Holographic Storage of Biphoton Entanglement
ABSTRACT Coherent and reversible storage of multi-photon entanglement with a multimode
quantum memory is essential for scalable all-optical quantum information
processing. Although single photon has been successfully stored in different
quantum systems, storage of multi-photon entanglement remains challenging
because of the critical requirement for coherent control of photonic
entanglement source, multimode quantum memory, and quantum interface between
them. Here we demonstrate a coherent and reversible storage of biphoton
Bell-type entanglement with a holographic multimode atomic-ensemble-based
quantum memory. The retrieved biphoton entanglement violates Bell's inequality
for 1 microsecond storage time and a memory-process fidelity of 98% is
demonstrated by quantum state tomography.
- SourceAvailable from: Nelly Ng[Show abstract] [Hide abstract]
ABSTRACT: Fundamental primitives such as bit commitment and oblivious transfer serve as building blocks for many other two-party protocols. Hence, the secure implementation of such primitives is important in modern cryptography. Here we present a bit commitment protocol that is secure as long as the attacker's quantum memory device is imperfect. The latter assumption is known as the noisy-storage model. We experimentally executed this protocol by performing measurements on polarization-entangled photon pairs. Our work includes a full security analysis, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of two-party protocols in this model using real-world quantum devices. Finally, we provide a general analysis of our bit commitment protocol for a range of experimental parameters.Nature Communications 12/2012; 3:1326. · 10.74 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: We propose a scheme that utilizes the collective enhancement of a photonic mode inside an atomic ensemble together with a proper Zeeman manifold in order to achieve a heralded polarization entangled Bell state. The entanglement is between two photons that are separated in time and can be used as a post selected deterministic source for applications such as quantum repeaters where a subsequent entanglement swapping measurement is employed. We present a detailed analysis of the practical limitation of the scheme.10/2013;
- [Show abstract] [Hide abstract]
ABSTRACT: Long-lived and high-fidelity memory for a photonic polarization qubit (PPQ) is crucial for constructing quantum networks. We present a millisecond storage system based on electromagnetically induced transparency, in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy and, thus, the PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of the polarization states are 98.6% at 200 μs and 78.4% at 4.5 ms, respectively.Physical Review Letters 12/2013; 111(24):240503. · 7.73 Impact Factor
Holographic Storage of Biphoton Entanglement
Han-Ning Dai*,1Han Zhang*,1Sheng-Jun Yang,1Tian-Ming Zhao,1Jun Rui,1You-Jin Deng,1Li
Li,1Nai-Le Liu,1Shuai Chen,1Xiao-Hui Bao,2,1Xian-Min Jin,1Bo Zhao,1,3and Jian-Wei Pan1
1Hefei National Laboratory for Physical Sciences at Microscale and Departmentof Modern Physics,
University of Science and Technology of China,Hefei,Anhui 230026, China
2Physikalisches Institut, Reprecht-Karls-Universitat Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
3Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
(Dated: April 9, 2012)
Coherent and reversible storage of multi-photon entanglement with a multimode quantum memory
is essential for scalable all-optical quantum information processing. Although single photon has
been successfully stored in different quantum systems, storage of multi-photon entanglement remains
challenging because of the critical requirement for coherent control of photonic entanglement source,
multimode quantum memory, and quantum interface between them. Here we demonstrate a coherent
and reversible storage of biphoton Bell-type entanglement with a holographic multimode atomic-
ensemble-based quantum memory. The retrieved biphoton entanglement violates Bell’s inequality
for 1 µs storage time and a memory-process fidelity of 98% is demonstrated by quantum state
PACS numbers: 03.67.Bg, 42.50.Ex
Faithfully mapping multi-photon entanglement into
and out of quantum memory is of crucial importance
for scalable linear-optical quantum computation  and
long-distance quantum communication .
storage of nonclassical light [3, 4] and single photons [5–
12] has been demonstrated in various quantum systems,
such as atomic ensemble, solid system, and single atom.
Among these, the atomic-ensemble-based quantum mem-
ory holds the promise to implement multimode quan-
tum memory for multi-photon entanglement. A natural
method for this purpose is to select spatially separated
sub-ensembles of a large atomic ensemble as different
quantum registers [8, 13], for which the number of stored
modes is limited by the spatial dimension of the atomic
ensemble.More powerful methods, such as exploring
large optical depth of an atomic ensemble [14, 15], or uti-
lizing photon echoes  or atomic frequency combs tech-
niques , have been employed to demonstrate atomic-
ensemble-based multi-mode memories.
An alternative and elegant method is to implement
the atomic ensemble as a holographic multimode quan-
tum memory [18–20], using spatially overlapped but
orthogonal spin waves as different quantum registers.
