  We show that gravitational waves create phonons in a Bose-Einstein condensate
(BEC). A traveling spacetime distortion produces particle creation resonances
that correspond to the dynamical Casimir effect in a BEC phononic field
contained in a cavity-type trap. We propose to use this effect to detect
gravitational waves. The amplitude of the wave can be estimated applying
recently developed relativistic quantum metrology techniques. We provide the
optimal precision bound on the estimation of the wave's amplitude. Finally, we
show that the parameter regime required to detect gravitational waves with this
technique could be, in principle, within experimental reach in a medium-term
timescale.
