Hamiltonian design to prepare arbitrary states of four-level systems

TL;DR

This paper introduces a Hamiltonian engineering method for four-level quantum systems that enables fast, arbitrary state preparation by leveraging four-dimensional rotation geometry and inverse Hamiltonian design.

Contribution

It presents a novel inverse Hamiltonian engineering approach utilizing four-dimensional rotation geometry for precise state control in four-level systems.

Findings

Effective state preparation using inverse Hamiltonian design

Application of Cayley's factorization for rotation decomposition

Potential for faster-than-adiabatic quantum control

Abstract

We propose a method to manipulate, possibly faster than adiabatically, four-level systems with time-dependent couplings and constant energy shifts (detunings in quantum-optical realizations). We inversely engineer the Hamiltonian, in ladder, tripod, or diamond configurations, to prepare arbitrary states using the geometry of four-dimensional rotations to set the state populations, specifically we use Cayley's factorization of a general rotation into right- and left-isoclinic rotations.