Robust optical clock transitions in trapped ions using dynamical decoupling

We present a novel method for engineering an optical clock transition that is robust agaiast external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic field shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble ofions, and is relevant for several types of ions, such as 40Ca, Sr1", l38BiT and 176Lo". Taking a spherically symmetric Coulomb crystal formed by 400 40Ca+ ions as an example, we show through numerical simulations that the in homogeneous linewidth of teas of Hertz in such a crystal together with linear Zeeman shifts of order 10 MHz are reduced to form a linewidth of around 1 Hz. We estimate a two-order-of-magnitude reduction in averaging time compared tostate-of-the art single ion frequency references, assuming a probe laser fractional instability of 10~1 Furthermore, a statistical uncertainty reaching2.9 x 10"16 in 1 s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an 2/Al clock.