Atomic excitation and ionization in
strong laser fields
Recent experiments on short-pulse
(duration of 100 fs), high-intensity (peak intensity of
10^13 Watts/cm^2) laser irradiation of noble gases have
found significant amounts
of ionization and residual excited-state populations to occur simultaneously.
These observations have caused some controversy because the prevailing
"shell" model asserts that ionization under such conditions is
dominated by multiphoton ionization mediated by an excited state that is
field-shifted into resonance at the peak of the pulse. In this model,
ionization is viewed as a coherent process, in which the resonant intermediate
state greatly enhances multiphoton ionization of the initial state without
itself becoming populated. It is difficult to reconcile efficient ionization
with the survival of this intermediate state after the laser pulse has passed.
We have investigated this effect in a model system by integration of the
time-dependent Schroedinger equation.
This figure shows the energy levels of the
model atom along with the size of the laser photon. Model atom energy
levels are designated by labels E1, E2, etc., where E1
is the ground state. Each level has definite parity with the ground
state having even parity and each succeeding level has a parity opposite
that of its predecessor. On the right one sees the shifted energy levels
of this atom in the laser field, as a function of the field intensity.
Note the six-photon resonance condition between the shifted ground
state and the level E5, just below 2 x 10^13 Watts/cm^2.
This resonance is responsible for most of the ionization observed in the
experiments.
This figure shows the population of
level E5 after the passage of the pulse as a function of peak pulse
intensity. Dashed line: numerical calculation; solid line: Landau-Zener-type
treatment of two-level system.
Note that the population rises by four orders-of-magnitude
at the resonance intensity after which it executes small
oscillations around a slowly increasing value. These oscillations
are due to interference of the amplitudes for resonant excitation
on the rising and falling edges of the pulse.
Main conclusions
Ionization occurs when the
resonance condition obtains, and so the total ionization yield should be
proportional to a time interval t during which the laser intensity
is "close" in some sense to the resonance intensity Ir. For realistic
pulse profiles, t is exhibits a sharp maximum when the peak intensity
is comparable to Ir,
and eventually decreases with increasing peak intensity. Thus the ionization rate
eventually decreases with increasing intensity.
On the other hand, the
probability for multiphoton excitation increases slowly with peak intensity. This
means that for a given laser pulse, ions will come predominantly from a
spatial "shell," whereas excited states will be produced more or less
uniformly within the volume enclosed by that shell. Thus the ratio of net
excitation to net ionization will be much larger than would be the case in a
spatially homogeneous field. We believe this fact accounts for much of the
apparent inconsistency of the data between experiments that measure excited-state populations and ions.
