Inner-shell magnetic dipole transition in Tm atoms: A candidate for optical lattice clocks

Abstract

We consider a narrow magneto-dipole transition in the $^{169}\text{Tm}$ atom at the wavelength of $1.14 \ensuremath{\mu}\mathrm{m}$ as a candidate for a two-dimensional-optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $[\text{Xe}]4{f}^{13}6{s}^{2}(J=7/2)$ and $[\text{Xe}]4{f}^{13}6{s}^{2}(J=5/2)$ in the spectral range from 250 to 1200 nm, we find a ``magic'' wavelength for the optical lattice at 807 nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction, and other effects which can perturb the transition frequency are calculated. The transition at $1.14 \ensuremath{\mu}\mathrm{m}$ demonstrates low sensitivity to the BBR shift corresponding to $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ in fractional units. By direct excitation of the $1.14 \ensuremath{\mu}\mathrm{m}$ transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $[\text{Xe}]4{f}^{13}6{s}^{2}(J=5/2)$ of 112 ms which corresponds to a natural spectral linewidth narrower than 1.4 Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at 532 nm.