  We investigate the dynamics of a gas of ultracold atoms that are trapped in
an array of harmonic potentials and that interacts with a Bose-Einstein
condensate (BEC) that acts as a reservoir of Bogoliubov excitations. The ground
and excited energy levels of these trapped ultracold atoms are coupled to each
other via detuned Raman lasers with corresponding Rabi frequencies. Once
excited via the Raman lasers, these trapped ultracold atoms then return to
their ground energy levels, but not necessarily to their original trap
locations, by emitting Bogoliubov excitations into the BEC. This combination of
driving via Raman lasers to excited energy levels and dissipation via
interaction with the BEC resulting in emission of Bogoliubov excitations into
it will result in the trapped ultracold atoms approaching a steady state,
whereby the expectation value of the number of trapped ultracold atoms in each
harmonic trap of the array will attain a constant value over time. One can then
use this system to prepare states that require a definite number of atoms in a
particular energy level, such as BECs and atom lasers used for atom
interferometry and for tests of the foundations of quantum mechanics.
