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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.

PRL 96, 030404 (2006)

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030404-2

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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030404-3

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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PHYSICAL REVIEW LETTERS

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