Physics Letters A 372 (2008) 7117–7123
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Physics Letters A
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Dynamical creation of entanglement versus disentanglement in a system
of three-level atoms with vacuum-induced coherences
Łukasz Derkacz, Lech Jakóbczyk
∗
Institute of Theoretical Physics, University of Wrocław, Plac Maxa Borna 9, 50-204 Wrocław, Poland
article info abstract
Article history:
Received 24 September 2008
Accepted 27 October 2008
Available online 29 October 2008
Communicated by P.R. Holland
PACS:
03.67.Mn
03.65.Yz
42.50.-p
Keywords:
Three-level atoms
Vacuum-induced coherence
Entanglement production
The dynamics of entanglement between three-level atoms coupled to the common vacuum is investi-
gated. We show that the collective effects such as collective damping, dipole–dipole interaction and the
cross coupling between orthogonal dipoles, play a crucial role in the process of creation of entanglement.
In particular, the additional cross coupling enhances the production of entanglement. For the specific ini-
tial states we find that the effect of delayed sudden birth of entanglement, recently invented by Ficek
and Tana
´
s[Ficek,R.Tana
´
s, Phys. Rev. A 77 (2008) 054301] in the case of two-level atoms, can also be
observed in the system. When the initial state is entangled, the process of spontaneous emission causes
destruction of correlations and its disentanglement. We show that the robustness of initial entanglement
against the noise can be changed by local operations performed on the state.
©
2008 Elsevier B.V. All rights reserved.
1. Introduction
In a system of coupled multi-level atoms having closely lying
energy states and interacting with the vacuum, quantum interfer-
ence between different radiative transitions can occur, resulting
in coherences in a system which are known as vacuum-induced
coherences. For example, when the distance between atoms is com-
parable to the wavelength of the emitted radiation and transition
dipole moments involving the decay processes are parallel, the
coupling between the atoms via common vacuum gives rise to the
collective effects such as collective damping and dipole–dipole in-
teraction. Such effects are well known [1,2], particularly in the case
of two-level atoms. In the system of three-level atoms, radiative
coupling can produce a new interference effect in the spontaneous
emission. This effect manifests by the cross coupling between
radiative transitions with orthogonal dipole moments [3] and is
strongly dependent on the relative orientation of the atoms [4,5].
All such collective properties of the system influence the quan-
tum dynamics, which can significantly differ from a correspond-
ing single atom dynamics. There were many studies on the effect
of quantum interference on various physical processes including:
resonance fluorescence [6], quantum jumps [7], the presence of
*
Corresponding author.
E-mail address: ljak@ift.uni.wroc.pl (L. Jakóbczyk).
ultranarrow spectral lines [8] or amplification without population
inversion [9].
In our research we consider entanglement properties of a pair
of three-level atoms in the V configuration with vacuum induced
coherences. We study a dynamical creation of entanglement due
to the collective effects which are present in the system, as well as
the process of degradation of correlations, resulting in disentangle-
ment of initially entangled pairs of atoms. Both processes crucially
depend on the interatomic distance compared to the wavelength
of the emitted radiation. For large separation we expect that the
collective properties of two atoms are negligible and dissipation
causes disentanglement. On the contrary, for small distance the
collective effects are so strong that they can partially overcome de-
coherence. As a result, the system can decay to a stationary state
which can be entangled, even if the initial state was separable [10].
In the present Letter, we study the case of distance comparable
to the radiation wavelength
λ
. Although the dynamics brings all
initial states into the asymptotic state in which both atoms are in
their ground states, still there can be some transient entanglement
between the atoms. In particular we show that the dynamical cre-
ation of entanglement is possible in a system where only one atom
is in the excited state. Moreover the production of entanglement is
enhanced, when the cross coupling between orthogonal dipoles is
present. In the more accessible initial state when the both atoms
are excited, and if the cross coupling is absent, the interesting phe-
nomenon of delayed sudden birth of entanglement [11] can be
observed: unentangled atoms become entangled after some finite
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©
2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2008.10.053