Preparation of an ensemble of thulium atoms in different vibrational levels in an optical lattice

The deterministic excitation of thulium atoms from the ground vibrational state of the optical lattice potential to the first and second vibrational levels with efficiencies of 40 and 24%, respectively, has been demonstrated. The purity of the prepared vibrational states is at least 93 and 95% in the former and latter cases, respectively, and is limited by both the purity of the initial state and the non-resonant excitation of the clock transition carrier frequency. The obtained high efficiency and quality of the preparation of atoms in a given vibrational level make it possible to characterize and control the frequency shift of the clock transition due to the interaction of thulium atoms with the field of the optical lattice, which is necessary to achieve an uncertainty of 10$^{-17}$ for the thulium optical clock.