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Observation of Entanglement of a Single Photon with a Trapped Atom
Ju
¨
rgen Volz,
1,
*
Markus Weber,
1,†
Daniel Schlenk,
1
Wenjamin Rosenfeld,
1
Johannes Vrana,
1
Karen Saucke,
1
Christian Kurtsiefer,
2
and Harald Weinfurter
1,3
1
Department fu
¨
r Physik, Ludwig-Maximilians-Universita
¨
tMu
¨
nchen, D-80799 Mu
¨
nchen, Germany
2
Department of Physics, National University of Singapore, Singapore
3
Max-Planck-Institut fu
¨
r Quantenoptik, 85748 Garching, Germany
(Received 13 October 2005; published 25 January 2006)
We report the observation of entanglement between a single trapped atom and a single photon at a
wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step
towards long range quantum networks. To verify the entanglement, we introduce a single atom state
analysis. This technique is used for full state tomography of the atom-photon qubit pair. The detection
efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled
atoms at large distances, ready for a final loophole-free Bell experiment.
DOI: 10.1103/PhysRevLett.96.030404 PACS numbers: 03.65.Ud, 03.67.Mn, 32.80.Qk, 42.50.Xa
Entanglement is a key element for quantum communi-
cation and information applications [1]. Demonstrations of
quantum computers with ions in linear chains nowadays
almost routinely create deterministically any desired en-
tangled state with up to eight ions [2]. The currently largest
quantum processor consisting of some tens of (not yet
distinguishable) qubits in a so-called cluster state was
implemented with neutral atoms in an optical lattice [3].
For future applications such as quantum networks or the
quantum repeater [4], it is mandatory to achieve entangle-
ment also between separated quantum processors. For this
purpose, entanglement between different quantum objects
such as atoms and photons—recently demonstrated for
ions and photons [5]—forms the interface between atomic
quantum memories and photonic quantum communication
channels [6], finally allowing the distribution of quantum
information over arbitrary distances.
Atom-photon entanglement is not only crucial for many
applications in long range quantum communication but is
also the key element to give the final answer to Einstein’s
question on the real properties of nature [7]. Together with
Podolsky and Rosen, he pointed out the inconsistencies
between quantum mechanics and their ideal of a local and
deterministic description of nature [8]. They implied that
parameters of a physical system (local hidden variables),
which might not—yet—be known to us, could solve the
problem. Until now, the results of many experiments based
on Bell’s inequality [9] indicate that hidden variable theo-
ries would result in incorrect predictions and, thus, are not
a valid description of nature [10–12]. But all these tests are
subject to loopholes [11,13], and none so far could defi-
nitely rule out all alternative concepts.
Here we describe the observation of entanglement be-
tween the polarization of a single photon and the internal
state of a single neutral atom stored in an optical dipole
trap. For this purpose, we introduce a new state-analysis
method enabling full state tomography of the atomic qubit.
This now allows for the first time the direct analysis of the
entangled atom-photon state formed during the spontane-
ous emission process. Moreover, we can show that the
results achieved indeed suffice to test Einstein’s objections.
Atom-photon entanglement can be prepared best by ex-
citing an atom to a state which ideally has two decay chan-
nels ( configuration). The hyperfine structure of
87
Rb
offers a good approximation to such a level scheme
[Fig. 1(a)]. Excited to the 5
2
P
3=2
, F
0
0 hyperfine level,
the atom can spontaneously decay into the three magnetic
sublevels jm
F
0;1i of the 5
2
S
1=2
, F 1 hyperfine
ground level by emitting a photon at a wavelength of
780 nm.
If the emitted photon is
-polarized, the atom will be
in the state jm
F
1i. If the photon is linearly
-polarized, the atom will be in the state jm
F
0i, and
for
polarization we find the state jm
F
1i. Since the
emitted photons are collected along the quantization axis,
-polarized light (emitted into a different spatial mode) is
not collected. Therefore, only spontaneous decay into the
states jm
F
1i is observed. As long as these emission
processes are indistinguishable in all other degrees of free-
dom, one obtains a coherent superposition of the two decay
possibilities, i.e., the maximally entangled state
j
i
1
2
p
jm
F
1ij
ijm
F
1ij
i: (1)
Here in each of the terms the first ket describes the state of
the atom and the second one the polarization of the photon.
The quantum mechanical phase of the atom-photon state is
well defined and follows from the Clebsch-Gordan coef-
ficients of the transitions.
In our experiment, atoms are cooled from a shallow
magneto-optical trap (MOT) into an optical dipole trap
located in the center of the MOT [14]. For the dipole trap
waist size of 3:5 m, a collisional blockade mechanism
ensures that only single atoms are captured [15].
