Dynamical tunneling and control

TL;DR

This paper reviews how dynamical tunneling phenomena like chaos-assisted and resonance-assisted tunneling impact the ability to control quantum systems, highlighting limitations in control strategies.

Contribution

It provides a comparative analysis of two types of dynamical tunneling and their effects on quantum control, emphasizing the challenges they pose.

Findings

Chaos-assisted tunneling hampers bichromatic control in double well systems.

Resonance-assisted tunneling prevents control of dissociation in Morse oscillators.

Control efforts are often thwarted by dynamical tunneling phenomena.

Abstract

This article summarizes the recent work on the influence of dynamical tunneling on the control of quantum systems. Specifically, two examples are discussed. In the first, it is shown that the bichromatic control of tunneling in a driven double well system is hampered by the phenomenon of chaos-assisted tunneling. The bichromatic control landscape exhibits several regions indicating lack of control with every such region involving chaos-assisted tunneling. The second example illustrates the failure of controlling the dissociation dynamics of a driven Morse oscillator due to the phenomenon of resonance-assisted tunneling. In particular, attempts to control the dissociation dynamics by rebuilding local phase space barriers are foiled due to resonance-assisted tunneling.