Observation of large continuous-wave two-photon optical amplification
Hope M. Concannon, William J. Brown, Jeff R. Gardner, and Daniel J. Gauthier
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708
Received 10 June 1996; revised manuscript received 8 April 1997
We observe 30% two-photon optical amplification of a probe laser-field propagating through a laser-pumped
potassium vapor. This amplification is spectrally isolated and substantially larger than that of previously
reported continuous-wave two-photon amplifiers. The combination of large amplification and spectral isolation
of the two-photon gain feature will greatly facilitate precise studies of the photon statistics of this highly
nonlinear quantum amplifier and the development and characterization of a two-photon laser based on this gain
medium. We also observe spectrally-distinct three-photon amplification ( 5% in the same system under
different experimental conditions. We present a simple model of the interaction that gives qualitative agree-
ment with our observations and explains the dependence of the two-photon gain on the various system
parameters. This model predicts that the size of the two-photon gain is quite sensitive to an interference
between two different quantum pathways. S1050-29479700208-4
PACS numbers: 42.65.Dr, 42.50.Hz, 42.65.Pc, 42.65.Vh
The study of light-matter interactions in the regime where
the coupling between the atoms and the radiation field is
highly nonlinear is a subject of fundamental importance in
quantum optics. Devices that operate exclusively in this re-
gime, such as two-photon amplifiers and two-photon lasers
1–3, have intrigued researchers for years because their dy-
namical behavior 4, photon statistics, and coherences 5
are predicted to be very different from their one-photon
counterparts. Despite the fundamental and practical interest
in these devices, there have been few experimental tests of
the numerous, often conflicting, predictions regarding their
behavior. The primary limitation on these tests has been the
difficulty in realizing practical two-photon lasers and ampli-
fiers in the laboratory.
In this work, we demonstrate a new two-photon optical
gain medium that amplifies a beam of light by 30%. The
observed two-photon gain is approximately 300 times larger
than that obtained previously in continuous-wave two-
photon optical amplifiers 6,7. This large gain is obtained
using a relatively simple apparatus: a laser-driven potassium
vapor contained in a glass cell. Furthermore, the observed
two-photon gain is spectrally isolated from other competing
processes, facilitating precise studies of the characteristics of
two-photon amplifiers and lasers. This amplifier operates in
the degenerate mode, where both photons generated in the
stimulated emission process have the same frequency.
The two-photon gain in this system arises from a stimu-
lated emission process that we call two-photon stimulated
Raman scattering, shown schematically in Fig. 1a8. In-
tense pump solid and probe dashed fields stimulate the
atom to make a transition between the initial state | g and the
final state | g ' by absorbing two photons from the pump
field frequency
d
) and adding two new photons to the
probe field frequency
p
) via virtual intermediate states.
Energy conservation requires that
p
=
d
-
gg
'
/2, where
gg
'
is the energy separation between | g and | g ' . We
stress that this scattering process is a pure gain process based
on the stimulated emission of two probe photons; that is, the
stimulated transition rate does not depend on the relative
phase of the fields. Hence, we expect this gain medium to
display all of the properties associated with a generic, phase-
insensitive, two-photon amplifier. This is in contrast to any
parametric wave-mixing process which might also result in
the addition of photons to the probe field when
p
=
d
-
gg
'
/2. To obtain continuous-wave two-photon
gain based on this stimulated Raman process, a steady-state
population imbalance must exist between states | g and
| g ' such that the population of state | g is larger than that of
state | g ' . In this system, this imbalance is maintained via
optical pumping of atoms by the intense pump field.
We note that n -photon Raman scattering processes can
occur in this system for probe-beam frequencies
p
=
d
-
gg
'
/ n , for n =1,2,3, ... . Kumar and co-
workers 9 have studied extensively the one-photon Raman
process ( n =1) in a laser-driven sodium vapor, while Hem-
merich et al. 10 have observed multiphoton Raman scatter-
ing in cooled rubidium atoms trapped in the potential wells
of a three-dimensional optical lattice. Trebino, Rahn, and
FIG. 1. a The two-photon stimulated Raman transition be-
tween long-lived atomic states | g and | g ' is resonantly enhanced
by the excited state | e . The process involves the annihilation of
two pump photons of frequency
d
solid and the creation of two
probe photons of frequency
p
dashed. b The strong pump
beam, which interacts on both the | g →| e and | g ' →| e transi-
tions, creates a population imbalance in | g and | g ' via optical
pumping.
PHYSICAL REVIEW A AUGUST 1997 VOLUME 56, NUMBER 2
56 1050-2947/97/562/15195/$10.00 1519 © 1997 The American Physical Society