For clarity, we illustrate this in the example of stor-
ing a single-photon state in an atomic ensemble of N
atoms that have two long-lived ground states |g? and
|s? [21–24]. Initially, a “vacuum” state |vac? = |g1...gN?
is prepared such that all the atoms are at the |g?
state. The single-photon state is then mapped into
the ensemble as a collective state |1,q? = S†
jeiq·xj|g1···sj···gN?, where xj is the po-
[∗] These authors contributed equally to this work.
FIG. 1: (a) Schematic view of the quad-mode holographic
quantum memory.The control field is shined into the
atomic cloud horizontally, and the signal modes are inci-
dent from different directions in the same plane, with an-
gles (θ1,θ2,θ3,θ4) = (−1◦,−0.6◦,0.6◦,1◦) relative to the the
control field. (b) The typical Λ-type energy levels, with two
ground states |g? and |s? and an excited state |e?. The |e?−|g?
and the |e?−|s? transition are coupled to the signal and con-
trol fields, respectively. (c) Illustration of the wave vectors
of the spin waves. The input signal field with wave vector of
ks,i (i = 1,2,3,4) is mapped to a spin wave with wave vector
qi = ks,i− kc, with kc the wave vector of the control field.
sition of the jth atom, S†
is the collective creation operator of a spin wave with
wave vector q. For N ? 1, one has [Sq1,S†
namely, the collective states satisfy the orthogonality re-
lation ?1,q1|1,q2? ≈ δq1q2. Therefore, one can encode
different qubits by different phase patterns and employ a
single atomic ensemble as a holographic multimode quan-
tum memory. Since the information is stored globally
throughout the medium, one can achieve high-capacity
data storage. Recently, holographic storage of classical
light and microwave pulses have been demonstrated [25–
q2] ≈ δq1q2,
Here we report an experimental demonstration of holo-
arXiv:1204.1532v1 [quant-ph] 6 Apr 2012
FIG. 2: Illustration of the experimental setup. The two polarization-entangled photons produced by a narrowband SPDC source
are directed to the memory lab through 20-m fibers. Different polarization components are separated by the polarization beam
splitter (PBS) 1, and are coupled to the quad-mode holographic quantum memory. All the light fields are turned into right-
hand circular polarization (σ+) by wave plates. The biphoton entanglement are stored into the four quantum registers by
adiabatically switching off the control light. After a controllable delay, the photons are retrieved out, transferred back to their
original polarization states by wave plates and combined on PBS2. Then the retrieved entangled photons are guided into
filters, containing a Fabry-Perot cavity and a hot atomic cell to filter out the leakages from the control light, and detected by
single photon detectors. The path length difference between PBS1 and PBS2 is actively stabilized by an additional phase beam
(dashed line). Inset: The experimental laser lights and atomic levels.
graphic storage of biphoton Bell-type entanglement with
a single atomic ensemble, in which four orthogonal spin
waves with different wave vectors are used as a quad-
mode quantum memory. The posterior biphoton entan-
glement is mapped into and out of the quad-register holo-
graphic quantum memory, via a technique based on elec-
tromagnetically induced transparency (EIT). Violation
of Bell’s inequality is observed for storage time up to 1
µs and a memory-process fidelity of 98%, calculated by
quantum state tomography, is achieved.
The experimental scheme and setup are shown in Fig. 1
and 2, respectively.In the memory lab, we prepare,
within 14 ms, a cold87Rb atomic ensemble consisting
of about 108atoms in a dark Magnetic-Optical-Trap
(MOT). The temperature of the atomic cloud is about
140 µK, and the optical depth (OD) is about 10. The typ-
ical Λ-type energy-level configuration is shown in Fig. 1b,
where |g?, |e?, and |s? correspond to the87Rb hyper-fine
states |5S1/2,F = 1?, |5P1/2,F = 2?, and |5S1/2,F = 2?,
respectively. All the atoms are initially prepared at |g?.
A strong classical control field couples |e?-|s? transition
with wave vector kcand beam waist diameter wc≈ 850
µm, while the to-be-stored quantum field, which has four
components (see below), couples |g?-|e? transition with
beam waist diameter ws ≈ 450 µm. The control field
is focused at the ensemble center, and the four compo-
nents of the signal field are guided through the atomic
cloud along four different directions, which are in the
same plane but with different angles θi(i = 1−4) relative
to the control-light direction . We set (θ1,θ2,θ3,θ4) =
(−1◦,−0.6◦,0.6◦,1◦), as illustrated in Fig. 1a. By care-
fully adjusting the directions of the control and signal
beams, we make all the light modes overlap in the cen-
ter of the atomic ensemble. The atomic ensemble has a
length L ≈ 2 mm, and the signal fields propagate within
the control field during storage.
