Propagation dynamics in an autoionization medium
E. Paspalakis, N. J. Kylstra, and P. L. Knight
Optics Section, Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
Received 15 December 1998
We demonstrate that an autoionizing medium can, under specific conditions, become transparent to a short
laser pulse propagating in the medium. The interference that leads to transparency is intrinsic to the system and
relies on the establishment of a ‘‘dark,’’ or ‘‘trapped,’’ state that exists as a consequence of Fano interference
between direct and resonant photoionization processes. S1050-29479906607-X
PACS numbers: 42.50.Gy, 32.80.Dz, 42.65.-k, 42.50.Md
I. INTRODUCTION
The study of the propagation of electromagnetic pulses in
multi-level media has lead to the discovery of a number of
interesting phenomena. These include the simultaneous
propagation of two pulses having different fundamental fre-
quencies ‘‘simultons’’1,2, electromagnetically induced
transparency under matched pulse conditions 3–7 and the
creation and propagation of ‘‘adiabatons,’’ a general class of
pulses which show solitonic behavior in adiabatically evolv-
ing atomic systems 8–11. Pulse propagation effects have
also been investigated within other contexts. Examples in-
clude the study of lasing without population inversion 12,
the influence of the quantized nature of laser fields 13,14,
‘‘dragging and cloning’’ of laser pulses 15, the effects of
initial superpositions of the atomic states 16,17, and the
effects of Doppler broadening 18. Furthermore, systems
where a spatial excitation can be controlled 19 or even
imaged in the temporal profile of laser pulses 20 have been
discussed.
In these studies, systems involving bound states were con-
sidered. The introduction of dissipative processes are detri-
mental to, and can even destroy, the coherence required for
the manifestation of the above mentioned phenomena. How-
ever, recently it has been shown that, using the laser-induced
continuum structure LICS scheme 21,22, atomic coher-
ence can be preserved even in systems in which dissipative
processes e.g., ionization are present. These latter studies
utilize two lasers in a probe-coupling configuration. Interfer-
ing processes arising from the coherent laser-matter interac-
tion involving both of these lasers are necessary for transpar-
ency or solitonlike propagation in the medium.
In this paper, we investigate the propagation dynamics of
a short laser pulse interacting with an autoionizing medium.
We show that Fano interference 23 can lead to transpar-
ency in the medium, thereby allowing the laser pulse to
propagate without absorption. This phenomenon is closely
related to the transparency predicted in a four-level medium
via spontaneous-emission interference 24. The essential
feature of the present system is the presence of a continuum
of atomic states, so that dissipation is intrinsic to the system.
However, the decay processes can interfere and this can give
rise to transparency in the medium, as will be discussed be-
low. In contrast to the LICS scheme 21,22, here only a
single laser, the probe laser that couples the ground state to
both the autoionizing state and the continuum, is involved.
The configuration interaction which couples the autoionizing
state to the continuum is responsible for the necessary inter-
ference in this case, rather than a second laser field.
Since Fano’s original work, a number of studies have con-
sidered the total absorption of a laser field in the autoionizing
medium in the weak-field limit 25. Numerical studies of
the Maxwell-Bloch equations for the pulse propagation have
also been carried out 26. In this article, we re-examine
short laser pulse propagation in an autoionizing medium. We
place emphasis on establishing the connection between adia-
batic population trapping in short, pulsed laser fields 27,28
and transparency in the propagation of the laser pulse in the
medium. Furthermore, we calculate both analytically and nu-
merically corrections to the adiabatic behavior and show that
in the first approximation the laser pulse retains its shape and
only its group velocity is modified.
In the following section we derive the Maxwell-
Schro
¨
dinger equations of motion for the atomic system and
the laser field. We then discuss the conditions under which a
‘‘dark’’ or ‘‘trapped’’ state 29 occurs in the atomic sys-
tem, and consider the possibility of satisfying these condi-
tions for not too intense laser pulses. In Sec. III we establish
the link between adiabatic population trapping in the atomic
system and the transparency of the medium to the probe laser
pulse. We demonstrate, both analytically and numerically,
that when the system evolves adiabatically the propagation
of the pulse is both loss- and dispersion-free when the trap-
ping conditions are satisfied. Nonadiabatic effects, which can
lead either to the reduction of the group velocity of the pulse
or even to both absorption and dispersion, are also discussed.
Finally, we summarize and conclude in Sec. IV.
II. BASIC EQUATIONS
The system under consideration is shown in Fig. 1, where
we depict a laser-driven autoionizing system 27,30,31
which consists of a bound state | 0 , an autoionizing state | 1
and a continuum of states | c , . The state | 0 is coupled to
| 1 by a laser field. Both of these states are also coupled to
the continuum: the autoionizing state via the configuration
interaction V
c
and the bound state via the laser field. Spon-
taneous emission and other types of decoherence processes
e.g., collisions are assumed to be unimportant on the time
scales of interest, and we therefore analyze the behavior of
the system using the Maxwell-Schro
¨
dinger equations. The
position and time-dependent Hamiltonian of the atomic sys-
tem is written as
PHYSICAL REVIEW A JULY 1999 VOLUME 60, NUMBER 1
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