The analytical solution of the system of three-level atom in \(\Lambda \) configuration interaction with two modes in the presence of a degenerate parameter amplifier term is presented. We investigate the effects of a degenerate parameter amplifier on the quantum properties of the atomic system. Specifically, we analyze how the presence of the parametric amplifier influences the atomic Fisher information, which quantifies the amount of information that can be extracted about a parameter from measurements on the quantum state. Additionally, we study the quantum coherence, which measures the superposition of states, and the second-order correlation function, which provides insights into the statistical properties of the emitted photons. In our analysis, we assumed that the atom in the upper state and the field in the squeezed-pair coherent state. Our results reveal that the presence of the degenerate parameter amplifier significantly enhances the quantum coherence of the atomic states. Furthermore, we demonstrate that the atomic Fisher information, a crucial quantity for parameter estimation in quantum metrology, is substantially influenced by the amplifier’s parameters. The second-order correlation function, which characterizes the statistical properties of the emitted photons, exhibits notable modifications due to the atom-amplifier interaction. These findings provide new insights into the control and manipulation of quantum states in three-level atomic systems, with potential applications in quantum information processing and metrology.
