  We study quantum control techniques, specifically Adiabatic Rapid Passage
(ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms
trapped in an optical lattice between different vibrational states. We compare
them with each other and with previously studied coupling schemes in terms of
performance. In our study of ARP, we realize control of the vibrational states
by tuning the frequency of a spatial modulation through the inhomogeneously
broadened vibrational absorption spectrum. We show that due to the presence of
multiple crossings, the population transfer depends on the direction of the
frequency sweep, in contrast to traditional ARP. In a second study, we control
these states by applying a pulse sequence involving both the displacement of
the optical lattice and modulation of the lattice depth. This pulse is
engineered via the GRAPE algorithm to maximize the number of atoms transferred
from the initial (ground) state to the first excited state. We find that the
ARP and the GRAPE techniques are superior to the previously tested techniques
at transferring population into the first excited state from the ground state:
$38.9\pm0.2\%$ and $39\pm2\%$ respectively. GRAPE outperforms ARP in leaving
the higher excited states unpopulated (less than $3.3\%$ of the ground state
population, at $84\%$ confidence level), while $18.7\pm0.3\%$ of the ground
state population is transferred into higher excited states by using ARP. On the
other hand, ARP creates a normalized population inversion of $0.21\pm0.02$,
which is the highest obtained by any of the control techniques we have
investigated.
