Anticrossings in solid-state laser spectroscopy

We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-Å zero-phonon transition ${}_{}{}^3{}_{}{}^{}H_4^{}{}_{}{}^{}\left({\Gamma }_1\right)\leftrightarrow {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\left({\Gamma }_1\right)$ of ${\mathrm{Pr}}^{3+}$ in a YAl${\mathrm{O}}_3$ crystal at 2° K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction $V$ between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\leftrightarrow 3$ transition. Ground- and excited-state gyromagnetic ratios ${\gamma }_i\mathrm{}(i=X,Y,Z)\mathrm{}$ and the interactions $V$ are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}_{}^{3+}{}_{}{}^{}$ which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of ∼ 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.