Squeezing in a -type three-level atom via spontaneously generated coherence
Isabel Gonzalo,
1
M. A. Antón,
2
F. Carreño,
2
and Oscar G. Calderón
2,3
1
Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040, Spain
2
Escuela Universitaria de Óptica, Universidad Complutense de Madrid, C/ Arcos de Jalón s/n, 28037 Madrid, Spain
3
Stanford Picosecond FEL Center, Hansel Experimental Physics Laboratory, Stanford University, Stanford,
California 94305-4085, USA
Received 15 July 2004; revised manuscript received 30 June 2005; published 13 September 2005
The squeezing spectrum of the fluorescent light is investigated for a laser-driven three-level atom of the
configuration when quantum interference of the decay channels is accounted for. We show that when the two
atomic transitions contribute to the detected fluorescence field, squeezing at certain frequency intervals is
obtained in both the weak- and the high-Rabi-frequency regimes even for equally decay rates of the transitions.
Unlike in two-level atoms in free space, squeezing can be obtained in both the in-phase and out-of-phase
quadrature spectra although in different spectral regions. We also show that the squeezing spectrum can be
controlled by an adequate selection of the Rabi frequencies and atomic detunings. Another remarkable effect is
that squeezing can be achieved with proper relative phases of the driving fields. We provide an analytical
description in the dressed basis which accounts for the main features of the squeezing spectra obtained from the
numerical work.
DOI: 10.1103/PhysRevA.72.033809 PACS numbers: 42.50.Dv, 42.50.Gy, 42.50.Hz
I. INTRODUCTION
Resonance fluorescence is a central topic in quantum op-
tics and has been shown to be a successful way to investigate
the fundamentals of the interaction of matter and radiation
1–4. Using this technique, a manifold of interesting phe-
nomena have been observed or predicted such as photon an-
tibunching 4–6, sub-Poissonian statistics 7, and squeez-
ing 8, among others.
In contrast to fluorescence spectra which are detected
without phase sensitivity, squeezing spectra are obtained by
homodyne detection of scattered radiation from free atoms
driven by a coherent field. In these experiments, the scattered
radiation field of the atoms, E, is mixed with a local oscilla-
tor LO field |E
LO
|e
i
, having a controllable fixed phase ,
relative to the driving field. Thus, the signal Pt reaching the
detector is proportional to the interference term between the
LO and the scattered field, that is, Pt |E
LO
|x
, where x
is
a quadrature of the scattered field given by x
=1/2e
-i
E
+ e
i
E
†
. Squeezing in the radiation field can be measured by
analyzing the fluctuations in the detected power. In this way,
the normally ordered variance of the quadrature components,
either in total phase quadratures or in frequency components
squeezing spectrum, can be obtained. In the last case, the
field must be frequency filtered 9,10. Moreover, the phe-
nomenon of phase-sensitive squeezing in resonance fluores-
cence, first predicted by Mandel 7 and Walls and Zöller
11, has received considerable attention in the context of
two-level atoms. Theoretical calculations in a two-level atom
have shown that the squeezing can be found in the out-of-
phase quadrature component spectra in a weak coherent ex-
citation regime under the condition 2 12–14, where
and are the Rabi frequency and the atomic decay rate,
respectively.
In spite of receiving considerable attention, squeezing in
resonance fluorescence has eluded experimental observation,
one of the problems being that atomic motion produces
phase shifts which destroy the squeezing 15. However, in a
recent work 16, precision near-resonant phase-dependent
spectra have been obtained by using a homodyne detection
technique that suppresses excess noise by subtracting trans-
mitted power signals from two identically prepared atomic
samples. With this scheme, Lu et al. 16 and Zhao et al. 17
have found some evidence of squeezing when measuring the
phase-dependent fluorescent spectra of coherently driven
174
Yb atoms at a phase near ± / 4 relative to the exciting
field. This important result has renewed the exploration of
phase-dependent spectra of resonance fluorescence in two-
level atoms. Since the fluorescence field quadrature compo-
nents in two-level systems depend on the difference between
the upper-level population and the square of the dipole mo-
ment 18, it was claimed 19–22 that three-level atoms of
the type would be more suitable than two-level atoms, due
to the possibility of reducing the upper-state population via
the coherent population trapping effect. This dynamically in-
duced atomic coherence also lead to many phenomena, such
as electromagnetically induced transparency 23–25, lasing
without inversion 26–28, refractive index enhancement
without absorption 29–31, and giant nonlinearity 32–34.
Squeezing of the fluorescent field emitted by -type atoms
has been previously discussed in terms of the variance of
quadrature components of the total electric field rather than
in terms of the squeezing spectrum. Vogel and Blatt 15
found steady-state squeezing only when the two spontaneous
emission rates and the two Rabi frequencies were signifi-
cantly different from each other. Ficek et al. 22 also found
that steady-state squeezing is limited to the case when the
fluorescence of only one atomic transition is detected and the
decay rate of the transition, which exclusively contributes to
the detected fluorescence field, is larger than the decay of the
other transition. Moreover, they did not find squeezing when
the two atomic transitions equally contribute to the detected
fluorescence field.
PHYSICAL REVIEW A 72, 033809 2005
1050-2947/2005/723/03380913/$23.00 ©2005 The American Physical Society 033809-1