  Thermal fluctuations tend to destroy long-range phase correlations.
Consequently, bosons in a lattice will undergo a transition from a
phase-coherent superfluid as the temperature rises. Contrary to common
intuition, however, we show that non-equilibrium driving can be used to reverse
this thermal decoherence. This is possible because the energy distribution at
equilibrium is rarely optimal for the manifestation of a given quantum
property. We demonstrate this in the Bose-Hubbard model by calculating the
non-equilibrium spatial correlation function with periodic driving. We show
that the non-equilibrium phase boundary between coherent and incoherent states
at finite bath temperatures can be made qualitatively identical to the familiar
zero-temperature phase diagram, and we discuss the experimental manifestation
of this phenomenon in cold atoms.
