Simple determination of dark states in a general multi-level system
Quantum Physics
2025-12-17 v2
Abstract
In a multi-level energy system with energy transitions, dark states are eigenstates of a Hamiltonian that consist entirely of ground states, with zero amplitude in the excited states. We present several criteria which allows one to deduce the presence of dark states in a general multi-level system based on the submatrices of the Hamiltonian. The dark states can be shown to be the right-singular vectors of the submatrix that connect the ground states to the excited states. Furthermore, we show a simple way of finding the dark state involving the determinant of a matrix constructed from the same submatrix.
Cite
@article{arxiv.2211.16832,
title = {Simple determination of dark states in a general multi-level system},
author = {Kaixuan Zhou and June Wu and Junheng Shi and Tim Byrnes},
journal= {arXiv preprint arXiv:2211.16832},
year = {2025}
}