Download PDF

Storage and long-distance distribution of telecom-band
polarization entanglement generated in optical fiber
Xiaoying Li, Paul L. Voss, Jun Chen, Jay E. Sharping, and Prem Kumar
Center for Photonic Communication and Computing, ECE Department,
Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA
Compiled December 9, 2004
We demonstrate storage of polarization-entangled photons for 125 µs, a record storage time to date, in
a 25 km-long fiber spool using a telecom-band fiber-based source of entanglement. With this source we also
demonstrate distribution of polarization entanglement over 50 km by separating the two photons of an entangled
pair and transmitting them individually over separate 25 km fibers. The measured two-photon fringe visibilities
were 82% in the storage experiment and 86% in the distribution experiment. Preservation of polarization
entanglement over such long-distance transmission demonstrates the viability of all-fiber sources for use in
quantum memories and quantum logic gates.
c 2004 Optical Society of America
°
OCIS codes: (270.0270) Quantum optics; (190.4370) Nonlinear optics, fibers; (190.4410) Nonlinear optics, parametric
processes; (999.9999) Quantum information processing.
Storage and distribution of quantum entanglement are
essential capabilities for implementing many of the novel
functions of quantum information processing (QIP).
Over the past decade, various quantum-communication
applications, such as quantum teleportation,1 quantum
dense coding,2 and quantum cryptography (QC)3 have
been realized. Also, researchers are actively pursuing a
variey of methods to advance quantum computing, the
leading technologies to date are ion-traps4 and nuclear
magnetic resonance (NMR).5 Recent developments in
linear-optics quantum communications have shown that
quantum logic gates can be realized with a success rate
arbitrarily close to unity by using linear-optical elements
and post selection based on the results of measurements
made on ancilla photons.6, 7 Quantum memory8 and
logic devices9 which exploit the quantum-correlated photon pairs produced by χ(2) crystal have been experimentally demonstrated. However, because of the formidable
engineering problems in coupling the entangled photons
from the χ(2) crystal into standard optical fiber for storage, distribution, and manipulation, the implementation
of QC over long distances and the implementation of
fault-tolerant quantum computing remain challenging.
If the entangled-photon pairs can be generated within
the fiber itself, the coupling problem can be obviated.
Moreover, if their wavelengths are in the fiber’s lowloss propagation window near 1.5 µm, the transmission
losses can be minimized. Such a source has been recently developed by exploiting the χ(3) nonlinearity of
the fiber.10–13 When the pump wavelength is close to the
zero-dispersion wavelength of the fiber, phase-matching
is achieved and the probability amplitude for inelastic
four-photon scattering (FPS) is significantly enhanced.
In this process, two pump photons at frequency ωp scatter through the Kerr nonlinearity of the fiber to create
energy-time entangled signal and idler photons at fre-
quencies ωs and ωi , respectively, such that 2ωp = ωs +ωi .
Because of the isotropic nature of the Kerr nonlinearity in fused-silica-glass fiber, the scattered correlatedphotons are predominantly co-polarized with the pump
photons. By coherently adding two such orthogonallypolarized parametric processes, polarization entanglement is created as well.11, 13 In this Letter, following
our preliminary report,14 we demonstrate using the fiber
source of polarization-entangled photons (FSPEP) that
polarization entanglement is preserved, as evidenced by
two-photon interference (TPI), when only one photon
of the pair or when both photons are propagated over
25 km. In the former case, the results show that quantum entanglement is preserved when the system is used
as a quantum memory, i.e., one photon has been stored
in the fiber for 125 µs, which is a record storage time.
In the latter case, the results show that polarization entanglement is maintained when the photons of the pairs
are distributed 50 km apart in standard optical fiber.15
In Fig. 1(a) a conceptional diagram of the FSPEP is
presented. It is described in more detail in Ref. [11]. The
nonlinear-fiber Sagnac interferometer (NFSI), made up
of a fused-silica 50/50 fiber coupler spliced to 300 m
of dispersion-shifted fiber (DSF) with a zero-dispersion
wavelength at λ0 = 1536 ± 2 nm, is pumped by two
relatively-delayed orthogonally-polarized pump pulses,
PH and PV , respectively. The two pump pulses originate from a common pulse of 1536 nm central wavelength and ' 5 ps full-width at half maximum (FWHM);
PV is delayed by 30 ps with respect to PH . Correlated
signal-idler photon pairs |His |Hii and |V is |V ii at 1547
and 1525.1 nm, respectively, are scattered by PH and
PV through FPS in the NFSI in the time epochs of
the two pump pulses. Passing the scattered photon-pairs
through 20 m of polarization-maintaining (PM) fiber,
propagating |His |Hii along slow axis while sending
1
|V is |V ii along fast axis, removes the distinguishing time
delay between the orthogonally-polarized photon pairs.
