Results are reported from a search for a class of composite dark matter models with feeble , long-range interactions with normal matter . We search for impulses arising from passing dark matter particles by monitoring the mechanical motion of an optically levitated nanogram mass over the course of several days . Assuming such particles constitute the dominant component of dark matter , this search places upper limits on their interaction with neutrons of \alpha _ { n } \leq 1.2 \times 10 ^ { -7 } at 95 % confidence for dark matter masses between 1–10 TeV and mediator masses m _ { \phi } \leq 0.1 eV . Due to the large enhancement of the cross-section for dark matter to coherently scatter from a nanogram mass ( \sim 10 ^ { 29 } times that for a single neutron ) and the ability to detect momentum transfers as small as \sim 200 MeV/c , these results provide sensitivity to certain classes of composite dark matter models that substantially exceeds existing searches , including those employing kg-scale or ton-scale targets . Extensions of these techniques can enable directionally-sensitive searches for a broad class of previously inaccessible heavy dark matter candidates .