Atom recoil in collectively interacting dipoles using quantized vibrational states

Densely packed atom arrays have been shown to be useful in coherent control and quantum information, especially due to their high reflective properties. But as we move towards denser arrays, the forces due to the collective interactions become larger and cause unwanted decoherence in the system. Hence, we study the recoil resulting from the forces due to the near-field collective dipole interactions and far-field laser and decay interactions using quantized vibrational states for the atomic motion. Results show that the recoil effects are especially pronounced in highly subradiant systems which can lead to substantial decoherence. The contributions to the recoil and the dependence on the trap frequency of the different terms of the Hamiltonian and Lindbladian are also studied. These calculations are compared with previous results using the impulse model in the slow oscillation approximation.