Thus, a polarization-entangled state |Ψi = |His |Hii +
ei2φp |V is |V ii is created, where φp is the relative phase
difference between the two pump pulses. For such a state,
if polarization analyzers (PAs) [embodied as rotatable
polarization beam splitters (PBSs)] are placed in the signal and idler channels, then the single-count probability
is Ri = 21 ηi (i = 1, 2) and the coincidence-count probability for the signal and idler photons R12 can be expressed as R12 = 12 η1 η2 [cos2 θ1 cos2 θ2 + sin2 θ1 sin2 θ2 +
2 cos(2φp ) sin θ1 cos θ1 sin θ2 cos θ2 ], where ηi is the total
detection efficiency and θi is the angle of the PA in
each channel. Because the Kerr nonlinearity is relatively
weak, only about 0.1 photon-pair is produced by a typical 5-ps-duration pump pulse containing approximately
107 photons. To reliably detect the scattered photonpairs, an isolation between the pump and signal/idler
photons in excess of 100 dB is required. We achieve this
by exploiting the mirror-like property of NFSI,16 which
provides > 30 dB isolation, and by passing the output
of the PM fiber through a double-grating spectral filter
(DGSF) consisting of three identical diffraction gratings,
G1, G2, and G3, that provides a pump-rejection ratio in
excess of 75 dB. The passbands for the signal and idler
channels are determined by numerical apertures of the
fiber and the geometrical settings of the optical elements
comprising the spectral filter. In this experiment, the
FWHM of the filter in both the signal and idler channels
is about 0.6 nm.
The 25-km-long fiber spools used in our experiment
are commercially available single-mode fibers (Corning SMF-28 and Corning LEAF). The propagation loss
through each spool of fiber was measured to be approximately 0.2 dB/km. When entangled-photon pairs
travel through optical fiber, two phenomena may cause
decoherence: polarization-mode dispersion (PMD) and
chromatic dispersion (CD). PMD refers to the presence
of two different group velocities for the two orthogonal polarization modes. Because of asymmetries in all
real fibers, the so-called single-mode fiber actually guides
two stochastically coupled modes of polarization, causing a light pulse to broaden when travelling down a fiber.
PMD is usually described as a statistical distribution
of differential √
group delay
∆τ . In modern optical fiber,
√
∆τ ≈ (0.1ps/ km) · l, where l is the fiber length. In
contrast to the entangled-photon pairs based on the χ(2)
nonlinearity, which typically have a bandwidth > 5 nm,
the entangled-photon pairs used in our experiment have
a FWHM of 0.6 nm with a corresponding coherent time
> 10 ps. Thus, the delay caused by PMD in the 25-km
fiber spool, ∆τ ≈ 0.5ps, is much less than the coherent time of the signal and idler photons, so the PMD is
not a problem in our experiment. CD refers to the dependence of group delay upon wavelength; when a photon with non-zero bandwidth travels in optical fiber, it
becomes temporarily broadened. For the polarizationentangled state |Ψi = |His |Hii + eiφ |V is |V ii , the par-
tial wave packets |His |Hii and |V is |V ii experience the
same amount of broadening; so the overlap between the
two wave packets remains unaffected, i.e., CD does not
cause decoherence of the polarization entanglement.
The signal and idler photons are counted by photoncounting modules consisting of InGaAs/InP avalanche
photodiodes (APD, Epitaxx, Model EPM 239BA) operated in the gated Geiger mode at room temperature.10
The 1-ns-wide gate pulses arrive at a rate of 588 KHz,
which is 1/128 of the repetition rate of the pump pulses;
the gates coincide with the arrival of the signal and
idler photons at the APDs. The electrical signals produced by the APDs in response to the incoming photons
(and dark counts) are reshaped into 500 ns wide TTL
pulses, which are then acquired by a computer-controlled
16-bit analog-to-digital (A/D) board (National Instrument, PCI 6110E). Thus, single counts in both the signal
and idler channels and coincidences acquired from different time bins can be determined because the A/D card
records all counting events. The quantum efficiency of
APD1 (APD2) is about 25% (20%), with a corresponding dark-count probability of 2.2 × 10−3 (2.7 × 10−3 )
/pulse. The total detection efficiencies for the signal
and idler photons are about 8% and 6%, respectively,
when the efficiencies of the NFSI (82%), 90/10 coupler,
double-grating filter [45% (50%) in signal (idler) channel], and other transmission components (about 90%) are
included. When the photons have propagated through
the 25 km-fiber spool, the corresponding transmission
efficiency of about 30% and the subsequent 80% efficiency of the PA, consisting of a fiber polarization controller (FPC) and a fiberized polarization beam splitter
(FPBS), should also be included.
