Hyperfine Structure in the Spectrum of Erbium

William Jewell Carter

A. V. Lyaptsev, A. A. Kiselev, Vladimir G Bordo

Albert Frisch, K. Aikawa, Michael F. Mark +3 more

We have measured and analyzed the hyperfine structure of two lines, one at 583 nm and one at 401 nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the $J\ensuremath{\rightarrow}J+1$ laser cooling transitions from the $[\text{Xe}]4{f}^{12}6{s}^{2}{(}^{3}{H}_{6})$ ground state to two levels of the excited $[\text{Xe}]4{f}^{12}6s6p$ configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401 nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are ${A}_{e}/h=\ensuremath{-}100.1(3)\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$ and ${B}_{e}/h=\ensuremath{-}3079(30)\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, respectively. The hyperfine spectrum of the narrow transition at 583 nm, was previously observed and accurate ${A}_{e}$ and ${B}_{e}$ coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the ${A}_{e}$ and ${B}_{e}$ constants, respectively.

Optische Spektroskopie

Nicholas Jobbitt, J.‐P. R. Wells, Michael F. Reid +3 more

We report on the development and application of a parametrized crystal-field model for both ${\mathrm{C}}_{1}$ symmetry centers in trivalent erbium-doped ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. High-resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground $(^{4}\mathrm{I}_{15/2}{\mathrm{Z}}_{1})$ state and exited $(^{4}\mathrm{I}_{13/2}{\mathrm{Y}}_{1})$ state Zeeman and hyperfine structure, were simultaneously fitted in order to refine an existing crystal-field interpretation of the ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ system. We demonstrate that it is possible to account for the electronic, magnetic, and hyperfine structure of the full $4{f}^{11}$ configuration of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ telecommunications band.

Louis C. Marquet, W. E. Behring