General Einstein-Podolsky-Rosen-type entanglement of continuous variables for bosons

Abstract

We show that general Einstein-Podolsky-Rosen-type (EPR-type) entanglement of continuous variables with arbitrary eigenvalues for bosons can be yielded. For bosons of nonzero resting mass EPR-type entangled state can be achieved by the use of atomic beam splitters in particles of a position eigenstate and $n\ensuremath{-}1$ momentum eigenstates. For light field in which resting mass of the photon is zero, approximate EPR-type entanglement can be experimentally generated when we apply optical beam splitters to one position-squeezed coherence state and $n\ensuremath{-}1$ momentum-squeezed coherence states, this approximate version tends to perfect EPR entanglement in the limit of infinite squeezing.