  Subjecting a many-body localized system to a time-periodic drive generically
leads to delocalization and a transition to ergodic behavior if the drive is
sufficiently strong or of sufficiently low frequency. Here we show that a
specific drive can have an opposite effect, taking a static delocalized system
into the many-body localized phase. We demonstrate this effect using a
one-dimensional system of interacting hardcore bosons subject to an oscillating
linear potential. The system is weakly disordered, and is ergodic absent the
driving. The time-periodic linear potential leads to a suppression of the
effective static hopping amplitude, increasing the relative strengths of
disorder and interactions. Using numerical simulations, we find a transition
into the many-body localized phase above a critical driving frequency and in a
range of driving amplitudes. Our findings highlight the potential of driving
schemes exploiting the coherent suppression of tunneling for engineering
long-lived Floquet phases.
