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Vacuum induced transparency and photon number resolved Autler-Townes splitting in a three-level system
We study the absorption spectrum of a probe field by a {\Lambda}-type
three-level system, which is coupled to a quantized control field through the
two upper energy levels. The probe field is applied to the ground and the
second excited states. When the quantized control field is in vacuum, we derive
a threshold condition to discern vacuum induced transparency (VIT) and vacuum
induced Autler- Townes splitting (ATS). We also find that the parameter change
from VIT to vacuum induced ATS is very similar to that from broken PT symmetry
to PT symmetry. Moreover, we find the photon number resolved spectrum in the
parameter regime of vacuum induced ATS when the mean photon number of the
quantized control field is changed from zero (vacuum) to a finite number.
However, there is no photon number resolved spectrum in the parameter regime of
VIT even that the quantized control field contains the finite number of
photons. Finally, we further discuss possible experimental realization
New Generalizations of Cosmography Inspired by the Pade Approximant
The current accelerated expansion of the universe has been one of the most
important fields in physics and astronomy since 1998. Many cosmological models
have been proposed in the literature to explain this mysterious phenomenon.
Since the nature and cause of the cosmic acceleration are still unknown,
model-independent approaches to study the evolution of the universe are
welcome. One of the powerful model-independent approaches is the so-called
cosmography. It only relies on the cosmological principle, without postulating
any underlying theoretical model. However, there are several shortcomings in
the usual cosmography. For instance, it is plagued with the problem of
divergence (or an unacceptably large error), and it fails to predict the future
evolution of the universe. In the present work, we try to overcome or at least
alleviate these problems, and we propose two new generalizations of cosmography
inspired by the Pad\'e approximant. One is to directly parameterize the
luminosity distance based on the Pad\'e approximant, while the other is to
generalize cosmography with respect to a so-called -shift
, which is also inspired by the Pad\'e approximant.
Then, we confront them with the observational data with the help of the Markov
chain Monte Carlo (MCMC) code emcee, and find that they work fairly well.Comment: 16 pages, 3 tables, 5 figures, revtex4; v2: discussions added, Eur.
Phys. J. C in press; v3: published versio
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