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Persistent entanglement in three-level atomic systems

TL;DR: In this article, the evolution towards persistent entangled state in an atom-photon system is discussed, where a maximally entangled state can be stabilized at a local minimum of the system by draining some energy.
Abstract: We discuss the evolution towards persistent entangled state in an atom–photon system. A maximally entangled state can be stabilized at a local minimum of the system by draining some energy, thus obtaining a persistent entangled state. This scheme can be realized in three-level, Λ type atomic systems since the third level is a meta-stable state. In particular, we compare dynamical description based on the exact and effective models. Some experimental realizations are discussed.

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Summary

  • The authors discuss the evolution towards persistent entangled state in an atom–photon system.
  • A maximally entangled state can be stabilized at a local minimum of the system by draining some energy, thus obtaining a persistent entangled state.
  • This scheme can be realized in three-level, type atomic systems since the third level is a meta-stable state.
  • In particular, the authors compare dynamical description based on the exact and effective models.

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Journal of Optics B: Quantum and Semiclassical Optics
Persistent entanglement in three-level atomic
systems
To cite this article: M Ali Can et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S13
View the article online for updates and enhancements.
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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS
J. Opt. B: Quantum Semiclass. Opt. 6 (2004) S13–S17 PII: S1464-4266(04)66490-1
Persistent entanglement in three-level
atomic systems
MAliCan,
¨
Ozg
¨
ur ¸Cakir, Alexander Klyachko and
Alexander Shumovsky
Faculty of Science, Bilkent University, Bilkent, Ankara, 06533, Turkey
E-mail: cakir@fen.bilkent.edu.tr
Received 24 June 2003, accepted for publication 1 August 2003
Published 5 March 2004
Online at stacks.iop.org/JOptB/6/S13 (
DOI: 10.1088/1464-4266/6/3/003)
Abstract
We discuss the evolution towards persistent entangled state in an
atom–photon system. A maximally entangled state can be stabilized at a
local minimum of the system by draining some energy, thus obtaining a
persistent entangled state. This scheme can be realized in three-level, type
atomic systems since the third level is a meta-stable state. In particular, we
compare dynamical description based on the exact and effective models.
Some experimental realizations are discussed.
Keywords: entanglement, Jaynes–Cummings model, Markov approximation,
three-level atom
This paper reports some new results relating to the
entanglement in atomic systems. It builds upon our earlier
investigations [1–3].
The generation and manipulation of entangled states in
atom–photon systems has recently attracted a great deal of
interest in the context of quantum information processing and
quantum computing [4–10]. Most studies on entanglement in
atomic systems have used the two-level atoms, interacting with
photons via dipole transitions (e.g., see [11–13] and references
therein). In this case, the lifetime of maximum entangled state
(MES) in atomic subsystem is chiefly determined by the life
of excited atomic state, that is by the natural line breadth.
Usually, this time is quite short[14, 15]. At the same time, the
quantum information processing needs more or less durable
entanglement.
According to the result obtained in [1], the maximum
entanglement in a system corresponds to the maximum total
local variance, describing the quantum fluctuations of all
measurements. Thus, to achieve a long-lived maximum
entanglement, we should first prepare a state with maximum
quantum fluctuations and then stabilize it by draining energy
right up to a (local) minimum, conserving at the same time
thelevel of quantum fluctuations. This can be done via an
interaction with a proper environment.
It was noticed in [1, 2] that the lifetime of atomic
entanglement can be improved by entangling atoms with
respect to the two atomic states, between which the dipole
transition is forbidden. Besides that, since the system is
1
2
3
Figure 1. Scheme of three level type atomic configuration.
initially disentangled, to achieve the persistent entanglement
an irreversible evolution of the system should be realized.
An important example is provided by the so-called -type
three-level structure [16, 17], which is illustrated in figure 1.
Here the levels 1 and 2 are coupled by dipole transition as well
as the levels 2 and 3. Then, because of the selection rules with
respect to parity, dipole transition between the levels 3 and 1
is forbidden [14]. The level 3 can be populated by a sort of
Raman process, when atom rst absorbs a pumping photon
by 1 2transition and then emits Stokes photon by 2 3
transition. If Stokes photon is then discarded, the atom will
stay in the state 3 for a long time determined by either multipole
or non-radiative processes.
Elimination of Stokes photon can be caused by a number
of physical processes, involving dissipative environment. For
example, in the case of atom in a cavity, Stokes photon
can be absorbed by the cavity walls. Another possibility is
1464-4266/04/030013+05$30.00 © 2004 IOP Publishing Ltd Printed in the UK S13

