Abstract: We demonstrate greatly improved results for the productionof correlated photon-pairs using the four-photon scattering process in silicafiber. We achieve a true-coincidence-count to accidental-coincidence-countratio greater than 10, when the photon-pair production rate is about 0.04/pulse. This represents a four-fold improvement over our previous results.The contribution of spontaneous Raman scattering, the primary cause ofuncorrelated photons that degrades the fidelity of this source, is reducedby decreasing the wavelength detuning between the correlated photons andthe pump photons and by using polarizers to remove the cross-polarizedRaman-scattered photons. Excess Raman scattering could be furthersuppressed by cooling the silica fiber. Even without cooling the fiber, theachieved 10 to 1 ratio of true-coincidence to accidental-coincidence makesthe fiber source of correlated photon-pairs a useful tool for realizing variousquantum-communication protocols.
References and links1. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum tele-
portaion,” Nature 390, 575–578 (1997).2. I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long-distance teleportation of qubits at
telecommunication wavelengths,” Nature 421, 509–512 (2003).3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quamtum cryptography,” Rev. Mod. Phys. 74, 145–195 (2001).4. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communica-
tion,” Photon. Technol. Lett. 27, 491–493 (2002).5. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-enangled photon pairs in the
1550nm telecom band,” arXiv: quant-ph/0402191 (2004).6. J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical
fiber,” Opt. Lett. 26, 367–369 (2001).7. D. B. Mortimore, “Fiber Loop Reflectors,” J. Lightwave Technol. 6, 1217–1224 (1988).8. P. L. Voss, R. Tang, and P. Kumar, “Measurement of the photon statistics and the noise figure of a fiber-optic
parametric amplifier,” Opt. Lett. 28, 549–551 (2003).9. P. L. Voss and P. Kumar, “Raman-noise-induced noise-figure limit for χ(3) parametric amplifiers,” Opt. Lett. 29,
445–447 (2004).10. P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength
converters,” to appear in J. Opt. B: Quantum Semiclass. Opt. 6 (2004).11. R. H. Stolen and M. A. Bosch, “Low-Frequency and Low-Temperature Raman Scattering in Silica Fibers,” Phys.
Rev. Lett. 48, 805–808 (1982).
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3737#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
12. M. Hass, “Raman spectra of vitreous silica, germania, and sodium silicate glass,” J. Phys. Chem. Solids 31,415–422 (1970).
13. D. J. Dougherty, F. X. Kaertner, H. A. Haus, and E. P. Ippen, “Measurement of the Raman gain spectrum ofoptical fibers,” Opt. Lett. 20, 31–33 (1995).
14. F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
Entangled photon-pairs are a critical resource for realizing the various quantum informationprocessing protocols such as quantum teleportation [1][2] and quantum cryptography [3]. Be-cause of the requirement of distributing entangled photons over long distances and the difficultyof coupling entangled photons produced by χ (2) nonlinear crystals into optical fibers, a sourceemitting entangled photon-pairs in the low-loss 1550-nm telecommunication band of silica fiberthat could be directly spliced to the existing fiber network is desirable. Such a source has beenrecently developed by exploiting the χ (3) (Kerr) nonlinearity of the fiber itself [4][5]. Whenthe pump wavelength is close to the zero-dispersion wavelength of the fiber, phase-matching isachieved and the probability amplitude for inelastic four-photon scattering (FPS) is significantlyenhanced. In this process, two pump photons at frequency ω p scatter through the Kerr nonlin-earity of the fiber to create energy-time entangled Stokes and anti-Stokes photons at frequen-cies ωs and ωa, respectively, such that 2ω p = ωs + ωa. Because of the isotropic nature of theKerr nonlinearity in fused-silica-glass fiber, the scattered correlated-photons are predominantlyco-polarized with the pump photons. By coherently adding two such orthogonally-polarizedparametric processes, polarization entanglement can be created as well [5]. Following this ap-proach, all four Bell states can be prepared, and a violation of Bell’s inequalities by up to 10standard deviations of measurement uncertainty has been demonstrated [5]. However, in pre-vious experiments with this source, the number of measured total-coincidences exceeded thenumber of accidental-coincidences by only a factor of 2.5 [4]. In this paper, we show that spon-taneous Raman scattering accompanying FPS causes this problem. By reducing the detuningbetween the Stokes and pump photons and by using polarizers, we demonstrate that the acci-dental coincidences can be made less than 10% of the true coincidences at a production rateof about n = 0.04 photon-pairs/pulse. Further improvement could be obtained by cooling thesilica fiber.
