Coherent control of light shifts in an atomic medium driven by two orthogonally polarized
pulses: Effect of the pulse overlap
J. C. Delagnes and M. A. Bouchene
Laboratoire de Collisions Agrégats Réactivité, C.N.R.S. UMR 5589, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne,
31062 Toulouse Cedex 4, France
Received 13 June 2007; published 8 November 2007
We consider a duplicated two-level system where each two-level subsystem is driven by a strong resonant
femtosecond pulse and a weak resonant femtosecond pulse connects cross transitions. Strong interference
effects are induced in such a configuration leading to a modulation of the medium gain as a function of the
relative phase between the pulses J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 2007.
We study here the influence of the temporal overlap between the pulses on the dynamics of the system and the
medium gain. We show that the dynamics is dominated by two competing phenomena: Light shifts LS
induced by the driving pulse that prevails for small delays and free induction decay FID that prevails for large
delays. LS enhance the medium gain for = /2 and reduce it for =0, whereas FID always leads to a
decrease of the medium gain.
DOI: 10.1103/PhysRevA.76.053809 PACS numbers: 42.50.Gy, 42.50.Hz, 42.50.Md
I. INTRODUCTION
A lot of proposed methods to control physical and chemi-
cal processes rely on the interference effects produced by
excitation with coherent fields. The control is performed by
adjusting the relative phase between the exciting fields which
steers the interference of the quantum paths involved in the
process. Such control has been demonstrated in many con-
texts 1. An interesting scenario is the possibility to control
physical processes or pulse wave form when propagation ef-
fects are taken into account. Many previous studies have
shown the dramatic modifications that occur in the behavior
of the propagating pulses when the relative phase is modified
2–8. If strong pulses are used, light shifts LS are induced
in the medium and strong modification occurs in the atomic
structure. LS are the basis for many spectacular phenomena
in atomic and molecular physics. Rapid adiabatic passage,
stimulated Raman adiabatic passage, Stark-chirped adiabatic
passage 9 and light induced potential 10 are nonexhaus-
tive examples of effects where LS play a crucial role. The
possibility to control these effects has been demonstrated in
only few cases. One can use shaped intense femtosecond
pulses to realize a selective population of dressed states 11.
In a recent paper, we have demonstrated coherent control of
LS effects in a duplicated two-level system 2. A sequence
of two femtosecond coherent pulses— polarized strong
pulse and polarized weak pulse—excite resonantly the
S
1/2
- P
1/2
transition of atomic rubidium in an optically dense
sample. The pulse induces transitions between the adia-
batic states with a coupling that is different for either identi-
cally or oppositely light-shifted states, and that can be modi-
fied by tuning the relative phase between the pulses. An
efficient control of the medium gain for the pulse was
experimentally demonstrated. It was shown to be the result
of the interference between the absorption and the emission
quantum paths for photons. In that experiment, the delay
between the two pulses was smaller than the pulse durations
so the pulse overlap was almost perfect. In this paper, we
study the influence of the pulse overlap on the medium gain
and the LS effects. Spectacular changes occur with respect to
the previous situation of perfect overlap. Indeed, the modifi-
cation of the driving pulse area due to FID can no longer be
neglected and LS effects are reduced. The competition be-
tween FID and LS leads to a significant modification of the
medium gain. The situation =0 for which destructive inter-
ference occurs at zero delay may be more favorable for am-
plification than the situation = / 2 that was the previous
favorable case.
II. COHERENT CONTROL OF LIGHT SHIFTS
We consider the situation of a duplicated two-level
system |1 , |1' , |2 , |2' Fig. 1a excited resonantly by
two time delayed pulses. Pulse 1 strongly couples the par-
allel states while pulse 2 which is weak couples resonantly
the crossed states. In practice, this situation can be realized
by exciting the atomic rubidium with a pair of - and
-polarized pulses acting on the S
1/2
→ P
1/2
transition. The
|2'
>
|1'
>
P
1/2
S
1/2
-1/2 +1/2
|1
>
|2
>
M
J
π π σ
a) b)
c)
-iℏχ
2
sin φ
iℏχ
2
sin φ
-ℏχ
2
cos φ
|-
>
|+
>
|-'
>
|+'
>
|2'
>
|1'
>
|1
>
|2'
>
|2
>
|1'
>
+
|1
>
|2
>
π π π π σ
+
σ
-
e
+iφ
e
-iφ
d)
z
y
x
parallel
parallel
antiparallel
prop.
axis
strong
π pulse
weak
σ pulse
FIG. 1. a Energy levels and optical transitions involved in our
system. b Adiabatic representation. c Polarization configuration.
d Absorption and emission paths.
PHYSICAL REVIEW A 76, 053809 2007
1050-2947/2007/765/0538096 ©2007 The American Physical Society 053809-1