  The accelerated optical lattice has emerged as a valuable technique for the
investigation of quantum transport physics and has found widespread application
in quantum sensing, including atomic gravimeters and atomic gyroscopes. In our
study, we focus on the adiabatic evolution of ultra-cold atoms within an
accelerated optical lattice. Specifically, we derive a time bound that delimits
the duration of atomic adiabatic evolution in the oscillating system under
consideration. To experimentally substantiate the theoretical predictions,
precise measurements to instantaneous band populations were conducted within a
one-dimensional accelerated optical lattice, encompassing systematic variations
in both lattice's depths and accelerations. The obtained experimental results
demonstrate a quantitatively consistent correspondence with the anticipated
theoretical expressions. Afterwards, the atomic velocity distributions are also
measured to compare with the time bound. This research offers a quantitative
framework for the selection of parameters that ensure atom trapped throughout
the acceleration process. Moreover, it contributes an experimental criterion by
which to assess the adequacy of adiabatic conditions in an oscillating system,
thereby augmenting the current understanding of these systems from a
theoretical perspective.
