Characterization of quantum entanglement by concurrence, negativtiy and entrpy in interacting system between three level trapped ion and two-laser beam

Quantum Entanglement of the system which is formed by interacting of two photons and three levelled trapped ion. In this study th state of being Entanglement, which we see in many scientific researches, is examined if there is entanglement or not, by having the charts being formed depending on time with the correlations of Concurrence, Negativity and Entropy which are the measurements of entnglement and with the help of mathematica programme. four different value of Lamb Dicke paraeter?s chart is formed ( 0.01, 0.02, 0.05, 0.1) by using Concurrence, Negativity and Entropy measurements and totally there exists twelve charts. It takes finding probability amplitudes in trapped ion and these are formed fort he first position. those figure formed by mathematica programme are oscillation funciton and obtained in two level. In those 12 charts, we concluded that maximum values of Concurrence, Negativity and Entropy arise as the value of Lamb Dicke Parameter arises; in addition to that the amount of entanglement is at its maximum level between particular time periods.