Quantum Inf Process (2012) 11:777–785
Entanglement observation among single mode bosonic
ﬁeld and an atom
Received: 4 February 2011 / Accepted: 17 August 2011 / Published online: 1 September 2011
© Springer Science+Business Media, LLC 2011
Abstract We discuss the atom-ﬁeld entanglement by proposing a scheme for non-
locality of the atom-ﬁeld system via nonlocaling the ladder atomic and ﬁeld operators
by a nonlocal unitary operator. It is shown that the standard coherent states of the con-
structed nonlocal atom-ﬁeld quantum system are, as an issue of nonlocality, entangled.
On the other hand, by proposing a model Hamiltonian for the interacting atom-ﬁeld
system, the standard entangled coherent states can be generated by the dynamical time
evolution of the atom-ﬁeld system.
Keywords Entanglement · Nonlocality · Coherent states
Entanglement, as a pure quantum mechanical phenomena, is one of the main differ-
ences between the classical and quantum physics which appears in composite systems.
The description and quantiﬁcation of the entanglement in the complex systems are very
difﬁcult tasks . A state is said to be entangled if it cannot be factorized into tensor
product of the associated states of the subsystems. Entanglement is now recognized to
be of fundamental importance for developing new technologies notably those related
to quantum information processing, such as quantum teleportation , quantum key
distribution , superdense coding , and quantum computation . Entanglement
between the bosonic ﬁelds (such as photons or phonon) and atoms or ion, for its fun-
damental importance in quantum nonlocality [6,7] and quantum information , has
been extensively studied both in theoretical and experimental efforts [9–19].
N. Behzadi (
Research Institute for Fundamental Sciences, University of Tabriz, 51666-16471 Tabriz, Iran