Vibrational Resonance in the Morse Oscillator

Abstract

We investigate the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies \omega and \Omega with \Omega>>\omega. In the damped and biharmonically driven classical Morse oscillator applying a theoretical approach we obtain an analytical expression for the response amplitude at the low-frequency \omega. We identify the conditions on the parameters for the occurrence of the resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/(d\omega) where d is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. We have observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. We also report the occurrence of resonance and anti-resonance of transition probability of quantum mechanical Morse oscillator in the presence of the biharmonic external field.