  We introduce universally robust sequences for dynamical decoupling, which
simultaneously compensate pulse imperfections and the detrimental effect of a
dephasing environment to an arbitrary order, work with any pulse shape, and
improve performance for any initial condition. Moreover, the number of pulses
in a sequence grows only linearly with the order of error compensation. Our
sequences outperform the state-of-the-art robust sequences for dynamical
decoupling. Beyond the theoretical proposal, we also present convincing
experimental data for dynamical decoupling of atomic coherences in a
solid-state optical memory.
