  The coherence times achieved with continuous dynamical decoupling techniques
are often limited by fluctuations in the driving amplitude. In this work, we
use time-dependent phase-modulated continuous driving to increase the
robustness against such fluctuations in a dense ensemble of nitrogen-vacancy
centers in diamond. Considering realistic experimental errors in the system, we
identify the optimal modulation strength, and demonstrate an improvement of an
order of magnitude in the spin-preservation of arbitrary states over
conventional single continuous driving. The phase-modulated driving exhibits
comparable results to previously examined amplitude-modulated techniques, and
is expected to outperform them in experimental systems having higher phase
accuracy. The proposed technique could open new avenues for quantum information
processing and many body physics, in systems dominated by high frequency
spin-bath noise, for which pulsed dynamical decoupling is less effective.