APD1
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Fig. 1. Experimental setup: scattered Stokes and anti-Stokes photons emerging from theport labelled ”Out” are detected; FPC, fiber polarization controller; PBS, polarization beamsplitter; G, gratting; QWP, quarter-wave plate; HWF, half-wave plate; ”Signal-In” port isblocked during photon-counting measurement.
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3738#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
Our experimental setup is shown in Fig. 1. Stokes and anti-Stokes photon-pairs at frequen-cies ωs and ωa, respectively, are produced in a nonlinear-fiber Sagnac interferometer (NFSI).We have previously used this NFSI to generate quantum-correlated twin beams [6], correlatedphoton-pairs [4], and polarization entanglement [5]. The NFSI consists of a fused-silica 50/50fiber coupler spliced to 300 m of dispersion-shifted fiber (DSF) with a zero-dispersion wave-length at λ0 = 1535±2nm. The efficiency of FPS in DSF is low because of the relatively lowmagnitude of the Kerr nonlinearity; only about 0.1 photon-pair is produced by a typical 5-ps-duration pump pulse that contains approximately 10 8 photons. To reliably detect the scatteredphoton-pairs, a pump to photon-pair rejection ratio in excess of 100 dB is required. We achievethis by first exploiting the mirror-like property of the NFSI [7], which provides a pump re-jection greater than 30 dB, and then sending the transmitted scattered photons along with theleaked pump photons through a free-space double-grating spectral filter (DGSF) that provides apump-rejection ratio in excess of 75 dB. The filter consists of three identical diffraction gratings(holographic, 600 grooves/mm), G1, G2, G3, whose diffraction efficiencies for the horizontallyand vertically polarized light are 90% and 86%, respectively. The doubly-diffracted Stokes andanti-Stokes photons are then re-coupled into fibers. The passbands for the Stokes and anti-Stokes channels are determined by the numerical apertures of the fiber and the geometricalsettings of the optical elements composing the spectral filter.
The pump is a 5-ps-duration mode-locked pulse train with a repetition rate of 75.3 MHz,obtained by spatially dispersing the output of an optical parametric oscillator (OPO) (CoherentInc., model Mira-OPO) with a diffraction grating; its central wavelength can be tuned from1525 to 1536 nm. To achieve the required power, the pump pulses are then amplified by anerbium-doped fiber amplifier (EDFA). Photons at the Stokes and anti-Stokes wavelengths fromthe OPO that leak through the spectral-dispersion optics and from the amplified spontaneousemission (ASE) from the EDFA are suppressed by passing the pump through a 1nm-bandwidthtunable filter (Newport, model TBF-1550-1.0). For alignment purposes, weak signal pulses atthe Stokes wavelength, which are temporally synchronized with the pump pulses, are injectedinto the NFSI. During photon counting measurements, however, the input signal is blocked.
Photon counters consisting of InGaAs/InP avalanche photodiodes (APD, Epitaxx, modelEPM 239BA) operated in a gated-Geiger mode are used to count the Stokes and anti-Stokesphotons [4]. The 1-ns-wide gate pulses arrive at a rate of 588 kHz, which is 1/128 of the repeti-tion rate of the pump pulses. The quantum efficiency for one detector is 25%, that for the otheris 20%. The total detection efficiencies for the Stokes and anti-Stokes photons are about 8%and 6%, respectively, when the efficiencies of the NFSI (82%), 90/10 coupler, double gratingfilter (45% and 50% in anti-Stokes and Stokes channel, respectively), and other transmissioncomponents (about 90%) are included.