Figure 1(b) shows the experimental setup in which
the idler photons arrive at APD2 after passing through
a 25 km spool of LEAF fiber, while the signal photons
go to APD1 after about 2 m of standard fiber. A rotatable PBS is placed in the signal channel serving as a
PA. When the average pump powers for both PH and
PV are 0.55 mW, we make a polarization correlation
measurement of the signal and idler photons by setting
the respective PAs at 45◦ and −45◦ and scanning the
relative phase φP between PH and PV . The coincidence
counts are measured by choosing the right time bin in
the signal and idler channels; here the time bin in the
idler channel is 125 µs behind that of the signal channel.
The results are shown in Fig. 2(a): the single counts in
both the signal and idler channels stay the same, while
the true coincidence counts—the difference between the
measured coincidence counts and the accidental coincidence counts—vary with the relative phase φP . At the
production rate of about 0.26 photon-pairs/pulse, which
is deduced from the detected single counts, the visibility
of TPI is observed to be 82% by fitting the true coincidence counts with a cosine function.
Figure 1(c) portrays the experimental setup in which
the signal photons are transmitted through the 25 km
LEAF spool and the idler photons through the 25 km
2
SMF-28 spool. When the pump powers of PH and PV are
0.75 mW, we measure the polarization correlation again.
Here the coincidence counts are measured by choosing the same time bin in the signal and idler channels
because the fiber lengths in the two spools are equal.
The results shown in Fig. 2(b) are similar to those in
Fig. 2(a), except that the count rate in the signal channel is also decreased. At the deduced production rate of
about 0.32 photon-pairs/pulse, we obtain a TPI visibility of 86%, again by fitting the true coincidences with a
cosine function.
We note that the TPI results achieved in the above
experiments are obtained by subtracting the accidental
coincidences that mainly result from Raman scattering
(RS) in the DSF and dark counts of the uncooled detectors. The raw visibility of the TPI would be about
23% in Fig. 2(a) and 17% in Fig. 2(b). However, by
decreasing the detuning between the signal and pump
photons while using a PBS to further reduce the RS,
and by cooling the APDs to reduce the dark counts, an
accidental coincidence rate < 10% of the total measured
coincidence rate can be achieved, as demonstrated by
our recent experimental work.12 Also, FPS has recently
been demonstrated by Harvey et al.17 and Wadsworth
et al.18 in microstructure fiber, wherein the signal and
idler frequency difference is greater than 200 THz, yielding signal and idler photons that are not contaminated
by first-order RS.
Comparing the visibilities of TPI in Fig. 2 with the
93% visibility reported in Ref. [11], where the photons
did not propagate through 25 km fiber, we see a reduction to 82% and 86%. We believe three reasons can explain this: (i) Increased multi-photon events—when the
FPS photon-pair production rate Ppair increases, the visibility V decreases as V ≈ 1 − Ppair /2.19 After subtracting the RS,12 the photon-pair production rates in the
two experiments are about 0.12 and 0.16 pair/pulse, respectively, while in Ref. [11], the production rate was
about 0.06 pair/pulse. (ii) We adjusted the PA angle by
using an FPC in front of an FPBS after having the photons propagate through the 25 km fiber spool. So, it is
highly possible that the analyzer angle setting was not
exactly 45◦ . (iii) The lengths of fiber in the spools fluctuate with time, which causes some degradation since
the PA is kept fixed during the measurement time. By
replacing the PAs consisting of an FPC and an FPBS
with those consisting of a half-wave plate and a PBS
and using feedback at another wavelength to track and
control the phase changes, we expect that the TPI visibility in Figs. 2(a) and 2(b) would improve to 94% and
92%, respectively.
