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