Interaction of Subharmonic Light Modes with Three-Level Atom
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Date
2021-01-09
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Addis Ababa University
Abstract
In this dissertation we have studied the photon statistical and the quadrature
squeezing properties of the two-mode cavity light available following the interaction
of subharmonic light modes, emerging from a nonlinear crystal pumped by
coherent light, with a single three-level atom in a closed cavity. The cavity is coupled
to a vacuum reservoir via a single port mirror. We have considered the case in
which the top and bottom levels of the three-level atom are not coupled by the coherent
light emerging from the nonlinear crystal. Employing the pertinent Hamiltonian
and master equations, we have obtained the equations of evolution of the
expectation values for the cavity mode and atomic operators.
Applying the steady-state solutions of the equations of evolution of the expectation
values for the cavity mode and atomic operators, we have calculated the global
mean photon number for the two-mode cavity light. The global mean photon number
of the two-mode cavity light is found to be the sum of the mean photon number
due to the subharmonic generation and the mean photon number emitted and
absorbed by the atom. We have observed that the effect of the interaction of the
subharmonic light modes with the three-level atom is to decrease the global mean
photon number of the two-mode cavity light. This is due to the fact that the mean
number of photons absorbed is greater than the mean number of photons emitted.
Moreover, applying the time dependent solutions of the equations of evolution
of the expectation values for the cavity mode and atomic operators, we have also
obtained the local mean photon number for the two-mode cavity light. Our analysis
shows that the local mean photon number of the two-mode cavity light increases
with frequency and eventually approaches to the global mean photon number
within a relatively small frequency interval.
In addition, we have calculated the global photon-number variance for the twomode
cavity light. We have noticed that the photon statistics of the two-mode cavity
light is supper poissonian. Our analysis indicates that the global photon-number
variance in the presence of the interaction is less than that in the absence of the interaction.
This implies that the effect of the interaction is to decrease the global
photon-number variance.
Furthermore, we have determined the global quadrature squeezing for the twomode
cavity light with arbitrary ordering of the two-mode vacuum reservoir noise
operators. We have established that the two-mode cavity light is in squeezed state
and the squeezing occurs in the plus quadrature. We have also found that the global
quadrature squeezing in the presence of the interaction (43:5%) is less than the
global quadrature squeezing (50%) in the absence of the interaction. In addition,
We have seen that the maximum local quadrature squeezing for the two-mode cavity
light is 60:8% at _ = 0:17 and eventually approaches to the global quadrature
squeezing as the frequency increases.
Finally, applying the steady-state solutions of the equations of evolution of the
expectation values for the cavity mode operators, we have determined the global
quadrature squeezing for the two-mode cavity light when the two-mode vacuum
reservoir noise operators are in normal order. We have found that the global
quadrature squeezing for the two-mode cavity light is 100% for c = 16
15 _ 1:067
and is 88:3% for c = 1:25 with the vacuum noise operators in normal order.
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Keywords
Interaction, Subharmonic Light, Three-Level Atom