For the FPS occurring in the DSF, the scattered correlated photon-pairs are predominantlyco-polarized with the pump photons. An investigation into the origin of the low ratio betweenthe total coincidences and the accidental coincidences illustrates this point. A polarization beamsplitter (PBS) is placed in both the Stokes and anti-Stokes channels. With proper settings of thehalf-wave-plate (HWP) and the quarter-wave-plate (QWP), which are placed in front of thedouble grating filter, the Stokes and anti-Stokes photons that are either co-polarized or cross-polarized with the pump photons can be rejected. We measure the number of scattered photonsper pump pulse, co-polarized and cross-polarized with the pump, respectively, that are detectedin the anti-Stokes channel, Na, as a function of the number of pump photons per pulse, N p,and the coincidence rate between the detected Stokes and anti-Stokes photons as a function ofNa. In both co- and cross-polarized cases, we fit the measured data with Na = s1Np + s2N2
p ,where s1 and s2 are the linear and quadratic scattering coefficients, respectively. Figure 2 showsthe data obtained when the detuning Ω/2π of the Stokes (anti-Stokes) photons is 1.25 THz,
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3739#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
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Fig. 2. Measured coincidence rates as a function of the number of scattered photons perpump pulse (labelled Single Counts/Pulse) in the anti-Stokes channel for (a) scatteredphotons co-polarized with the pump and (b) scattered photons cross-polarized with thepump. In both cases λp = 1536nm and Ω/2π = 1.25THz; the diamonds represent the total-coincidence counts produced by a single pump pulse, the triangles represent the accidental-coincidence counts produced by two adjacent pump pulses, and the line represents the cal-culated coincidence counts for two independent light sources. The insets show the numberof scattered photons per pump pulse detected in the anti-Stokes channel as a function ofthe number of photons in the pump pulse (hollow circles). A second-order polynomial,Na = s1Np + s2N2
p , is shown to fit the experimental data (dot-dashed line). The contribu-
tions of linear scattering, s1Np, (dashed line) and quadratic scattering, s2N2p , (dotted line)
are plotted separately as well. For the inset in (a): s1 = 0.00436 and s2 = 0.01046; for theinset in (b): s1 = 0.00381 and s2 = 0.00033.
where Ω = ωp −ωs = ωa −ωp, and the full-width at half maximum (FWHM) of the DGSFis 0.8 nm. As shown in the inset of Fig. 2(a), for the photons co-polarized with the pump, thequadratic scattering owing to FPS dominates over the linear scattering when N p > 0.4× 108
photons/pulse, whereas the opposite is true when N p < 0.4× 108 photons/pulse. The mainbody of Fig. 2(a) shows that the total-coincidence rate of the Stokes and anti-Stokes photonsproduced by the same pump pulse is much higher than the accidental-coincidence rate. Thelatter is obtained by measuring the coincidence rate between the Stokes and anti-Stokes pho-tons produced by two adjacent pump pulses and fits the theory curve for two independent lightsources very well [4]. Comparing the coincidence-measurement results in Fig. 2(a) with ourprevious results in [4], the ratio between the total coincidences and the accidental coincidencesis improved. The results for the photons cross-polarized with the pump are shown in Fig. 2(b),
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3740#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
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Fig. 3. Same as in Fig.2, except λp = 1525nm. For the inset in (a): s1 = 0.00688 ands2 = 4.38×10−5; for the inset in (b): s1 = 0.005 and s2 = 0.
