Quantum optimal control within the rotating wave approximation

TL;DR

This paper explores how the rotating wave approximation simplifies quantum optimal control problems, enabling analytic solutions and efficient protocols for state transfer and entanglement in multi-level systems.

Contribution

It demonstrates that optimal control problems can be simplified to time-independent Hamiltonians under the rotating wave approximation, providing analytic solutions and practical protocols.

Findings

Analytic solutions for two-level and N-level star systems.

Numerical validation for connected acyclic N-level systems.

Protocol design for entangling Rydberg atoms with constant pulses.

Abstract

We study the interplay between rotating wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time-independent under the rotating wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multi-variable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an $N$-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic $N$-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulses atoms in an experimentally relevant range of parameters.