MACanet al
provided by a two-mode cavity that is resonant with respect
to the pumping mode and transparent for Stokes photons.
In the former case, Stokes photons interact with continuum
of ‘phonon’ modes, describing the standard Heisenberg–
Langevin mechanism of cavity losses [18, 19]. In the latter
case, atoms interact with continuum of modes, corresponding
to the natural line width for the level 2.
Following [1–3], we can assume now that there are two
identical three-level atoms in a cavity. The atoms are supposed
to be prepared initially both in the ground state 1, while the
cavity contains a single pump photon. Then, the irreversible
evolution caused by either of above mentioned processes will
lead to the following atomic state
1
2
(|3, 1 + |1, 3) (1)
that definitely manifests maximum entanglement. The process
of evolution towards the state (1) can be described through the
use of two models. Within the first model, the interaction part
of the Hamiltonian has the form
H
int
=
f
[λ
P
R
21
( f )a
P
+ λ
S
R
23
( f )a
S
]+H.c., (2)
where a
P
, a
S
are the annihilation operators of pumping and
Stokes photons, R
ij
=|i j |is the atomic transition operator,
f marks the atom, and λ
P
, λ
S
are the coupling constants.
Instead of the one-photon three-level process described by
theHamiltonian (2), an effective model of two-photon process
in two-level atom can also be considered [20, 21]. In this case,
it is assumed that the cavity is tuned consistent with two-photon
energy conservation, i.e.
E
3
E
1
ω
P
ω
S
,
where E
i
denotes the energy of atomic level i.Inthiscase,
only one detuning parameter
= E
2
E
1
ω
P
= E
2
E
3
ω
S
can be taken into account. Under the condition E
3
E
1
the level 2 can be adiabatically eliminated [20], so that the
dynamics of the system can be described by the effective
interaction Hamiltonian of the form
H
int
=
f
λR
31
a
+
S
a
P
+H.c., (3)
where λ = 2λ
S
λ
P
/ is a certain effective coupling constant.
The effective scheme of transitions is shown in gure 2.
The two main objectives of this paper are on the one hand
to show that both models describe the deterministic evolution
towards the state (1), and on the other hand to ascertain the
difference in the evolution process caused by the specific
structure of the models.
Assume that the two identical atoms ( f = 1, 2) are
located in a cavity that has quite high quality with respect to
pumping mode ω
P
,while absorb easily Stokes photons with
ω
S
.Weassume that interatomic distance is much less than
the wavelength of pumping and Stokes fields, so that the intra-
cavity registration of Stokes photon cannot be used to identify
1
2
3
Figure 2. Effective scheme in the existence of strong detuning.
which atom is the source of this radiation. Consider rst the
complete model with the Hamiltonian
H = H
0
+ H
loss
+ H
int
,
H
0
= ω
P
a
+
P
a
P
+ ω
S
a
+
S
a
S
+
f
21
R
22
( f ) + ω
31
R
33
( f )),
H
loss
=
q
η
q
(b
+
q
a
S
+ a
+
S
b
q
) +
q
q
b
+
q
b
q
,
(4)
where H
int
coincides with (2), ω
21
= E
2
E
1
, ω
31
= E
3
E
1
,
and b
+
q
and b
q
arethe Bose operators of ‘phonons’ in the cavity
walls [18, 19].
With the total Hamiltonian (4) in hand, we can now write
master equation for the reduced density matrix for the atom-
field system that is obtained through the use of the so-called
dressed-atom approximation (e.g., see [22–25]):
˙ρ =−i[H
0
+ H
int
]+κ{2a
S
ρa
+
S
a
+
S
a
S
ρ ρa
+
S
a
S
}. (5)
Here ρ denotes the density matrix and κ is a physical quantity
such that κ
1
determines the lifetime of Stokes photon in the
cavity and Q = ω
23
is the cavity quality factor with respect
to Stokes photons.
Assume that the system is initially prepared in the state
|ψ
1
=|1, 1⊗|1
P
, 0
S
, (6)
so that both atoms are in the ground state 1 and cavity contains
single pumping photon. Then, the evolution described by (5)
takes place in the Hilbert space H spanned by the states (6) and
|ψ
2
=
1
2
(|1, 2 + |2, 1) ⊗|0
P
, 0
S
|ψ
3
=
1
2
(|1, 3 + |3, 1) ⊗|0
P
, 1
S
|ψ
4
=
1
2
(|1, 3 + |3, 1) ⊗|0
P
, 0
S
.
(7)
Here |ψ
2
gives an intermediate entangled atomic state with
short lifetime determined by the dipole decay either to the
initial state |ψ
1
(6) or to another entangled state |ψ
3
.Inturn,
absorption of Stokes photon by cavity walls lead to irreducible
evolution from |ψ
3
to |ψ
4
that corresponds to the persistent
atomic entangled state (1). Then, the density matrix in H takes
the form
ρ(t) =
j,
ρ
j
(t)|ψ
j
ψ
|, j, = 1, 2, 3, 4. (8)
Use of (8) allows equation (5) to be cast into the form of
sixteen differential equations that can be analysed numerically
S14

