# Dynamics of three-Level Laser Pumped by Electron Bombardment and With Spontaneous Emission

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## Date

2018-09-03

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Addis Ababa University

## Abstract

In this PhD dissertation we have studied the statistical and squeezing properties of
the cavity light generated by a three-level laser. In this quantum optical system, N
three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir,
are pumped to the top level by means of electron bombardment at constant
rate. We have considered the case in which the three-level atoms and the cavity
modes interact with the two-mode vacuum reservoir. We have carried out our analysis
by putting the noise operators associated with the vacuum reservoir in arbitrary
order. Applying the solutions of the equations of evolution for the expectation
values of the atomic operators and the quantum Langevin equations for the cavity
mode operators, we have calculated the mean and variance of the photon number
as well as the quadrature squeezing for the cavity light. In addition, we have shown
that the presence of the spontaneous emission process leads to a decrease in the
mean and variance of the photon number. We have seen that the global mean photon
numbers of the light modes emitted from the top and intermediate levels are
the same both in the presence and absence of spontaneous emission, and are separately
in a chaotic state. However, we have observed that the two-mode cavity light
is in a squeezed state and the squeezing occurs in the minus quadrature. In addition,
we have found that the effect of the vacuum reservoir noise is to increase the
photon-number variance and to decrease the quadrature squeezing of the cavity
light. However, the vacuum reservoir noise does not have any effect on the mean
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photon number. Moreover, the maximum quadrature squeezing of the light generated
by the laser, operating far below threshold, is found to be 37:5% below the
vacuum-state level. In addition, our result indicates that the quadrature squeezing
is greater for = 0 than that for = 0:4 for 0.01 < ra < 0.35 and is smaller for = 0
than that for = 0:4 for 0.35 < ra < 1. We have also noted that the local quadrature
squeezing approaches the global quadrature squeezing as the frequency interval
increases.
Furthermore, applying the density operator for a pair of superposed two- mode
laser light beams, we have calculated the mean and variance of the photon number
as well as the quadrature squeezing. We have found that both the mean photon
number and the quadrature variance for the superposed two-mode laser light
beams is the sum of the mean photon numbers and the quadrature variances of
the constituent two-mode light beams. However, the variance of the photon number
of the superposed two-mode laser light beams is not the sum of the variances
of the photon numbers of the constituent two-mode light beams. Finally, our result
shows that the quadrature squeezing of the superposed two-mode laser light
beams is equal to the quadrature squeezing of one of the superposed the two-mode
light beams. This implies that the superposition of the two-mode laser light beams
does not affect the quadrature squeezing, but it increases the global mean photon
number and the global variance of the photon number. Thus we note that the
superposition of the two-mode laser light beams leads to a more bright squeezed
light.

## Description

## Keywords

Dynamics of three-Level Laser, Pumped, Electron Bombardment, Spontaneous, Emission