where $\omega_g$, $\omega_m$, and $\omega_e$ are the frequencies of the ground state $|g\rangle$, metastable state $|m\rangle$, and excited state $|e\rangle$, respectively. The interaction with an external magnetic field $\mathbf{B}$, $V_\mathrm{m} = - \bm{\mu}_\mathrm{m} \cdot\mathbf{B}$, where $\bm{\mu}_\mathrm{m}$ is the magnetic dipole moment, is included in the atomic Hamiltonian in the form of (linearly) Zeeman shifted levels, $$H_\mathrm{a,m} = \sum_{i=1}^8 \hbar\omega_i |i\rangle\langle i|.$$ Here $\omega_i = \omega_l + g_l m_{J,i} \mu_\mathrm{B} B/\hbar$, where $l$ is $g$, $m$, or $e$ and $g_l$ is the corresponding Landé factor, $m_{J,i}$ is the magnetic quantum number of the level $|i\rangle$, and $\mu_\mathrm{B}$ is the Bohr magneton. We have chosen the quantization axis (QA), i.e., the $z$ axis, along the magnetic field. The ion is located at the origin. It is first assumed to be stationary, later its motion is accounted for.

![\[fig:8-level\](Color online) The eight-level system. Fine-structure state designations are given at the left together with the respective Landé $g$ factors. Magnetic quantum numbers are shown at the bottom. Sublevels are labeled consecutively and the allowed transitions between them are shown as arrows together with the corresponding relative transition amplitudes $C_{ij}$.](Fig02-8-level-n){width="1\columnwidth"}

The system is interacting with two laser fields that can have arbitrary time-dependent polarizations. The 