Persistent entanglement in three-level atomic systems
Probability of Persistent Entanglement
0.0
0.2
0.4
0.6
0.8
1.0
0.0 5.0 10.0
κt
Figure 3. Evolution to the persistent entangled state in complete
model (dotted curve) and in effective model (solid curve) for
κ = 0.1λ
P
,
P
=
S
= 10λ
P
, λ
S
= λ
P
.
at different values of parameters. The results are shown in
figure 3. It is seen that always
ρ
j
(t)
1, at j = = 4
0, otherwise
at t κ
1
.Thus, the system described by the Hamiltonian (4)
and prepared initially in the state (6) evolves towards the
persistent entangled atomic state (1) without failure.
It is seen in figure 3 that evolution ρ
44
1isnot described
by a smooth curve but has a stairs-like structure that becomes
more visible with increase of κ.Thisspecific behaviour is
caused by the competition between the processes on transitions
1 2and2 3.
Consider now dynamics of the system within the
framework of effective model with adiabatically eliminated
excited level 2. Then, in the Hamiltonian (4), the interaction
Hamiltonian H
int
(3) should be substituted instead of H
int
(2)
and
H
0
H
0
= ω
P
a
+
P
a
P
+ ω
S
a
+
S
a
S
+
f
ω
31
R
33
( f ).
The master equation (5) can be used again with the same form
of the Liouville term but with the change
H
0
+ H
int
H
0
+ H
int
.
Since the level 2 is omitted, the state |ψ
2
in (7) should be
discarded. Thus, the density matrix involves the states |ψ
1
,
|ψ
3
and |ψ
4
and consists of only nine elements instead of
sixteen in previous case that enables us to fairly simplify the
numerical analysis.
It can be seen again that the system evolves towards the
persistent entangled state (1). At the same time, the absence
of the contribution coming from the transition 1 2leads to
amorerapidevolution at the same κ (figures 3, 4).
Consider now the case of two-mode cavity, such that
Stokes photons can leave it freely, while pumping-mode
excitations exist for averylong time. Let us again begin
with the one-photon three-level model. Then, the interaction
Probability of Persistent Entanglement
0.0
0.2
0.4
0.6
0.8
1.0
0.0 100.0 200.0
κt
Figure 4. Evolution to the persistent entangled state in complete
model (dotted curve) and in effective model (solid curve) for
κ = λ
S
= λ
P
,
P
=
S
= 10λ
P
.
Hamiltonian (2) should be changed by
H

