  We propose a scheme to entangle two mechanical nanocantilevers through
indirect interactions mediated by a gas of ultra cold atoms. We envisage a
system of nanocantilevers magnetically coupled to a Bose-Einstein condensate of
atoms and focus on studying the dark states of the system. These dark states
are entangled states of the two nanocantilevers, with no coupling to the atomic
condensate. In the absence of dissipation, the degree of entanglement is found
to oscillate with time, while if dissipation is included, the system is found
to relax to a statistical mixture of dark states which remains time independent
until the inevitable thermal dephasing destroys the nanocantilever coherence.
This opens up the possibility of achieving long-lived entangled nanocantilever
states.
