  We demonstrate the existence of entanglement between the spatial degrees of
freedom of a system of harmonic oscillators placed in the noncommutative Moyal
plane ("exotic oscillators") by computing the entanglement entropy as measured
by the von Neumann entropy of the reduced density matrix. It is explicitly
verified that the entanglement arises from the noncommutativity, which controls
the coupling strength between the spatial modes. This can easily be generalised
to the case where the momentum components also satisfy noncommutative
relations, so that the entire phase space becomes noncommutative. In the former
case, i.e. when only the spatial noncommutativity is present, the underlying
mathematical structure is reminiscent of the Unruh effect, as observed by a
Rindler observer whose acceleration now gets related to the noncommutative
parameter. It is shown that the Landau problem in the presence of a harmonic
interaction gives a concrete physical realisation of this effect. Finally, we
show that phase-space noncommutativity can give rise to a the non-classical
effect of squeezing, which results from the non-linearity of a medium in a
three-wave mixing process.