Each component i of the signal field is associated with
a wave vector ks,i, and is to be stored in a spin wave
with qi= ks,i− kc. By careful alignment, a holographic
quad-mode quantum memory, with approximately equiv-
alent optical depth and similar performance, is estab-
lished. We measure the EIT transmission spectrum and
perform slow-light experiment. For a control light with
a Rabi frequency of about 7 MHz, we observe an EIT
window of 2.2 MHz and a delay time of about 160 ns for
all the four modes. Note that such a holographic quan-
tum memory is different from the scheme in Ref. [8, 13],
where each signal mode requests a spatially separated
The biphoton entanglement comes from a narrowband
cavity-enhanced spontaneous parametric down conver-
sion (SPDC) entanglement source as in previous work [9,
29]. The source cavity contains three main parts, i.e.,
a nonlinear crystal, a tuning crystal and an output cou-
pler. The nonlinear crystal is a 25-mm type-II a period-
ically poled KTiOPO4 (PPKTP) crystal, whose opera-
tional wavelength λ ≈ 795 nm is designed to match the
D1 transition line of87Rb. The cavity is locked intermit-
tently to a Ti: Sapphire laser using the Pound-Drever-
Hall method. The linewidth and finesse of the cavity are
measured to be 5 MHz and 170, respectively.
Polarization-perpendicular photon pairs are created by
Storage Time (s)
age efficiency (blue, right axis) of the retrieved biphoton state
versus storage time. An exponential fitting (blue solid line)
of the storage efficiency yields a lifetime of τ = 2.8 ± 0.2
µs. The retrieved biphoton state is measured under |H/V ?,
|±?, and |R/L? bases with |±? = (|H? ± |V ?)/√2, and
|R/L? = (|H? ± i|V ?)/√2. The average visibility is fitted
using V = 1/(a + be2t/τ) (red solid line) with a and b the
fitting parameters. The result shows that within about 1.6
µs the visibility is above the threshold of 0.71 to violate the
CHSH-Bell’s inequality. Error bars represent ± standard de-
Average visibility (red, left axis) and overall stor-
applying a ultraviolet (UV) pumping light, which is up
converted from the Ti: Sapphire laser. Single-mode out-
put is achieved by using a filter cavity (made of a single
piece of fused silica of about 6.35 mm) with a finesse of
30, which removes the background modes. Polarization-
entangled photon pairs are post-selected by interfering
the twin photons at polarization beam splitters (PBSs).
The ideal outcome state corresponds to a Bell state
|φ+?p= (|H?1|H?2+ |V ?1|V ?2)/√2
with H(V) represents the horizontal(vertical) polariza-
tion of the photons. Under a continuous wave (CW)
pump with a pump power of 4 mW, the spectrum bright-
ness of the polarization-entangled pairs after the filter
cavity is about 50 s−1mW−1MHz−1.
experiment, the entangled signal photons are created
by a 200 ns pump pulse, which is cut from a 28 mW
CW pump laser. The production rate is about 33 s−1.
The measured ratio of counts under |HH?/|HV ? and
| + +?/| + −? bases are 14.3:1 and 23.1:1, respectively,
with |±? = (|H? ± |V ?)/√2.
The signal photon pair is directed to the memory lab
with 20-meter single-mode fibers. The different polariza-
tion components are spatially separated by PBS1, then
transferred to right-hand circular polarized (σ+) by wave
plates, and then guided to the four quantum registers by
lens (see Fig. 2). More precisely, the |H?1, |H?2, |V ?2,
and |V ?1polarization components are coupled to mode
1-4, respectively. After these components entering the
atomic ensemble, we adiabatically switch off the control
In the storage
light, and the photonic entanglement is mapped into the
atomic ensemble. This yields an entanglement among the
four quantum registers
After a controllable delay, we adiabatically switch on
the control light and convert the atomic entanglement
back into photonic entanglement. The polarization states
of the output photons are transferred back linearly po-
larized by wave plates and combined by PBS2to recon-
struct the biphoton entanglement. The two retrieved en-
tangled photons are respectively guided into a filter con-
sisting of a Fabry-Perot cavity (transmission window 600
MHz) and a pure87Rb vapor cell with atoms prepared
in |5S1/2,F = 2?, and then detected by single-photon de-
tectors. The measured overall average storage efficiency
is shown in Fig. 3, which yields a 1/e lifetime of 2.8±0.2
µs. The measured coincidence rate without storage and
after 1 µs storage time is 1.3 s−1and 0.03 s−1, respec-
tively. The propagating phase between PBS1and PBS2
is actively stabilized within λl/30 by an additional phase
lock beam with λl≈ 780 nm [9, 28].
