The Scaling of Weak Field Phase-Only Control in Markovian Dynamics

TL;DR

This paper analyzes how weak field phase-only control in open quantum systems scales, showing that at leading order, population transfer depends only on the autocorrelation function, with phase dependence appearing only at higher orders.

Contribution

It demonstrates that in Markovian open quantum systems, phase dependence of population transfer emerges only at higher perturbation orders, clarifying the limitations of weak field phase control.

Findings

Population transfer depends on the autocorrelation function at leading order.

Phase dependence appears only at the next order in perturbation.

Weak field phase control is limited in Markovian dynamics at leading order.

Abstract

We consider population transfer in open quantum systems, which are described by quantum dynamical semigroups (QDS). Using second order perturbation theory of the Lindblad equation, we show that it depends on a weak external field only through the field's autocorrelation function (ACF), which is phase independent. Therefore, for leading order in perturbation, QDS cannot support dependence of the population transfer on the phase properties of weak fields. We examine an example of weak-field phase-dependent population transfer, and show that the phase-dependence comes from the next order in the perturbation.