When a single atom is loaded into the trap and its fluo-
rescence is registered, the sequence entangling the atom
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with a photon is started by pumping it into the F 1,
m
F
0 state. Next, a 30 ns optical pulse excites the
atom to the F
0
0 level, from which it will decay back to
F 1. Photons emitted along the quantization axis are
collected and guided via a single mode optical fiber to a
single photon polarization analyzer to determine the state
of the photonic qubit [see Fig. 1(b)]. Because the emitted
photon is detected with an overall efficiency of
ph
5
10
4
, the whole process has to be repeated approximately
2000 times to observe the photon. The repetition rate of
this process is 1:25 10
5
s
1
. However, in the atomic
state detection, the atom is lost with a probability of 0.5
(see below). Therefore, the mean time to load an atom into
the dipole trap limits the total rate for the generation of
entangled atom-photon pairs to 0:2s
1
.
Once the emitted photon is detected, the state analysis of
the atom is initiated. Standard spectroscopy techniques
probing only the populations of the states jm
F
1i
and jm
F
1i are not sufficient to confirm entanglement.
Instead, a projection onto general superposition states is
required. We thus apply a state selective stimulated Raman
adiabatic passage (STIRAP) technique [16], which allows
one to transfer an arbitrary superposition state j i
sinjm
F
1ie
i
cosjm
F
1i adiabatically to
the F 2 ground level (Fig. 2). Because of the selection
rules of atomic dipole transitions, the orthogonal quantum
state does not couple to the STIRAP light field
1
and
remains in the F 1 level. The angles and in this
process are defined by the relative amplitude and phase of
the
and
polarization components of the STIRAP
laser
1
, respectively. In essence, the polarization of the
STIRAP laser defines which superposition state is trans-
ferred, thus allowing a full tomographic analysis of the
atomic state without the necessity to perform any state
manipulation on the atomic qubit.
After the STIRAP pulse, the atom is in a superposition
of the hyperfine ground levels F 1 and F 2, which
now can be distinguished by standard methods. We apply a
detection laser pulse (resonant to the closed transition F
2 ! F
0
3), removing atoms in the F 2 level from the
trap. Finally, to read out the atomic state, the cooling lasers
of the MOT are switched on and atomic fluorescence is
measured for 30 ms to decide whether the atom is still in
the trap or not. Thereby, we obtain the binary result of the
projective atomic state measurement on the state j i and
the orthogonal state j
?
i. For the results shown in Fig. 3,
we repeated the experimental cycle approximately
300 times per data point from which we obtain the proba-
bility of the atom to remain in F 1 with a statistical error
of 2%.
To verify the entanglement of the generated atom-
photon state, we perform ^
x
( =4, 0) as well
as ^
y
( =4, =2) state analysis of the atomic
qubit for different polarization measurements of the photon
(Fig. 3, ^
i
are the spin-1=2 Pauli operators). Thereby, the
probability of the atom to be transferred by the STIRAP
pulse sequence, or the probability to remain in the F 1
FIG. 2 (color online). Experimental procedure for the atomic
state detection. To analyze the atomic state, a two-photon
STIRAP-process state selectively transfers a superposition of
the states jm
F
1i and jm
F
1i to the F 2 hyperfine
level. To read out the atomic qubit, a hyperfine-level selective
detection pulse is applied before standard fluorescence detection.
FIG. 1 (color online). (a) Preparation of atom-photon entan-
glement in
87
Rb. The excited hyperfine level with F
0
0 can
decay to three possible ground states with the magnetic quantum
numbers m
F
1, 0, or 1, by spontaneously emitting a
, ,
or
polarized photon, respectively. If the light is collected
along the quantization axis, -polarized photons are suppressed.
Thus, an effective configuration is obtained which allows the
preparation of a maximally entangled state between the photon
polarization and the orientation of the atomic magnetic moment.
(b) Scheme of the experimental setup. The dipole trap light (
856 nm, P 30 mW) is focused by a microscope objective
(NA 0:38) to a waist of 3:5 m. The photon from the sponta-
neous decay is collected with the same objective, separated from
the trapping beam by a dichroic mirror, and coupled into a single
mode optical fiber guiding it to the polarization analyzer. The
analyzer consists of a rotable half- and quarter-wave plate, a
polarizing beam splitter (PBS), and two avalanche photodiodes
(APD) for single photon detection. Triggered by the detection of
the photon in either APD
1
or APD
2
, the atomic state is analyzed
using a STIRAP light field whose polarization defines the atomic
measurement basis.
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ground level, respectively, is measured, conditioned on the
polarization measurement outcome of the photon. Varying
the photon polarization analyzer, this probability shows the
expected sinusoidal dependence for both ^
x
and ^
y
. From
the fits to the measured data, we obtain an effective visi-
bility (peak to peak amplitude) of V
atph
0:85 0:01 for
analysis in ^
x
and V
atph
0:87 0:01 for analysis in ^
y
.
This clearly proves entanglement of the generated atom-
photon state.
