Controlling Quantum Chaos: Optimal Coherent Targeting

TL;DR

This paper extends classical chaos control techniques to quantum systems in the semiclassical regime, demonstrating how tailored perturbations can achieve precise quantum state targeting with errors diminishing as Planck's constant approaches zero.

Contribution

It introduces a method for quantum targeting in chaotic systems using tailored perturbations, bridging classical chaos control and quantum dynamics.

Findings

The method is applied to the quantum kicked rotor.

Error can be minimized as 7 approaches zero.

The approach demonstrates effective quantum state targeting.

Abstract

One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as $\hbar \rightarrow 0$