Driven-Dissipative Dynamics of Ultracold Atoms Trapped in an Array of Harmonic Potentials

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.