by tuning the pulse length or laser intensity, a very different
mechanism is triggered for highly intense fields. This is further discussed in the next
subsection.
2.5.2 Non-linear Effects in (1 + 1)-REMPI
An extensive effort has been devoted to explore the non-linear effects that arise
with intense fields in the UV and XUV regions. Among them, the most well-known
phenomenon is the emergence of Rabi-type oscillations between electronic states
[82], which are actually responsible of the variation of the DI/NDI ratio with intensity. Rabi oscillations between atomic levels have been extensively treated in
quantum mechanics textbooks [83]. The simplest picture is that of a coherent superposition of resonant quantum states in a two-level system under the influence of an
external periodic field, which leads to an oscillation in the state population between
the lower and the upper levels. Its frequency is given by the amplitude of the field
(equivalently, the laser intensity I ) and the dipole transition moment between the
states (μ), such that Ω = μ
√
I /. In this context, a common description for this
high-intensity regime is the Floquet picture. Within its frame, one could view the
resonant states coupled by the field as “dressed” electronic states. A schematic representation of the intermediate single excited states of H 2 dressed by the field with
an intensity of 2 · 10 14 W/cm 2 is shown in Fig. 2.6(a). One can see the characteristic
Autler-Townes splitting of the states separated by an energy approximately equal to
the Rabi frequency. This energy splitting induced in the intermediate states that are
accessible by one-photon absorption is expected to leave its signature in the ionization signal after absorption of the second photon. In a reduced two-level picture, one
would expect two well defined peaks in the electron energy differential ionization
probabilities, as displayed in the scheme given in Fig. 2.6(a). In fact, simple twolevel system models have been successfully applied to characterize Rabi oscillations
occurring in molecular targets subject to pulses longer than the typical times for vibrational and rotational motions. These experiments used nanosecond (ns) pulses
39
Fig. 2.5 where the variation of DI and NDI probabilities are plotted as a function
of the pulse duration for a fixed photon energy of 13.3 eV and a moderate intensity
of 10 12 W/cm 2 . Both contributions vary monotonously with the pulse length, but
the DI probability increases by more than two orders of magnitude when the pulse
duration varies from 2 to 12 fs. Consequently, the ratio between DI and NDI can be
controlled by varying the pulse duration.
The analogous behavior and control can be achieved by varying the laser intensity. It is illustrated in panel (c) of Fig. 2.5 for the same photon energy, 13.3 eV, and
for a 10 fs pulse. For intensities below 10 14 W/cm 2 , DI becomes the major ionization
channel. The increase of the field intensity is qualitatively equivalent to shortening
the pulse duration. Increasing intensity, i.e. the amplitude of the field, ionization
takes place progressively faster, making the effective pulse duration decrease. Thus,
when using high intensities one loses the vibrational selectivity through the intermediate states that favors the DI channel. However, although an equivalent behavior is
qualitatively achieved by tuning the pulse length or laser intensity, a very different
mechanism is triggered for highly intense fields. This is further discussed in the next
subsection.
2.5.2 Non-linear Effects in (1 + 1)-REMPI
An extensive effort has been devoted to explore the non-linear effects that arise
with intense fields in the UV and XUV regions. Among them, the most well-known
phenomenon is the emergence of Rabi-type oscillations between electronic states
[82], which are actually responsible of the variation of the DI/NDI ratio with intensity. Rabi oscillations between atomic levels have been extensively treated in
quantum mechanics textbooks [83]. The simplest picture is that of a coherent superposition of resonant quantum states in a two-level system under the influence of an
external periodic field, which leads to an oscillation in the state population between
the lower and the upper levels. Its frequency is given by the amplitude of the field
(equivalently, the laser intensity I ) and the dipole transition moment between the
states (μ), such that Ω = μ
√
I /. In this context, a common description for this
high-intensity regime is the Floquet picture. Within its frame, one could view the
resonant states coupled by the field as “dressed” electronic states. A schematic representation of the intermediate single excited states of H 2 dressed by the field with
an intensity of 2 · 10 14 W/cm 2 is shown in Fig. 2.6(a). One can see the characteristic
Autler-Townes splitting of the states separated by an energy approximately equal to
the Rabi frequency. This energy splitting induced in the intermediate states that are
accessible by one-photon absorption is expected to leave its signature in the ionization signal after absorption of the second photon. In a reduced two-level picture, one
would expect two well defined peaks in the electron energy differential ionization
probabilities, as displayed in the scheme given in Fig. 2.6(a). In fact, simple twolevel system models have been successfully applied to characterize Rabi oscillations
occurring in molecular targets subject to pulses longer than the typical times for vibrational and rotational motions. These experiments used nanosecond (ns) pulses