Theory and numerics of vibrational resonance in a three-level atomic optical bistable system

The vibrational resonance phenomenon in a three-level atomic optical bistable system driven by two kinds of different frequency signals is investigated. By virtue of the method of the direct separation of fast and slow motions, the approximate analytical expression for the response amplitude Q at the low-frequency is obtained. It is found that the response amplitude presents a peak with the amplitude and frequency of the high-frequency signal varying, and it is identified as the characteristic signature of the vibrational resonance. Meanwhile, the position, at which the vibrational resonance occurs, is determined by the analytical expression of the response amplitude. The effects of the other parameters on vibrational resonance in the three-level atomic optical bistable system are also investigated. The mechanism of vibrational resonance phenomenon is given by the phase synchronization between the input and output signals. The numerical simulation and theoretic results are in basic agreement.