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We demonstrate the existence of entanglement between the spatial degrees offreedom of a system of harmonic oscillators placed in the noncommutative Moyalplane ("exotic oscillators") by computing the entanglement entropy as measuredby the von Neumann entropy of the reduced density matrix. It is explicitlyverified that the entanglement arises from the noncommutativity, which controlsthe coupling strength between the spatial modes. This can easily be generalisedto the case where the momentum components also satisfy noncommutativerelations, so that the entire phase space becomes noncommutative. In the formercase, i.e. when only the spatial noncommutativity is present, the underlyingmathematical structure is reminiscent of the Unruh effect, as observed by aRindler observer whose acceleration now gets related to the noncommutativeparameter. It is shown that the Landau problem in the presence of a harmonicinteraction gives a concrete physical realisation of this effect. Finally, weshow that phase-space noncommutativity can give rise to a the non-classicaleffect of squeezing, which results from the non-linearity of a medium in athree-wave mixing process.

Emergent entropy of exotic oscillators and squeezing in three-wave mixing process