Al$^{+}$ optical clocks for fundamental physics, geodesy, and quantum metrology*

Laser-cooled trapped atoms have long been recognized as potentially very accurate frequency standards for clocks. Ultimate accuracies of 10$^{-18}$ to 10$^{-19}$ appear possible, limited by the time-dilation of trapped ions that move at laser-cooled velocities. The Al$^{+}$ ion is an attractive candidate for high accuracy, owing to its narrow electronic transition in the optical regime and low sensitivity to ambient field perturbations. Precision spectroscopy on Al$^{+}$ is enabled by quantum information techniques. With Al$^{+}$ ``quantum-logic'' clocks, the current accuracy of 8.6$\times $10$^{-18}$ has enabled a geo-potential-difference measurement that detected a height change of 37$\pm $17 cm due to the gravitational red-shift. We have also observed quantum coherence between two Al$^{+}$ ions with a record Q-factor of 3.4$\times $10$^{16}$, and compared the Al$^{+}$ resonance frequency to that of a single Hg$^{+}$ ion to place limits on the temporal variation of the fine-structure constant. This work is done in collaboration with D. B. Hume, M. J. Thorpe, D. J. Wineland, and T. Rosenband.