  We measure the application of simple and compound pulses consisting of
time-dependent spatial translations to coupling vibrational states of ultracold
85Rb atoms in a far-detuned 1D optical lattice. The lattice wells are so
shallow as to support only two bound states, and we prepare the atoms in the
ground state. The lattice is oriented vertically, leading to a tilted-washboard
potential analogous to those encountered in condensed-matter systems.
Experimentally, we find that a square pulse consisting of lattice displacements
and a delay is more efficient than single-step and Gaussian pulses. This is
described as an example of coherent control. It is striking that contrary to
the intuition that soft pulses minimize loss, the Gaussian pulse is
outperformed by the square pulse. Numerical calculations are in strong
agreement with our experimental results and show the superiority of the square
pulse to the single-step pulse for all lattice depths and to the Gaussian pulse
for lattice depths greater than 7 lattice recoil energies. We also compare the
effectiveness of these pulses for reviving oscillations of atoms in vibrational
superposition states using the pulse-echo technique. We find that the square
and Gaussian pulses result in higher echo amplitudes than the single-step
pulse. These improved echo pulses allow us to probe coherence at longer times
than in the past, measuring a plateau which has yet to be explained. In
addition, we show numerically that the vibrational state coupling due to such
lattice manipulations is more efficient in shallow lattices than in deep
lattices.
