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Distribution of Time-Energy Entanglement over

100 km fiber using superconducting single-

photon detectors

Qiang Zhang1, Hiroki Takesue2, Sae Woo Nam3, Carsten Langrock1, Xiuping Xie1, M. M.

Fejer1, Yoshihisa Yamamoto1,4

1 Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305

2 NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198,

Japan

3 National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305

4National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-843, Japan

qiangzh@stanford.edu

Abstract: In this letter, we report an experimental realization of distributing

entangled photon pairs over 100 km of dispersion-shifted fiber. In the

experiment, we used a periodically poled lithium niobate waveguide to

generate the time-energy entanglement and superconducting single-photon

detectors to detect the photon pairs after 100 km. We also demonstrate that

the distributed photon pairs can still be useful for quantum key distribution

and other quantum communication tasks.

© 2007 Optical Society of America

OCIS codes: (190.4410) Nonlinear optics, parametric processes; (230.7380) Waveguides,

channeled

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References and links

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1. Introduction

Entanglement distribution is one of the core components in the field of long-distance quantum

communication (LDQC), for example, quantum key distribution (QKD) [1,2] and quantum

teleportation [3,4]. So far there are many experimental implementations of entanglement

distribution over free-space links [5,6], or optical fibers [7-11].

Very recently, 100-km entanglement distribution over optical fiber has been reported by

several groups [9-11]. One of the main problems in long-distance entanglement distribution is

the dark count rate of the detectors. Here, we utilized a reverse-proton-exchange (RPE)

periodically poled lithium niobate (PPLN) waveguide and superconducting single-photon

detectors (SSPD) to improve the distribution distance to 100 km over dispersion-shifted fiber

(DSF). RPE PPLN waveguides [12] were used due to their high nonlinear efficiencies and low

propagation loss (<0.1 dB/cm), while the SSPDs [13,14] had very low dark count rates (<200

Hz) and a fast timing response (~65 ps full width at half maximum), which resulted in a low

dark count probability per time window. We demonstrated that the entanglement after 100 km

still showed quantum nonlocality and violated Bell’s inequality by observing the two-photon-

interference fringes.

2. Time-Energy Entanglement

Time-energy-entangled photon pairs at telecom wavelengths are thought to be good

candidates for LDQC over fiber-based networks [7-9] due to the low propagation loss in

standard optical fiber and insensitivity to polarization-mode dispersion compared with

polarization-entangled photon pairs. Time-energy entanglement was first proposed by J. D.

Franson in 1989 [15]. In his original paper, an atom cascade process is utilized to generate the

entanglement. However, current experimental realizations of the protocol are mainly based on

parametric down conversion (PDC) [7].

As shown in Fig. 1, a continuous-wave laser with an ultra-long coherence time

χ

nonlinearity, generating correlated photon pairs via the PDC

process. The down-converted photon pairs usually have a much broader spectrum than the

pump photons and hence a significantly shorter coherence time

bandwidth limit. Since the two photons of a photon pair are always generated simultaneously

and the down conversion process obeys energy conservation, both the total energy and the

time difference of the two photons are well defined as the pump photon’s energy and zero,

respectively. However, we do not know the exact time and energy of each photon. This kind

of entangled state is called time-energy entanglement, and can be mathematically expressed

1 τ pumps a

crystal possessing a

) 2(

2 τ according to the time-

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as,

0)()(

2211

) )(2/(

16/)()(

21

21

2

1

2

21

2

2

4/2

21

tataeee dt dtC

tti

tttt

p

++

+−

+−−−

∫

=

ω

τ

τ

ψ

, where C is a

normalization constant, wp is the pumping frequency and ai

in mode i at time ti [16]. It has been widely used for testing of quantum nonlocality and

quantum key distribution.

+(ti) is the photon creation operator

Fig. 1. Scheme of generation and detection of time-energy entanglement. The small dotted pulses represent the

possible photon pairs, which can be generated during the long time span of the pump light, while the dotted red

envelope of the photon pairs is from the long pump.

