  We investigated how the presence of an additional lattice potential, driven
by a harmonic noise process, changes the transition rate from the ground band
to the first excited band in a Wannier-Stark system. Alongside numerical
simulations, we present two models that capture the essential features of the
dynamics. The first model uses a noise-driven Landau-Zener approximation and
describes the short time evolution of the full system very well. The second
model assumes that the noise process' correlation time is much larger than the
internal timescale of the system, yet it allows for good estimates of the
observed transition rates and gives a simple interpretation of the dynamics.
One of the central results is that we obtain a way to control the interband
transitions with the help of the second lattice. This could readily be realized
in state-of-the-art experiments using either Bose-Einstein condensates or
optical pulses in engineered potentials.
