Spectroscopic calculations for trivalent lanthanide ions

Optically addressable solid-state defects are sensitive to electric and magnetic fields, making them suitable for coherent manipulation of quantum states. Notably, it has been demonstrated that solid-state defects can be coherently manipulated using electric fields [1,2], enabling precise control of the photoluminescence spectra of these spin defects when integrated into electrical junctions. In this study, we examine trivalent lanthanide ion defects in crystals using a semi-empirical Hamiltonian, with parameters empirically fitted to experimental data. By diagonalizing the Hamiltonian, we predict key spectroscopic properties of these defects, including optical transition rates, oscillator strengths, magnetic dipole transitions, parity-forbidden electric dipole transitions, and g-tensors of low-energy excitations. Our results are compared with the well-established calculations from Carnall et al. [3] for lanthanide ions in LaF3, and we provide the qlanth software for reproducibility. These findings are crucial for advancing the control of rare-earth-based quantum devices and for understanding the mechanisms of their decoherence.

[1] P.V. Klimov, A.L. Falk, B.B. Buckley, and D.D. Awschalom, PRL 112, 087601 (2014)

[2] A.M. Day, M. Sutula, J.R. Dietz, A. Raun, D.D. Sukachev, M.K. Bhaskar, and E.L. Hu, Nat. Comm. 15, 4722 (2024)

[3] W.T. Carnall, G.L. Goodman, K. Rajnak, and R.S. Rana, The J. Chem. Phys. 90, 3443 (1989)