  We study entanglement of the motional degrees of freedom of two tethered and
optically trapped microdisks inside a single cavity. By properly choosing the
position of the trapped objects in the optical cavity and driving proper modes
of the cavity it is possible to equip the system with linear and quadratic
optomechanical couplings. We show that a parametric coupling between the
fundamental vibrational modes of two tethered mircodiscs can be generated via a
time modulated input laser. For a proper choice of the modulation frequency,
this mechanism can drive the motion of the microdisks into an inseparable state
in the long time limit via a two-mode squeezing process. We numerically confirm
the performance of our scheme for current technology and briefly discuss an
experimental setup which can be employed for detecting this entanglement by
employing the quadratic coupling. We also comment on the perspectives for
generating such entanglement between the oscillations of optically levitated
nanospheres.
