### Abstract:

We have studied the statistical and squeezing properties of the light generated by
a three-level laser coupled to a two-mode vacuum reservoir. The three-level atoms
available in a closed cavity are pumped from the bottom to the top level by electron
bombardment. We have carried out our analysis by taking the noise operators
associated with the two-mode vacuum reservoir in arbitrary order. Applying the solutions
of the equations of evolution of the cavity mode and atomic operators, we
have determined the global mean photon number, the global photon number variance,
and the global quadrature squeezing of the one-mode aswell as the two-mode
cavity light. In addition, we have calculated the local mean photon number, the local
photon number variance, and the local quadrature squeezing of the two-mode
cavity light.
We have found the maximum global quadrature squeezing of the two-mode cavity
light to be 37.5% below the vacuum level. This result happens to be less than
that obtained by putting the noise operators in normal order. On the other hand,
the global photon number variance calculated by taking the noise operators in arbitrary
order turns out to be greater than that obtained by putting the noise operators
in normal order. In addition, our analysis shows that a large part of the mean and
variance of the photon number are confined in a relatively small frequency interval.
Furthermore, employing the density operator for the superposition of a pair of
two-mode cavity light beams, we have calculated the mean photon number, the
photon number variance, and the quadrature squeezing. It so happens that the
global (local) mean photon number of the superposed two-mode cavity light beams
is the sum of the global (local) mean photon numbers of the component two-mode
cavity light beams. On the other hand, the global (local) photon number variance
of the superposed two-mode cavity light beams is four times that of the separate
two-mode cavity light beams. Moreover, our results show that the global (local)
quadrature squeezing of the superposed two-mode cavity light beams is the same
as the global (local) quadrature squeezing of the component two-mode cavity light
beams.