Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors

TL;DR

This paper develops invariant-based inverse engineering techniques to achieve fast, robust population transfer in two-level quantum systems, effectively countering dephasing noise and systematic frequency errors, with optimized protocols balancing robustness and energy constraints.

Contribution

It introduces a method to design robust control protocols for quantum state transfer that are insensitive to noise and errors, optimizing for energy constraints.

Findings

Optimal protocols are insensitive to perturbations but require infinite energy.

A flat π pulse is most robust against phase noise under energy constraints.

A family of optimized protocols reduces sensitivity to systematic frequency shifts.

Abstract

We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat $\pi$ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.