The time evolution of the field quantum entropy and entanglement in a system of multi-mode coherent light field resonantly interacting with a two-level atom by degenerating the multi-photon process is studied by utilizing the Von Neumann reduced entropy theory, and the analytical expressions of the quantum entropy of the multimode field and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle and the phase angle of the atom dipole on the evolution of the quantum field entropy and entanglement. The results obtained from the numerical calculation indicate that: the stronger the quantum field is, the weaker the entanglement between the quantum field and the atom will be, and when the field is strong enough, the two subsystems may be in a disentangled state all the time; the quantum field entropy is strongly dependent on the atomic distribution angle, namely, the quantum field and the two-level atom are always in the entangled state, and are nearly stable at maximum entanglement after a short time of vibration; the larger the atomic distribution angle is, the shorter the time for the field quantum entropy to evolve its maximum value is; the phase angles of the atom dipole almost have no influences on the entanglement between the quantum field and the two-level atom. Entangled states or pure states based on these properties of the field quantum entropy can be prepared.field quantum entropy, Von Neumann reduced entropy, degenerate multi-photon process, quantum entanglement LIU WangYun et al.

The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.