int
=
f
λ
P
R
21
( f )a
P
+
k
λ
Sk
R
23
( f )a
Sk
+H.c., (9)
where summation over wavenumber k corresponds to the
natural line breadth of the level 2 with respect to the transition
2 3. In turn, the unperturbed partofthe Hamiltonian should
be chosen as follows
H

0
= ω
P
a
+
P
a
P
+
k
ω
Sk
a
+
Sk
a
Sk
+
f
[ω
21
R
22
( f ) + ω
31
R
33
( f )]. (10)
The Hilbert space of the system with the Hamiltonian
H

= H

0
+ H

int
is spanned by the vectors |ψ
1
(6), |ψ
2
in (7), and
|ψ
3k
=
1
2
(|1, 3 + |3, 1) ⊗|0
P
, 1
Sk
, (11)
forming an infinite dimensional subspace.
The time-dependent wavefunction of the system (10) has
the form
|(t)=C
1
(t)|ψ
1
+ C
2
(t)|ψ
2
+
k
C
3k
(t)|ψ
3k
(12)
with the initial conditions
C
(0) =
1, if = 1
0, otherwise.
(13)
Then, the Schr
¨
odinger equation
i
t
|(t)=H

|(t)
with the Hamiltonian H

leads to the following set of linear
differential equations
i
˙
C
1
= ω
P
C
1
+ λ
P
2C
2
i
˙
C
2
= ω
21
C
2
+ λ
P
2C
1
+
k
λ
Sk
C
3k
i
˙
C
3k
=
31
+ ω
Sk
)C
3k
+ λ
Sk
C
2
.
(14)
S15

