# Invariant-based pulse design for three-level systems without the rotating-wave approximation

## TL;DR

This paper presents a method for designing control pulses for three-level quantum systems that works without relying on the rotating-wave approximation, enabling faster quantum information processing.

## Contribution

The authors introduce a reverse engineering scheme based on Lewis-Riesenfeld invariants that allows pulse design without RWA, with controllable amplitudes and detunings.

## Key findings

- Pulse amplitudes and detunings can be controlled by adjusting parameters.
- The method avoids additional couplings and singularities in pulse design.
- Applicable to systems where RWA is invalid, enabling faster quantum operations.

## Abstract

In this paper, a scheme is put forward to design pulses which drive a three-level system based on the reverse engineering with Lewis-Riesenfeld invariant theory. The scheme can be applied to a three-level system even when the rotating-wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.