In conclusion, we have demonstrated TPI with a visibility up to 86% (Bell’s inequalities are expected to be
violated for this visibility) after propagating the individual photons of entangled pairs over 25 km of fiber.
We show that the quantum correlation is preserved after
one photon has been stored in the fiber for 125 µs, and
that polarization entanglement can be maintained over
distances of 50 km in standard optical fiber. The main
limitation in the present experimental setup due to RS
in the DSF can be significantly reduced by modifying the
passed band of the DGSF, by using a PBS, and alternatively, by using a specially designed microstructure fiber.
The experimental setup is integrable with existing fiberoptic technology. Moreover, because the spatial mode of
the photon-pair is the very-pure guided transverse mode
of the fiber, complex networks involving several entangling operations can be envisioned.
This work was supported by the U.S. Army Research
Office under a MURI grant DAAD19-00-1-0177.
References
1. D. Bouwmeaster, J. W. Pan, K. Mattle, and A. Zeilinger,
Nature. 390, 1997 (1998).
2. K. Mattle, H. Weinfunter, P. G. Kwiat, and A. Zeilinger,
Phys. Rev. Lett. 76, 4656 (1996).
3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev.
Mod. Phys. 74, 145 (2002).
4. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano,
and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
5. J. A. Jones, M. Mosca, and R. H. Hansen, Nature 393,
344 (1998).
6. E. Knill, R. Laflamme, and G. J. Milburn, Nature 409,
46 (2001).
7. J. D. Franson, M. M. Donegan, M. J. Fitch, B. C. Jacobs,
and T. B. Pittman, Phys. Rev. Lett. 89, 137,901 (2002).
8. T. B. Pittman and J. D. Franson, Phys. Rev. A 66,
062,302 (2002).
9. T. B. Pittman, B. C. Jacobs, and J. D. Franson, Phys.
Rev. A 64, 062,311 (2001).
10. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar,
IEEE Photon. Technol. Lett. 14, 983 (2002).
11. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, arXiv:
quant-ph/0402191 (2004).
12. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar,
Opt. Exp. 12, 3337 (2004).
13. H. Takesue and K. Inoue, Phys. Rev. A 70, 031,802
(2004).
14. X. Li, P. L. Voss, J. E. Sharping, J. Chen, and P. Kumar, Feontiers in Optics, Oct.5-9, 2003, Tucson, Arizona/WAA4 .
15. I. Marcikec, H. de Riedmatten, W. Tittel, H. Zbinden,
M. Legre, and N. Gisin, Phys. Rev. Lett. 93, 180,502
(2004).
16. D. B. Mortimore, J. Lightwave Tech. 6, 1217 (1988).
17. J. D. Harvey, R. Leonhardt, S. Goen, and G. K. L. Wong,
Opt. Lett. 28, 2225 (2003).
18. W. Wadsworth, P. Russel, J. Rarity, J. Duligall, and
J. Fulconis, CLEO/IQEC postdeadline paper/IPDA7
(2004).
19. I. Marcikec, H. de Riedmatten, W. Tittel, V. Scarani,
H. Zbinden, and N. Gisin, Phys. Rev. A 66, 062,308
(2002).
3
FSPEP
FPC1
G3
PH
G2
PM Fiber
(a)
50/50
H
90/10
s
H
i
e iI V
PBS
Signal
FSPEP
Idler
Signal
300 m
DSF Loop
PV
s
V
FPC2
Idler
G1
i
APD1
Computer
APD2
FPBS
(b)
25 km Fiber
25 km Fiber
FPC3 FPBS APD1
Signal
Computer
FSPEP
Idler
FPC2 FPBS
(c)
APD2
25 km Fiber
4
0
2
(a)
-70
0
0
2
4
Relative phase I p (rad)
6
8
270
6.4
180
4.8
90
3.2
0
1.6
(b)
-90
0
0
2
4
4
360
Single Counts (X10 /40s)
70
Coincidences (/40s)
Coincidences (/15s)
6
140
4
8
210
Single Counts (X10 /15s)
Fig. 1. Experimental setup; see text for details.
6
Relative Phase I p (rad)
Fig. 2. True coincidence- and single-count rates as the
relative phase φp is varied with PAs set at 45◦ /−45◦ .
Solid curves are theoretical fits. (a) Only idler photons
travel through 25 km of fiber. (b) Both signal and idler
photons travel through separate spools of 25 km fiber.
4