For the determination of the full atom-photon state, we
perform two-qubit state tomography. This involves a new
set of measurements determining correlations of all com-
binations of the operators ^
x
, ^
y
, and ^
z
on the atom and
the photon [17]. The density matrix
atph
determined this
way clearly proves the state to be of the form of (1) [see
Fig. 4(a)]. The fidelity, defined as the overlap between
j
ih
j and
atph
, in this measurement was F
0:87 0:01. The limited visibility in the atom-photon
correlations is caused mainly by errors in the atomic state
detection (5%), accidental photon detection events due to
the dark counts of the single photon detectors (3%), off-
resonant excitation to the hyperfine level 5
2
P
3=2
, F
0
1
(1%), and polarization errors of the STIRAP laser beams
(2%). Applying the Peres-Horodecki criterion [18] to the
combined density matrix proves the entanglement with a
negativity of 0:382. Figures 4(b) and 4(c) show the density
matrices of the atomic and the photonic state after tracing
over the partner qubit. Obviously, these states are in a
complete statistical mixture. However, it becomes clear
that the resulting atom-photon state is not a mixture of
all possible contributions but is instead a well defined
(ideally) pure entangled state.
In view of these results, let us now analyze the perform-
ance of a possible loophole-free Bell experiment with a
pair of entangled atoms. Crucial for such a test is a highly
efficient state analysis by spacelike separated observers. To
generate entanglement between atoms at remote locations,
they are first entangled with a photon each. The two pho-
tons are brought together and then are subject to a Bell-
state measurement, which serves to swap the entanglement
to the atoms [19]. If we use the average visibility observed
in our experiment and extrapolate results of recent two-
photon interference experiments [20–22], we derive an
expected atom-atom visibility of V
atat
V
2
atph
0:74
0:01. Thus, the violation of a Clauser-Horne-Shimony-Holt
(CHSH)-type Bell inequality [23], which is achieved above
the threshold visibility of 0.71, is feasible.
We emphasize that, triggered on the detection of a
photon, every atomic state measurement yields a result.
In this sense, the atomic detection efficiency is equal to
FIG. 4 (color online). (a) Graphical representation of the real
part of the measured density matrix of the entangled atom-
photon state. The fidelity (overlap with the expected state
j
i) from this measurement is F 0:87 0:01. Insets (b)
and (c) show the single particle density matrices for the atom and
photon state, respectively, indicating that the single particles
when observed on their own are found in a completely mixed
state.
FIG. 3 (color online). Probability of detecting the atom in the
ground level F 1 (after the STIRAP pulse) conditioned on the
detection of the photon in detector APD
1
(-䊉-) or APD
2
(--) as
the linear polarization of the photonic qubit is rotated by an
angle . (a) The atomic qubit is measured in ^
x
and (b) in ^
y
,
whereas the photonic qubit is projected onto the states
1=
2
p
j
ie
2i
j
i.
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one. In certain cases, as, e.g., the loss of the atom from the
trap, a wrong measurement outcome may occur, but one
always obtains a result. Moreover, entanglement swapping
enables a so-called event-ready scheme [11,19,24]. If mea-
surement results are reported for every joint photon detec-
tion event, this scheme is independent of any additional
assumptions and, thus, is not subject to any detection
related loopholes at all. To close at the same time the
locality loophole, the atoms have to be spacelike separated
with respect to the measurement time of the atomic states.
The minimum distance of the atoms is determined by the
duration of the atomic state detection. In detail, the atomic
state collapses by scattering photons from the detection
laser for 350 ns. Together with the STIRAP process, this
yields an overall measurement time of less than 0:5 s and
requires a separation of the atoms of 150 m. Thus, we
expect the generation of one entangled atom-atom pair per
minute [25]. A loophole-free violation of a CHSH-type
Bell’s inequality [23] by 3 standard deviations would
require approximately 7000 atom pairs at the expected
visibility of 0.74. This would be feasible within a total
measurement time of 12 days.
In this Letter, we presented a successful implementation
of a source of high-fidelity entangled atom-photon pairs.
We introduced a single atom STIRAP state analysis which
does not require additional atomic state manipulations and,
thus, can be performed with increased fidelity. This al-
lowed us to perform the first full state tomography of an
atom-photon system and proved that the spontaneous
emission of the atom results in the entangled state j
i.
In the experiment, we achieved a state fidelity of F
0:87 0:01 and a mean visibility of the atom-photon
correlations of V
atph
0:86 0:01. These methods, pos-
sibly combined with high-Q cavities to enhance the col-
lection efficiency [22,26], form the basic elements in future
quantum information experiments for building the inter-
face between quantum computers and a photonic quantum
communication channel. In addition, these tools also help
to find an answer to the long-standing question of whether
local realistic extensions of quantum mechanics can de-
scribe nature at all. The experimental demonstration of
high-fidelity entanglement provides the most important
step towards a final, loophole-free test of Bell’s inequality.
We acknowledge stimulating discussions with T. W.
Ha
¨
nsch and his group. This work was supported by the
Deutsche Forschungsgemeinschaft and the European
Commission through the EU Project QAP (IST-3-015848).
*Electronic address: juergen.volz@physik.uni-
muenchen.de
†
Electronic address: markus.weber@physik.uni-
muenchen.de
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