Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator

TL;DR

This paper demonstrates how phase space control techniques can suppress dissociation in a driven Morse oscillator by recreating invariant tori, highlighting differences between classical and quantum effects, especially near resonances.

Contribution

It introduces a control method to recreate phase space barriers in a driven Morse oscillator, effectively suppressing dissociation in both classical and quantum regimes.

Findings

Control fields can recreate invariant tori to suppress dissociation.

Near two-photon resonance, barriers are ineffective due to resonance-assisted tunneling.

Quantum dissociation involves specific nonlinear resonances in phase space.

Abstract

This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in the phase space. The control algorithm proposed by Huang {\it et al.} (Phys. Rev. A {\bf 74}, 053408 (2006)) is used to obtain an analytic expression for the control field. We show that the control term, approximated as an additional weaker field, is efficient in recreating the desired tori and suppresses the classical as well as the quantum dissociation. However, in the case when the field frequency is tuned close to a two-photon resonance the local barriers are not effective in suppressing the dissociation. We establish that in the on-resonant case quantum dissociation primarily occurs via resonance-assisted tunneling and controlling the quantum dynamics requires a local perturbation of the specific nonlinear resonance in the underlying phase space.