Artificial Dark Matter in Bose--Einstein Condensates: Healing Length as Analogue Jeans Scale

Abstract We propose a quantitative connection between the healing length of a Bose–Einstein condensate (BEC) and the Jeans length of a self-gravitating dark matter fluid. The Jeans length defines the critical scale below which density fluctuations collapse under gravity, while the healing length marks the transition between collective and single-particle excitations in a condensate. We show that both quantities arise from the balance between dispersive and interaction effects, leading to a direct correspondence between condensate stability and gravitational instability. Using realistic parameters for rubidium-87 BECs, we demonstrate that the analogue of the Jeans instability can be studied through phonon dispersion relations, density correlations, and collapse thresholds that are accessible in current ultracold atom experiments. This framework positions Bose–Einstein condensates as a laboratory analogue for dark matter structure formation, enabling controlled studies of hidden-sector physics using tabletop experiments.