Coherently Driven $N$ Number of Degenerate Three-Level Atoms with Parametric Amplifier

Abstract

We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equation for the cavity mode operator, the mean photon number and the quadrature squeezing of the cavity light are calculated. And a large part of the mean photon number is confined in a relatively small frequency interval. Furthermore, we also obtain the antinormally ordered characteristic function defined in the Heisenberg picture. With the aid of the resulting characteristic function, we determine the Q function which is then used to calculate the photon number distribution.

Enhanced Squeezing and Entanglement in Nondegenerate Three-Level Laser Coupled to Squeezed Vacuum Reservoir

“…On the basis of these definitions, a two-mode light is said to be in a squeezed state if either Δc 2 + < 1 and Δc 2 − > 1 or Δc 2 + > 1 and Δc 2 − < 1, such that Δc + Δc − ≥ 1. The variances of the quadrature operators can be expressed as…”

“…The ladder-type three-level laser has received a considerable interest over the years in light of its potential application as a source of radiation with various quantum properties [1][2][3][4][5][6][7][8]. The quantum properties of the light, in this device, is attributed to atomic coherence that can be induced either by preparing the atoms initially in a coherent superposition of the top and bottom levels [7,8] or coupling these levels by an external radiation [9][10][11] or using these mechanisms together [12].…”