Phase control of group velocity: From subluminal to superluminal light propagation
D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann
Department of Chemistry, Bar-Ilan University, Ramat Gan 52900, Israel
Received 25 September 2000; published 20 March 2001
We show that the group velocity of a weak pulse can be manipulated by controlling the phases of two weak
optical fields applied to a V-shaped three-level system. Such control can even cause the probe propagation to
change from subluminal to superluminal. We consider two schemes: in the first, the excited states are coupled
by decay-induced coherence, which is an inherent property of the medium, and in the second, quantum
coherence is created by coupling the excited states to each other by a strong microwave field. We also discuss
the group velocity reduction experienced by a single weak propagating probe due to decay-induced coherence.
DOI: 10.1103/PhysRevA.63.043818 PACS numbers: 42.50.Gy, 42.25.Kb, 42.25.Bs
I. INTRODUCTION
Recently, the study of subluminal and superluminal light
propagation has attracted a great deal of interest, especially
due to the publication of a number of impressive experiments
1–6. In 1, Hau et al. measured a group velocity v
g
as low
as 17 m/s in a gas of sodium atoms, cooled sufficiently to
form a Bose-Einstein condensate. The atomic system was
modeled as a -type three-level system in an electromag-
netically induced transparency EIT setup, in which a region
of lossless normal dispersion is created between two absorp-
tion lines. The effect relies on the quantum coherence created
by applying a strong pump pulse to one transition of the
system. The weak probe pulse, applied to the other transi-
tion, experiences transparency and very steep positive disper-
sion. The combination of low absorption and steep positive
dispersion can lead to a dramatic slowing down of the group
velocity of light and consequently large time delay. Most of
the experimental demonstrations of subluminal group veloc-
ity 1–4 have been performed using the EIT setup in a
system. In another recent experiment Wang et al. 6 dem-
onstrated superluminal light propagation using the region of
lossless anomalous dispersion between two closely spaced
gain lines. The gain doublet is created by applying two in-
tense detuned cw pumps with slightly different frequencies
to one transition of a type three-level system in atomic
caesium. A weak probe pulse is then applied to the other
transition and the gain doublet is produced when the fre-
quency of the probe is such that two-photon Raman reso-
nance is achieved.
In this paper we exploit the fact that the properties of an
atomic medium can be dramatically modified by controlling
the phases of the applied fields, allowing us to manipulate
the group velocity at which light propagates. The system we
investigate here is a V-shaped closed three-level system,
with lower level | 1 and upper levels | 2 and | 3 . Two weak
fields couple the ground state to the two excited states. We
apply phase control PC in two different schemes. First,
when the excited states are coupled by their interaction with
the vacuum, scheme A shown in Fig. 1b, and second, when
quantum coherence is created by coupling the two close-
lying excited states by a strong microwave field, scheme B
shown in Fig. 1c. We show how the group velocity of a
weak pulse can be controlled by adjusting the relative phase
of the two weak optical fields applied to the V-type three-
level system and can even cause the probe propagation to
change from subluminal to superluminal.
Since decay-induced interference is an essential compo-
nent of the former system Fig. 1b, we first consider the
effect of decay-induced interference on the propagation of a
single weak pulse. This mechanism of creating quantum co-
herence by spontaneous emission, rather than by the applica-
tion of a strong coupling field, can lead to similar effects to
those observed in the EIT setup. These include ultranarrow
resonances and transparency 7 and modification of the
fluorescence spectrum 8 in a V-shaped three-level system
FIG. 1. a V-shaped three-level system illuminated by a single
weak pulse with center frequency
P
. b Scheme A: a V-shaped
three-level system illuminated by two weak pulses with equal cen-
ter frequencies
a
=
b
= , but different phases
a
and
b
. The
excited states are coupled by their interaction with the vacuum. c
Scheme B: a V-shaped three-level system illuminated by two weak
pulses with frequencies
a
and
b
, and phases
a
and
b
. The
excited states are coupled by a strong microwave field.
PHYSICAL REVIEW A, VOLUME 63, 043818
1050-2947/2001/634/0438187/$20.00 ©2001 The American Physical Society 63 043818-1