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We study the entanglement dynamics of the two two-level atoms coupling with asingle-mode polarized cavity field after incorporating the atomic centers ofmass classical harmonic vibrations with micro amplitudes and low frequencies.We propose a quantitative vibrant factor to modify the concurrence of the twoatoms states. When the vibrant frequencies are very low, we obtain that: (i)the factor depends on the relative vibrant displacements and the initial phasesrather than the absolute amplitudes, and reduces the concurrence to threeorders of magnitude; (ii) the concurrence increases with the increase of theinitial phases; (iii) the frequency of the harmonic vibration can be obtainedby measuring the maximal value of the concurrence during a small time. Theseresults indicate that even the extremely weak classical harmonic vibrations canbe monitored by the entanglement of quantum states.

optical review

The Classical Harmonic Vibrations of the Atomic Centers of Mass with  Micro Amplitudes and Low Frequencies Monitored by the Entanglement between  the Two Two-level Atoms in a Single mode Cavity