To verify that the biphoton Bell-type entanglement is
faithfully mapped into and out of the four holographic
quantum registers, we first measure the retrieved bipho-
ton state in |H/V ?, |±?, and |R/L? = (|H? ± i|V ?)/√2
bases at different storage time. The average visibility
is shown in Fig. 3, which for storage time less than
1.6 µs, exceeds the threshold 0.71 to violate CHSH-
Bell’s inequality. Note that the reduction of the visibil-
ity with storage time is mainly due to the background
coincidences caused by the dark counts and the leak-
age from the control field. We further measure the cor-
relation function E(φ1,φ2), with φ1(φ2) the polariza-
tion angle for signal photon 1(2), and calculate quantity
S = | − E(φ1,φ2) + E(φ1,φ?
S = 2.54 ± 0.03 for the input state, and S = 2.25 ± 0.08
for the retrieved state after 1 µs storage. The violation
of the CHSH-Bell’s inequality (S > 2 ) confirms the
entanglement has been coherently and reversibly stored
in the quad-mode holographic quantum memory.
To quantitatively assess the fidelity of the storage pro-
cess, we perform the quantum state tomography [31, 32]
to construct the density matrix ρinof the input and ρout
of the output state after 1 µs storage, in which the polar-
ization state of each photon is measured with two single-
photon detectors under different detection settings. The
results are illustrated in Fig. 4, from which the fidelity of
the measured state ρ on the ideal Bell state ρφ+ is calcu-
lated as F(ρφ+,ρ) = (Tr
Carlo simulation technique  is applied to calculate
the uncertainties of the fidelity. Briefly, an ensemble of
100 random sets of data are generated according to Pos-
sionian distribution and then the density matrices are
2) + E(φ?
1,φ2) + E(φ?
2) = (0◦,45◦,22.5◦,67.5◦). We obtain
)2. A Monte
output state after 1 µs storage (c, d), obtained from quantum
state tomography. a and c are for the real parts, and b and
d are for the imaginary parts.
Density matrix of the input state (a, b) and of the
obtained by means of the maximum likelihood method.
This yields a distribution of fidelities, from which the
mean value and uncertainties of the fidelity are calcu-
lated. We obtain F(ρφ+,ρin) = (87.9 ± 0.5)% for the
input state ρin and F(ρφ+,ρout) = (81 ± 2)%, beyond
the threshold  78% for Werner states to violate Bell’s
inequality. The fidelity of the memory process is given
by F(ρin,ρout) = (98.2 ± 0.9)%.
In summary, we have experimentally demonstrated the
coherent mapping of a biphoton Bell-type entanglement,
created from a narrowband SPDC source, into and out
of a four-register holographic quantum memory, with a
high memory-process fidelity of 98% for 1 µs storage time.
The narrowband photonic entanglement source inherits
the advantage of conventional broadband SPDC source,
and can be used to generate multi-photon entanglement
beyond biphoton entanglement. A novel feature of the
holographic quantum memory is that one can use more
modes by simply choosing the directions of the signal
and control fields. The memory capacity Nmfor a copla-
nar configuration may be estimated by the geometric
mean of the Fresnel numbers of the illuminated regions as
Nm∼ wcws/(λL) , which is Nm∼ 240 for our experi-
mental parameters. Increasing the beam waist diameters
or extending to a three-dimensional geometry would al-
low much more modes. Individual control of each quan-
tum register may be achieved by using an optical cavity
and employing the stimulated Raman adiabatic passage
technique  or employing the phase match method .
To extend our work to storage of multi-photon entan-
glement, we have to improve the brightness of the entan-
glement source, and increase the retrieval efficiency and
lifetime of the quantum memory. The storage efficiency is
about 15%, which can be improved by further increasing
the optical depth and reducing the linewidth of the nar-
rowband entanglement source. The storage time is about
1 µs, which is limited by inhomogeneous broadening in-
duced by residual magnetic field, and can be improved to
be of order of millisecond by trapping the atoms in optical
lattice and using the magnetic-insensitive state [34, 35].
Our work opens up the possibility of scalable preparation
and high-capacity storage of multi-photon entanglement,
and also sheds light on the emerging field of holographic
quantum information processing.
This work was supported by the National Natural Sci-
ence Foundation of China, the National Fundamental
Research Program of China (grant no. 2011CB921300),
the Chinese Academy of Sciences, the Austrian Science
Fund, the European Commission through the European
Research Council Grant and the Specific Targeted Re-
search Projects of Hybrid Information Processing.
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