To characterize and utilize the entanglement, one usually launches the entangled photon pairs

into two unbalanced Mach-Zehnder interferometers (MZI) and then implements a coincidence

measurement by detecting the outputs of the two MZIs with single-photon detectors. Suppose

the timing jitter of the single-photon detector is

τ . When a photon with quantum state t passes through the MZI at time n, it

will split, propagate in the short and long arms and come out with the quantum state

(

2/

4

τ

++

tet

,ττττ

>>>

, such that there will be no single-photon coherence fringe in the MZI’s

3 τ and the time unbalance between the MZI’s

two paths is

4

)

θ

i

, where θ is the phase between the two different arms. Suppose

3241

output. When a photon pair is detected in the two MZI’s outputs at time

have been generated at time t , propagated in the MZI’s long arm or could have been

generated at a later time

+

t

, propagated in the short arm. Since the photon pairs generated

1 τ were all in phase and

possibilities were interfered and

i

is

tette

444

phase in signal and idler’s channel and the angular frequency of the pump light.

4 τ

+

t

, it could either

4 τ

during the pump light coherence time

41

ττ >>

, the two

the

, where

final

iθ , ω denote the MZI’s

state was,

is

i

t

iS

4

)2(

)(

4

ττττ

τ∗ω

θ+θ

+++++

S

θ ,

3. Experimental Setup

A tunable external cavity diode laser with 100 kHz linewidth was used to generate the pump

light. The central wavelength of the laser was 1559 nm and the full width at half maximum

(FWHM) of the coherence time was 4 μs. The output of the laser was amplified by two

erbium-doped fiber amplifiers (EDFA) and then launched into a RPE PPLN waveguide to

generate frequency-doubled pump light for the PDC process via second harmonic generation

(SHG) as shown in Fig. 2. One 3.0-nm-wide tunable bandpass filters was inserted after each

EDFA, respectively, to filter out the EDFA’s spontaneous emission noise. Since these

waveguide devices only accept TM-polarized light, an in-line fiber polarization controller was

used to adjust the polarization of the input. The residual pump was attenuated by 180 dB using

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dichroic mirrors and pump filters. The second-harmonic (SH) wave was then launched into a

second RPE PPLN waveguide to serve as the pump pulse for the PDC process. Waveguide-

based PDC sources exhibit higher conversion efficiencies than bulk crystals and can be

integrated with fiber-optic-based components.

Since RPE PPLN waveguides fabricated in z-cut substrates only support TM-polarized waves,

separation of the near degenerate signal and idler waves via polarization de-multiplexing is

not possible. To solve this problem, we took advantage of higher order mode interactions in

combination with integrated mode multiplexers / demultiplexers via asymmetric Y-junctions

[17, 18].

Fig. 2. Diagram of the experimental setup. TBPF: tunable band-pass filter. PPLN1: a RPE PPLN waveguide for

second harmonic generation of the pump source. PPLN2: a fiber pigtailed asymmetric Y-junction RPE PPLN

waveguide for parametric down-conversion. LPF: long-pass filter to remove the 780 nm pump light and other

parasitics. BPF: 0.8-nm-wide bandpass filter. SSPD: superconducting single-photon detector. TIA: time interval

analyzer. Solid lines represent optical fibers and dotted lines represent free-space propagation.

The generated entangled photon pairs and residual pump light were collected at the output of

the RPE PPLN waveguide via a fiber pigtail. The spectral bandwidth of the entangled photon

pairs was around 40 nm [17]. A long-pass filter was inserted into each output fiber of the

second RPE PPLN chip to eliminate the residual pump light as well as other fluorescence.

Two 0.8-nm-wide bandpass filters were used to reduce the bandwidth of the photon pairs,

limiting the dispersion in the DSF. The band-pass filter also defined the photon pairs’ time

duration to be 4 ps FWHM. The photon pairs were then input into two spools of 50-km-long

DSF, respectively. The center wavelength of the photon pairs was 1559 nm and the dispersion

after 50 km broadened the photon pairs’ pulse duration to 25 ps [19], which was smaller than

the timing jitter of the SSPD.