MACanet al
To nd solution of (14), let us express C
3k
in terms of C
2
:
C
3k
(t) =−iλ
Sk
t
0
C
2
)e
i
31
+ω
Sk
)(τ t )
dτ,
convert summation over k into an integration over continuum
of Stokes modes corresponding to the natural line breadth of
the level 2, and use Markovianapproximation [19]. Then, the
irreversible dynamics of the system is described by the two
equations
˙
C
1
=−iω
P
C
1
iλ
P
2C
2
˙
C
2
=−iω
21
C
2
iλ
P
2C
1
C
2
,
(15)
where = πρ
23
)|λ
Sk
|
2
(k = ω
23
/c) is thespontaneous
decay rate for the transition 2 3andρ(ω
23
) denotes the
density of states of Stokes photons.
To within the second order in |λ
P
/Z |,whereZ = i
P
and
P
= ω
P
ω
12
is the detuning for the pumping mode, we
get
C
1
(t) e
iω
P
t
2λ
2
P
Z
2
e
Zt
+
Z
2
2λ
2
P
Z
2
e
2λ
2
P
t
Z
, (16)
C
2
≈−
λ
P
2
iZ
[e
t
e
2λ
2
P
+iZ
P
Z
t
]e
iω
12
t
. (17)
The above approximations are reasonable because
λ
P
Sk
.
In view of equation (12), the probability to achieve the
states,corresponding to the persistent entanglement (1), is
P(t) =
k
|C
3k
(t)|
2
= 1 −|C
1
(t)|
2
−|C
2
(t)|
2
. (18)
Since equations (16) and (17) describe the damped oscillations,
we get
lim
t→∞
P(t) = 1.
The detailed evolution of the probability (18) is shown in
figure 5. It is seen that the typical time required for persistent
entanglement is
τ
|Z |
2
λ
2
P
. (19)
Since |Z|
2
=
2
+
2
P
,theincrease of detuning for the
pumping mode leads to a deceleration of evolution towards
the persistent atomic entanglement.
Dynamics of the system described by the effective
Hamiltonian in the cavity transparent for Stokes photons was
examined in [2]. Comparing the above results with those
of [2], one can conclude that the effective model gives only
rough picture of purely exponential evolution toward the
state (1), completely deleting from the consideration the Rabi
oscillations between the levels 1 and 2. Besides that, the role
that detuning for the pumping mode
P
plays in acceleration
and deceleration of evolution is lost within the framework of
effective model.
Summarizing, we should stress that we have studied the
quantum irreversible dynamics of a system of two three-
level -type atoms, interacting with two modes of quantized
electromagnetic field in a cavity under the assumption that
Stokes photon either leave cavity freely or is strongly damped.
1
2
3
4
0.0
0.2
0.4
0.6
0.8
1.0
λt
Σ
k
|C
k
|
2
0.0 5000.0 10000.0 15000.0
Figure 5. Time evolution of probability (18) to have the persistent
entanglement at λ
P
= 0.001 for (1)
P
= 0; (2)
P
= ;
(3)
P
= 2;(4)
P
= 4.
It is shown that in both cases system evolves towards the
persistent atomic entangled state (1). Such an evolution takes
place if the atoms are initially prepared in the ground state,
while cavity contains single photon of the pumping mode. It
is easily seen that another realistic choice of the initial state,
when one of the atoms is excited and cavity field is in the
vacuum state, does not lead to evolution towards the persistent
entangled state (1).
It is also shown that the effective model with adiabatically
removed atomic state 2 predicts correct asymptotic behaviour,
while is incapable of description of details of evolution.
Concerning the experimental realization, let us point
out that the transitions 1 2and2 3should have
quite different frequencies. Only in this case it seems to be
possible to design a multi-mode cavity with high quality with
respect to ω
12
,permitting either leakage or strong absorption
of Stokes photons. An important example is provided by
the 3S 4P and 4P 4S transitions in sodium atom
and in other alkaline atoms (see [26]). These atoms are
widely used in quantum optics, in particular in investigation
of Bose–Einstein condensation [27]. The multimode cavities
are also usedinquantum optics for years (e.g., see [28] and
references therein). In particular, the cavities with required
properties may be assembled using distributed Bragg reflectors
(DBR) and double DBR structures to single out wavelengths
corresponding to ω
12
and ω
23
.
The initial state can be prepared in the same way as in
[29–31]. First, a single-photon excitation corresponding to
the pumping mode is prepared in the cavity. Then, the atoms
can propagate through the cavity, using either the same opening
or two different but closed openings. The velocity of atoms
should be chosen in a proper way, so that the time they spend in
the cavity obeys the condition τ |Z|
2
/(λ
2
P
), 1 (19). All
measurements aimed at the detection of atomic entanglement
can be performed outside the cavity.
Thus, the realization of persistent entanglement in three-
level -type atoms seems to be feasible with present
experimental technique. It should be emphasized that
the single-atom Raman-type process has been observed
recently [32]. At the same time, recent progress in
investigation of atomic entanglement in the presence of
S16

Citations
More filters
01 Jan 1999

643 citations

Journal ArticleDOI
TL;DR: In this article, the evolution of the atomic quantum entropy and the atom-field entanglement in a system of a V-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atomfield coupling is investigated.
Abstract: We investigate the evolution of the atomic quantum entropy and the atom-field entanglement in a system of a V-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analyzed.

15 citations


Cites methods from "Persistent entanglement in three-le..."

  • ...Furthermore, the evolution of the (atomic) field entropy for the three-level atom one-mode[16, 17] and two-mode[18–20] model has been studied....