where we find no difference between the total-coincidence rate and the accidental-coincidencerate. The linearly-scattered photons contribute much more than the quadratically-scattered pho-tons, as shown in the inset of Fig. 2(b). Absence of true coincidences, which is quantified bythe difference between the total-coincidence rate and the accidental-coincidence rate, impliesthat the Stokes and anti-Stokes photons that are orthogonally polarized with the pump are notcorrelated. We note that a small number of quadratically-scattered photons are observed; how-ever, these come mainly from the leakage of the quadratically-scattered photons co-polarizedwith pump owing to imperfect rejection by the PBS. We corroborate this by making classicalparametric-gain measurements in the low-gain region. When the polarization of the injectedweak signal is perpendicular to that of the pump, the four-wave-mixing (FWM) gain is meas-ured to be 20 dB less than the gain when the signal and pump are co-polarized.
The linear dependance of the scattering rate of the Stokes and anti-Stokes photons onNp, which is proportional to the pump power, indicates that the uncorrelated photons cross-polarized with respect to the pump are caused by spontaneous Raman scattering. This has alsobeen verified experimentally and theoretically in the context of the noise-figure of parametricamplifiers made with fused-silica fiber [8, 9, 10]. To further confirm this point, we tune thecentral wavelength of the pump to 1525 nm, which is in the normal dispersion region of theDSF, where the phase-matching condition for FPS is not satisfied, and, therefore, no corre-lated photon-pairs are expected to be produced by the FPS process. Setting the detuning Ω/2πof the Stokes and anti-Stokes channels to 1.25 THz, we make the same measurements again.For the photons co-polarized with the pump, linear scattering dominates in this region, thoughwe measure a very small probability of quadratic scattering (less than 150 times that of lin-ear scattering), as shown in the inset of Fig. 3(a). For the coincidence measurements shown
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3741#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
in the main body of Fig. 3(a), we find no difference between the total-coincidence rate andthe accidental-coincidence rate. Within the error bars of our experimental data, the true coinci-dence rate between the co-polarized photons in the Stokes and anti-Stokes channels is at most10−6 /pulse. For the photons cross-polarized with the pump, as shown in Fig. 3(b), we also findno difference between the total-coincidence rate and the accidental-coincidence rate, and thenumber of the scattered photons in the Stokes and anti-Stokes channels depends linearly on thepump power.
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It is well known that in the low-gain low-detuning region, the number of Stokes and anti-Stokes Raman-scattered photons in a given time interval is proportional to n th + 1 and nth,respectively, where nth = 1/[exp(hΩ/kT )− 1] is the Bose population factor and the resultantRaman-gain coefficient gR(Ω/2π) is very small [11, 12]. When the detuning Ω/2π is lessthan 1.5 THz, the co-polarized Raman-gain coefficient in pure-silica fiber follows g R(Ω/2π) =0.02(Ω/2π)+ 0.04(Ω/2π)3, where the peak of the Raman-gain coefficient is normalized toone [13]. It is then clear that at the frequency detuning we are interested in, the probabilityof Raman scattering depends on the detuning and the temperature; the lower the detuning andthe temperature, the lesser the probability of Raman scattering. Therefore, to improve the fi-delity of our photon-pair source, suppression of the Raman scattering is essential. So, to furtherimprove our results we reduce the detuning Ω/2π to 0.5 THz. The passband spectrum of theDGSF is shown in Fig. 4, wherein the isolation of the pump is still greater than 75 dB and theFWHM is about 0.8 nm, which is obtained by adjusting the DGSF. At this reduced detuning,the improved measurement results are shown in Fig. 5. Comparing the results with those in Fig.2, for the Stokes and anti-Stokes photons co-polarized with the pump, as shown in the insetof Fig. 5(a), the quadratic-scattering coefficient is increased, the linear-scattering coefficient isdecreased, and the ratio between the total-coincidence rate and the accidental-coincidence rateis improved. Taking into account the total detection efficiency of 6% in the anti-Stokes channel,at the production rate of about n = 0.04 photon-pairs/pulse, the ratio between the total coinci-dences and the accidental coincidences is 13. For the scattered photons cross-polarized withthe pump, as shown in Fig. 5(b), the results are similar to those in Fig. 2(b), except that thelinear-scattering coefficient is reduced. These improved results imply that when using this fibersource of correlated photons for creating polarization entanglement, a visibility of two-photoninterference greater than 85% would be obtained without subtracting the accidental-coincidencecounts.
