Vibrational Resonance in the Morse Oscillator

TL;DR

This paper explores vibrational resonance phenomena in classical and quantum Morse oscillators driven by biharmonic forces, providing analytical insights and identifying conditions for resonance occurrence.

Contribution

It offers the first analytical expression for response amplitude in classical Morse oscillators under biharmonic driving and investigates quantum resonance and anti-resonance effects.

Findings

Classical Morse oscillator shows a single resonance at specific parameters.

Response amplitude at resonance is inversely proportional to damping coefficient.

Quantum Morse oscillator exhibits resonance and anti-resonance in transition probability.

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.