Ultradispersive adaptive prism based on a coherently prepared atomic medium

PHYSICAL REVIEW A 81, 063824 (2010)

Ultradispersive adaptive prism based on a coherently prepared atomic medium
Vladimir A. Sautenkov,1'2 Hebin Li,' Yuri V. Rostovtsev,3,* and Marlan O. Scully1,4
'Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, Texas 77843-4242, USA
2P. N. Lebedev Institute of Physics, Moscow 119991, Russia
3Department of Physics, University of North Texas, 1155 Union Circle, No. 311427, Denton, Texas 76203, USA
4College of Engineering and Applied Science, Princeton University, Princeton, NJ 08544, USA
(Received 30 July 2009; revised manuscript received 23 February 2010; published 23 June 2010)
We have experimentally demonstrated an ultra-dispersive optical prism made from a coherently driven
Rb atomic vapor. The prism possesses spectral angular dispersion that is 6 orders of magnitude higher than
that of a prism made of optical glass; such angular dispersion allows one to spatially resolve light beams with
different frequencies separated by a few kilohertz. The prism operates near the resonant frequency of atomic
vapor and its dispersion is optically controlled by a coherent driving field.

DOI: 10.1103/PhysRevA.81.063824

PACS number(s): 42.50.Gy

I. INTRODUCTION
A single-frequency ray of light is bent by a prism at an
angle determined by the index of refraction [see Fig. 1(a)]. As
shown in [1], the dispersion of the index of refraction leads to
spread of deviation angles for different light frequencies.
Optical properties of matter, such as absorption, dispersion,
and a variety of nonlinear characteristics, can be manipulated
by electromagnetic fields [2-7]. For example, the applied
coherent fields can eliminate absorption, enhance the index of
refraction [8-10], induce chirality in nonchiral media [11], pro-
duce usually forbidden forward Brillouin scattering or strong
coherent backward scattering in ultradispersive resonant media
[12,13], slow down or speed up light pulses [14-16], provide
the optical imaging beyond diffraction limit [17], and the
optical analog of Stern-Gerlach experiment [18]. Optically
controlled giant nonlinearities may generate nonlinear signals
using single photons [19,20]. The enhanced nonlinearity can
be employed for quantum information storage [21] and for
manipulation of light propagating through a resonant medium,
such as stationary pulses of light in an atomic medium [22].
Here we experimentally demonstrate an ultradispersive
prism (we refer to it as "a prism" because it deflects light;
see Fig. 1). The prism is made of a coherently driven atomic
Rb vapor [4] that has a spectral angular dispersion (dO/d) X
103 nm-1) at least 6 orders of magnitude higher than that
of glass prisms (dO/d) ~ 10-4 nm-1) or diffraction gratings
(dO/d) ~ 10-3 nm-1).
The physics of refraction of the ultradispersive coherently
driven atomic medium is based on exciting quantum coher-
ence. The wave vector k depends on the light frequency
v as

k = -n,
c

(1)

where n is the index of refraction. Assuming that the
driving field has an inhomogeneous profile, then the index
of refraction has a spatial gradient. The light ray trajectories in
*rost@unt.edu

an inhomogeneous medium can be found by solving an eikonal
equation [23] given by

2
(V =)2 k2 2 n
C

where 4' is the phase of electromagnetic wave. Then the light
turning angle can be estimated as

0 LVn.

(3)

where n = 1 + 4E7X,, L is the length of a medium, and
Vn is the gradient of the index of refraction in the direction
perpendicular to propagation. The atomic susceptibility of a
coherently driven three-level medium X, [4] is given by

Q2 _ 2 _ 2
Re[X,] = r/o 2 cb
(O2- + YcbY - (02)2 S02(Ycb y)2

(4)

where r = 33Nyr/1672, N is the density of Rb vapor,
Yr is the spontaneous emission rate, y is the relaxation
rate at optical transition, Ycb is the relaxation rate at the
long-lived lower frequency (spin) transition, Q2 is the Rabi
frequency of control field, v is the frequency of the probe
field, 8w)= v - cab is the detuning of the probe field from
atomic transition oab = 27rc/; and k is the wavelength of
the resonant transition. Then, for realistic parameters, such as
Swo) 1 x 103 S-1, ycb 1 x 103 s-1, N2 1013 cm-3, and
L = 10cm, the estimate yields 0 ~ 0.1, which shows a lot
of potential for implementation of the predicted effect. Note
here that the spatial dependence of gradient of the driving
field is important and, also, that the effect can be increased
even more by using an enhanced index of refraction without
absorption [8-10].
II. EXPERIMENTAL SETUP AND RESULTS
A schematic of an experimental setup is shown in Fig. 2.
We have used a highly coherent extended-cavity diode laser
(ECDL) [20] that is tuned to the center of the Doppler
broadened hyperfine component of the D1 line of 87Rb [the
transition 5S1/2(F = 2) - 5P1/2(F' = 1)]. A part of the output
laser is used to control the laser frequency by observing the
Doppler-free saturation resonance in the rubidium reference

(2)

2010 The American Physical Society

1050-2947/2010/81(6)/063824(6)

063824-1

Sautenkov, Vladimir A.; Li, Hebin; Rostovtsev, Yuri V. & Scully, Marlan O. (Marlan Orvil), 1939-. Ultradispersive adaptive prism based on a coherently prepared atomic medium. [College Park, Maryland]. UNT Digital Library. http://digital.library.unt.edu/ark:/67531/metadc103269/. Accessed October 20, 2014.