Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems

TL;DR

This paper investigates how eigenvalue intersections in quantum Hamiltonians can degenerate from conical to semi-conical types under perturbations and explores the implications for ensemble controllability of quantum states.

Contribution

It introduces the concept of semi-conical eigenvalue intersections and analyzes their impact on the controllability of quantum systems with two controls.

Findings

Semi-conical intersections are generic in the space of Hamiltonians.

Normal forms are used to analyze ensemble controllability.

Degeneration of conical to semi-conical intersections affects control strategies.

Abstract

We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian.