  Quantum entanglement in macroscopic systems is not only essential for
practical quantum information processing, but also valuable for the study of
the boundary between quantum and classical world. However, it is very challenge
to achieve the steady remote entanglement between distant macroscopic systems.
We consider two distant nanoparticles, both of which are optically trapped in
two cavities. Based on the coherent scattering mechanism, we find that the
ultrastrong optomechanical coupling between the cavity modes and the motion of
the levitated nanoparticles could achieve. The large and steady entanglement
between the filtered output cavity modes and the motion of nanosparticles can
be generated, if the trapping laser is under the red sideband. Then through
entanglement swapping, the steady motional entanglement between the distant
nanoparticles can be realized. We numerically simulate and find that the two
nanoparticles with 10 km distance can be entangled for the experimentally
feasible parameters, even in room temperature environment.
