This work presents the entanglement between an electromagnetic field and two-level atom situated inside a quantum optical system. Our optical model is based on cylindrical tube with a hole diameter of the order of nanoscale which leads to only the lowest order mode can exist. Numbers of the statistical features of effective Hamiltonian such as the temporal evolution of the atomic inversion and the von Neumann entropy are evaluated. We have evaluated the atomic inversion and we demonstrate that the atom still in maximal entangled state when the radius of tube a is large. We have used the von Neumann entropy to measure the degree of that entanglement. The results illustrate that the effect of the radius of tube a changes the quasi-period of the field entropy and therefore the entanglement process.