Reverse engineering control of relative phase and populations of two-level quantum systems

TL;DR

This paper presents a reverse engineering method to analytically design control fields for manipulating the relative phase and populations in two-level quantum systems, enabling tailored quantum state control.

Contribution

It introduces an analytical reverse engineering approach that links control fields to user-defined dynamics, allowing customizable quantum control strategies.

Findings

Control fields depend on derivatives of chosen dynamical functions.

The method can reach various target states with simple control fields.

The approach is adaptable for broader quantum control applications.

Abstract

We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, which allows obtaining an analytical expression for the control field depending upon two user-defined functions that dictate the population and the relative phase dynamics. We show that, in general, the prescribed functions for the dynamics cannot be chosen arbitrarily. We implement the reverse engineering technique to reach several target states using different kinds of functions to specify the system dynamics. We show that by adjusting these dynamical functions, we can produce different kinds of control fields. These controls can be easily build, needing, apart from the dynamical function themselves, only their derivatives. The methodology presented here will certainly find many applications that go beyond simple two-level systems.