# Analytic Solutions to Coherent Control of the Dirac Equation

## TL;DR

This paper introduces an analytic framework for controlling Dirac spinors, enabling precise manipulation of quantum states and electromagnetic fields, with potential applications in quantum technology development.

## Contribution

It presents a novel, simple parametrization of Dirac spinors that allows for analytic construction of electromagnetic fields to achieve desired quantum evolutions.

## Key findings

- Achieves dispersionless rotation and translation of wave packets.
- Reveals flexibility of the Dirac equation for quantum control.
- Enables control interactions beyond electromagnetic fields.

## Abstract

A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.