Dynamic polarizabilities and magic wavelengths for dysprosium

We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there is a set of magic wavelengths of the unpolarized lattice laser field for each pair of states, which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula that, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.