Determining the Hyperfine Structure and Clock Transitions for Kramers Rare-Earth Ions in a Crystal under a Magnetic Field: Beyond Spin Hamiltonian

Abstract

Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173Yb3+:Y2SiO5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171Yb3+:Lu2Si2O7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.

Growth, Elastic, Thermal, and Crystal Field Analysis of the Yb3+:YScSi2O7 Laser Crystal

“…The four emission bands around 978, 999, 1033, and 1074 nm can roughly be attributed to the 5 → 1, 5 → 2, 5 → 3, and 5 → 4 transitions, respectively. The sublevel positions of the 2 F 7/2 and 2 F 5/2 of Yb 3+ :YScSi 2 O 7 and those of Yb 3+ :Lu 2 Si 2 O 7 , reported are listed in Table .…”

“…In the SPM, the crystal field parameters B q k can be written as , Re B q k = A̅ k ( R 0 ) ∑ i false( R 0 R i false) t k K q k ( θ i , ϕ i ) / α k , q Im .25em B q k = A̅ k ( R 0 ) ∑ i false( R 0 R i false) t k K − q k ( θ i , ϕ i ) / α k , q where notation i means the i th ligand, A̅ k ( R 0 ) is the intrinsic crystal field parameter, R 0 is the reference distance between central and ligand ions and is taken as 2.4 Å, , R i is the distance between the doped ion and ligand i , K ± q k (θ i ,ϕ i ) is the purely geometric coefficient expressed in spherical polar coordinates as given in ref with polar angle θ i and azimuthal angle ϕ i of ligand i , t k is the power-law exponent, and α k , q is the conversion factor between the extended Stevens operator and Wybourne notation. For the Yb 3+ :YScSi 2 O 7 crystal, t 2 = 6, t 4 = 5...…”

“…17 In the Yb 3+ :YScSi 2 O 7 crystal, as discussed above, the average cation field strength CFS of Y 3+ / Sc 3+ is larger than that of Lu 3+ in Yb 3+ :Lu 2 Si 2 O 7 , which would lead to the finding that more electron cloud of the coordinated oxygen ion O 2− of Yb 3+ is polarized to Y 3+ /Sc 3+ . Therefore, the electrostatic and covalent interactions to Yb 3+ in YScSi 2 O 7 decrease, and the intrinsic crystal field parameters and ξ 4f of Yb 3+ :YScSi 2 O 7 are generally smaller than those of Yb 3+ :Lu 2 Si 2 O 7 33 whose intrinsic crystal field parameters and ξ 4f are A̅ 2 (R 0 ) = 401 cm −1 , A̅ 4 (R 0 ) = 61 cm −1 , A̅ 6 (R 0 ) = 14 cm −1 , and 2902 cm −1 , respectively.…”

“…For the Yb 3+ :YScSi 2 O 7 crystal, t 2 = 6, t 4 = 5, and t 6 = 6.1 were adopted for the power-law exponents t k as for Yb 3+ :Lu 2 Si 2 O 7 . 33 The Yb 3+ −O 2− distance R i can be estimated by the empirical relation 41…”

Organometallic Ir(iii) complexes: post-synthetic modification, photophysical properties and binuclear complex construction

“…4B, Table S3 †). Thus, the arrangement of the Yb(III) energy levels 60,61 facilitates efficient energy transfer from the triplet level of the complex 6 to the emitting level of Yb(III) ion in the complex 11 Yb . This finding is in agreement with the observed emission lifetime.…”