The entangled photon pairs were analyzed by two 10-GHz unbalanced planar lightwave

circuit (PLC) MZIs. The phase between the two arms of the MZIs could be controlled by

adjusting the temperature of the interferometer using a Peltier element [20]. The time

difference between the two arms was 100 ps, i. e.

τττ

<<<

. Therefore, one observes the two-photon-coincidence condition and not the

single photon interference. Compared with previous entanglement distribution experiments,

our MZIs had a significantly higher bandwidth, i.e. much smaller

the entanglement flux.

However, a larger bandwidth needs a faster single-photon detector, i.e.

the previous LDQC experiments, the detector’s performance limited the distribution distance.

ps

100

4=

τ

, meeting the condition

142

4

τ , which could improve

43

ττ <

. In most of

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In our experiment, we used two SSPDs to detect the entangled photon pairs. The SSPDs used

in this experiment consisted of a 100-nm-wide, 4-nm-thick NbN superconducting wire, which

was coupled to a 9-μm core single-mode fiber [14]. The packaged detectors were housed in a

closed-cycle cryogen-free refrigerator with an operating temperature of 3 K. The quantum

efficiency and dark count rate of the SSPDs depended on an adjustable bias current. In the

experiment, we set the bias current to reach a quantum efficiency of 0.7% and 2.1% for the

signal and idler channel, respectively, and a dark count rate of around 100 Hz. These SSPDs

had an inherently small Gaussian timing jitter of 65 ps (FWHM). In the experiment, we set

our coincidence time window to 100 ps. Therefore, the dark count propability per time

window was

10−, which reduced the accidental coincidence rate caused by dark counts

compared to previous experiments [7-9].

The detected signals were sent to a time interval analyzer (TIA) whose timing response was

also faster than

event were used as the start and the idler channel as the stop signal.

8

4 τ to measure the time coincidence histogram. The signal-photon’s detection

4. Experimental Results

In the experiment, we input 316 mW of pump at a wavelength of 1559 nm into the first PPLN

waveguide from the EDFA and coupled 560 μW of the generated SH into the second PPLN

chip.

We set the time window to 60 ps (

Under this condition, we achieved 0.05 average photon pairs per time window. The total

channel loss before the 100-km-long fiber was 20 dB, with 10 dB due to the PPLN’s

propagation, reflection, scattering and fiber pigtailing loss, and 10 dB loss from the filters and

fiber U-benches. Each of the two PLC MZIs had a 5 dB insertion loss. The DSF’s loss was 0.2

dB/km. Including all the channel loss terms, we obtained entangled photon pairs at a 2 Hz

rate.

To qualify the entanglement after 100 km of fiber, we first set the PLC interferometer in the

signal channel to 22.5°C and varied the temperature of the interferometer in the idler channel

to obtain a coincidence interference-fringe pattern. To demonstrate entanglement, one

interference pattern is not enough; at least one other pattern in a non-orthogonal basis is

necessary. To observe this pattern, we set the signal interferometer to 24.5°C and observed the

interference fringes shown in Fig. 4(a). The two curves with an average visibility of

)%7 5 .80(

±

, which is well beyond the visibility of 71% necessary for violation of the Bell

inequality [21], demonstrate the achieved entanglement. The large uncertainty of the visibility

resulted from system instabilities, for example, temperature fluctuations of the two PPLN

chips, the polarization and timing fluctuations caused by the temperature change of the 100-

km long fiber, etc. To eliminate the timing fluctuations, we increased the coincidence time

window from 60 ps to 100 ps, even though this increased the accidental coincidence noise.

Besides the timing fluctuations, the imperfection of the PLC MZIs, the dark counts of the

SSPD and multi-photon-pair emissions will also introduce error to the visibility. In the

experiment, it took several hours to take each curve in Fig. 4(a) due to the low flux of

entangled photon pairs. The long measurement time accentuated polarization and timing

fluctuations between the two measurements, and is also the reason for the different heights of

the two curves in the figure.

3 τ ), which was equal to the timing jitter of the SSPD.