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 are a set of magic wavelengths of the unpoarized 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 which, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.Comment: 6 papers, 3 figure

Optimal Leapfrogging, A Complete Guide

Suppose we have some checkers placed in the lower-left corner of a Go board, and wish to move them to the upper right corner in as few moves as possible, where the pieces move as they would in the game of Chinese Checkers. In 1993, Auslander, Benjamin, and Wilkerson generalized this game for integer lattices, defined a measure of speed for a starting configuration of pieces, and proved that a maximum speed exists, which only three configurations, called "speed-of-light" configurations can attain. It was conjectured that the maximum speed of a non-speed-of-light configuration has a smaller upper bound, which we prove.Comment: In progress for submissio