January 10, 2010 / Vol. 8, No. 1 / CHINESE OPTICS LETTERS 115
Slow light deflection in Gaussian pumped atomic medium
Chunfang Wang (SSS)
1
, Jing Cheng (§§§ ···)
2
, and Shensheng Han (¸¸¸))))
1∗
1
Key Laboratory for Quantum Optics and Center for Cold Atom Physics, Shanghai Institute of Optics and Fine Mechanics,
Chinese Academy of Sciences, Shanghai 201800, China
2
School of Physical Science and Technology, South China University of Technology,
Guangzhou 510640, China
∗
E-mail: sshan@mail.shcnc.ac.cn
Received February 18, 2009
We present the moments formalism theory to study the deflection of the slow signal light in the cold
atomic media, which is under the condition of the Gaussian control laser and electromagnetically induced
transparency. Deflection, the interesting phenomenon on quantum coherence, is testified by analytic and
numerical methods. Results show that, as the signal light propagating in the medium, there would be
an observable deflection before the general diffraction. Influences of the coupling intensity on deflection
phenomenon and the beam waist of the signal light in the medium are also investigated.
OCIS co des: 270.1670, 270.5530, 350.5500.
doi: 10.3788/COL20100801.0115.
The characterization of the spatial behavior of laser
profiles constitutes a field of current interest
[1−8]
. As
is well known, the key shape parameters of every laser
source are the minimum beam waist and the far-field
beam divergence, which can be expressed in terms of the
so-called second-order moments of the intensity and ra-
diant intensity of the field. Moments formalism is a pow-
erful tool to derive the propagation laws. In this letter,
we use the moments formalism to study the deflection
phenomena in the cold atomic media.
As an optical phenomenon, deflection has been stud-
ied for ages. Deflection always takes place where there
is an inhomogeneous medium
[9]
, and it can be easily ob-
served in our daily lives. As a result, researchers take
much interest in it and do much work about it. Re-
cently, many researchers found that, under the condition
of external field, the atomic media could be induced to
the inhomogeneous media
[10−18]
. The gradient refrac-
tive index (GRIN) is induced by magnetic-field-modified
optical pumping
[11]
, while the spatial inhomogeneity of
the refractive index is induced by an expanded Gaussian-
profile pump beam
[15−18]
. It should be mentioned that,
in Refs. [15-18], since the conditions for electromagneti-
cally induced transparency (EIT)
[19,20]
are satisfied, the
probe light transmitting in the cold atomic media is very
slow. The deflection of the slow light in atomic media
has been observed experimentally
[21,22]
and studied in
theory
[23]
. In Ref. [23], the relations between the deflec-
tion angle, the injection position, and the probe detuning
were illustrated with the semiclassical theory.
In this letter, we investigate the deflection of the slow
light in the cold atomic media by the classical theory.
With the help of the Fresnel propagation program
[9]
, we
can easily gain the analytical expression of propagation
equation, by which the ray path of the signal light and the
real beam-waist can be induced by the moments formal-
ism. Results show that, as the signal light propagating
in the medium, there would be an observable deflection
before the general diffraction. Influences of the coupling
intensity on deflection phenomenon and the beam waist
of the signal light in the medium are also investigated.
In our recent work
[15−18]
, we consider the cold atomic
gas cell composed of Λ-type three-level atoms (Fig. 1).
Under the condition of EIT, the linear susceptibility of
the incident field can be written as
[19]
χ(∆
p
, r) = −
|µ
13
|
2
ρ
ε
0
¯h
×
(
4∆
p
(Ω
2
c
− 4∆
2
p
) − 4∆
p
Γ
2
2
(Ω
2
c
+ Γ
2
Γ
3
− 4∆
2
p
)
2
+ 4∆
2
p
(Γ
2
+ Γ
3
)
2
+i
8∆
2
p
Γ
3
+ 2Γ
2
(Ω
2
c
+ Γ
2
Γ
3
)
(Ω
2
c
+ Γ
2
Γ
3
− 4∆
2
p
)
2
+ 4∆
2
p
(Γ
2
+ Γ
3
)
2
)
, (1)
where ρ is the atomic density, Γ
2
and Γ
3
are the de-
cay rates of the meta-stable state |2i and |3i, Ω
c
and
Ω
p
are Rabi frequencies of control and probe beams, re-
spectively, µ is the electric dipole moment of transition
|1i → |3i. Under the control of the Gaussian beam with
Rabi frequency Ω
c
(r) = Ω
0
exp(−r
2
/σ
2
), where σ is the
waist of the control beam, if r
2
¿ σ
2
, the index distribu-
tion of an EIT medium with a negative frequency detun-
ing (∆
p
< 0) can be approximated by a GRIN medium
as
n
2
(x, y) = n
2
0
[1 − g
2
(x
2
+ y
2
)], (2)
where
n
0
=
1
Ω
0
q
(Ω
2
0
+ η∆
p
), (3)
Fig. 1. Closed three-level Λ-type atom.
1671-7694/2010/010115-04
c
° 2010 Chinese Optics Letters
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