    [...]

Journal ArticleDOI
TL;DR: In this article, the von Neumann entropies of an entangled atom-field system were modeled using the full microscopical Hamiltonian approach or the two-photon Jaynes-Cummings model, and numerical simulations furnish the explicit expressions for each sub-system entropy, which allow us to estimate the multiperiodicity in the evolution of the entangled atom field system.
Abstract: The dynamics of an entangled atomic system, partially interacting with entangled cavity fields and characterizing an entanglement swapping, has been studied through their von Neumann entropies. The aforementioned interaction is implemented via a two-photon process, given by either the full microscopical Hamiltonian approach or the two-photon Jaynes–Cummings model. Numerical simulations furnish the explicit expressions for each sub-system entropy, which allow us to estimate the multiperiodicity in the evolution of the entangled atom–field system. The effects of the detuning parameter upon the period and the amplitude of the entropies are also discussed as well as the power spectrum of the entropy.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the evolution of the atomic quantum entropy and the atom-field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom−field coupling is investigated.
Abstract: We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a non-correlated two-mode squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analysed.

14 citations

Journal ArticleDOI
TL;DR: In this article, the effect of multiplicity, Kerr-like medium, detuning and different forms of intensity-dependent coupling functional on the degree of entanglement (DEM) is discussed.
Abstract: General formalisms of a three-level atom in different configurations (namely, V, Λ, and Ξ configurations) interacting with multi-photon process of a single-mode field are investigated. Analytical expressions of the unitary operator within the framework of the dressed states and density operators of the consideration systems are derived. The temporal evolution of atomic quantum entropy when the field is initially in the binomial state and the atom is initially in its upper most state is considered. The effect of multiplicity, Kerr-like medium, detuning and different forms of intensity-dependent coupling functional on the degree of entanglement (DEM) are discussed. Details of the phenomenon differ from one configuration to the other.

14 citations

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TL;DR: In this paper, the quantum mechanical method is applied to the theory of complex spectra and the Russell-Saunders case is used to obtain the energy levels of one-electron spectra.
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01 Jan 1935
TL;DR: In this paper, the quantum mechanical method is applied to the theory of complex spectra and the Russell-Saunders case is used to obtain the energy levels of one-electron spectra.
Abstract: 1. Introduction 2. The quantum mechanical method 3. Angular momentum 4. The theory of radiation 5. One-electron spectra 6. The central-field approximation 7. The Russell-Saunders case: energy levels 8. The Russell-Saunders case: eigenfunctions 9. The Russell-Saunders case: line strengths 10. Coupling 11. Intermediate coupling 12. Transformations in the theory of complex spectra 13. Configurations containing almost closed shells. X-rays 14. Central fields 15. Configuration interaction 16. The Zeeman effect 17. The Stark effect 18. The nucleus in atomic spectra Appendix. Universal constants and natural atomic units.

2,552 citations

Journal ArticleDOI
23 Oct 1998-Science
TL;DR: The first realization of unconditional quantum teleportation where every state entering the device is actually teleported is realized, using squeezed-state entanglement.
Abstract: Quantum teleportation of optical coherent states was demonstrated experimentally using squeezed-state entanglement. The quantum nature of the achieved teleportation was verified by the experimentally determined fidelity Fexp = 0.58 +/- 0.02, which describes the match between input and output states. A fidelity greater than 0.5 is not possible for coherent states without the use of entanglement. This is the first realization of unconditional quantum teleportation where every state entering the device is actually teleported.

2,345 citations

Journal ArticleDOI
TL;DR: The concept of entanglement plays an essential role in quantum physics as mentioned in this paper, and it is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world.
Abstract: After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.

2,303 citations

Frequently Asked Questions (1)
Q1. What are the contributions in "Persistent entanglement in three-level atomic systems" ?

The authors discuss the evolution towards persistent entangled state in an atom–photon system. Some experimental realizations are discussed.