In principle, further reduction of the detuning will further reduce the contribution of the
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3742#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
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Fig. 5. Same as in Fig.2, except Ω/2π = 0.5THz. For the inset in (a): s1 = 0.00317 ands2 = 0.0132; for the inset in (b): s1 = 0.00259 and s2 = 0.00025. In (a), taking into accountthe detection efficiency of 6% in the anti-Stokes channel, at a photon-pair production rateof 0.04 (0.067) per pulse the ratio between the total coincidence rate and the accidentalcoincidence rate is 13:1 (7.5:1).
Raman-scattered photons, which are proportional to (n th + 1) gR(Ω/2π) on the Stokes sideand nth gR(Ω/2π) on the anti-Stokes side. Although it is hard to bring the frequencies of thecorrelated Stokes and anti-Stokes photons closer to the pump frequency while maintaining thenecessary isolation of the pump photons with use of the DGSF presently employed in oursetup, such reduction in detuning is possible by employing array-waveguide gratings or similardense-wavelength-division-multiplexing (DWDM) filters that are used in modern fiber-opticcommunication systems. Ultimately how small a detuning can be achieved is limited by thespectral bandwidth of the Gaussian-shaped pump pulse. The detuning should be large enough tomake sure that the number of pump photons leaking into the Stokes and anti-Stokes channels isnegligible. Since the Raman-gain coefficient gR(Ω/2π) may vary from fiber to fiber, a detailedinvestigation of the Raman gain in the low-detuning regime, which we are presently conducting,is necessary before one can determine the optimal detuning for generating correlated photonswith the highest true-coincidence to accidental-coincidence ratio.
In conclusion, we have demonstrated a four-fold improvement over our previous results forthe production of quantum-correlated photon pairs using the four-photon scattering processin silica fiber. This was achieved by suppressing the creation of Raman-scattered photons byreducing the detuning of the Stokes and anti-Stokes photons from the pump and by placing aPBS in both the Stokes and anti-Stokes channels. At a production rate of about n = 0.04 photon-
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3743#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
pairs/pulse, the accidental coincidences measured are less than 10% of the true coincidences.Further improvement could be achieved by cooling the fiber.
An additional feature of our fiber-based source of quantum-correlated photon pairs is thatit is integrable with the modern fiber-optic technology. The OPO used for obtaining the pumppulses could be replaced by a mode-locked fiber laser, leading to the possibility of repetitionrates well over 10 GHz. Moreover, the DGSF could be replaced by fiber-pigtailed DWDM filtersthat have lower loss. We also emphasize that the spatial profile of the photon-pair generated isthe well characterized, guided, transverse mode of the optical fiber. Thus the main advantageof a fiber source of quantum-correlated photon pairs is the almost perfect coupling efficiency(0.01 dB fiber-to-fiber splice loss) that is possible from the source to the transmission fiber inlong-distance quantum communication applications. In contrast, fiber coupling of correlatedphotons from a χ (2)-crystal based source is very delicate; the best result to date is a couplingloss of 2.4 dB [14]. The main disadvantages of the fiber source are the existence of Ramanscattered photons and the loss incurred in filtering of the pump, which, in principle, could bemade very small by use of fiber Bragg-grating filters. Finally, the coupling efficiency advantageof the fiber source would become even more significant when it is used for realizing complexquantum networks involving multiple entangling operations. Thus, our improved results showthat an all-fiber source of entangled photon pairs can be a very promising tool for realizingvarious quantum information processing protocols.
This research was supported in part by the U.S. Army Research Office under a collaborativeMURI grant DAAD190010177.
(C) 2004 OSA 9 August 2004 / Vol. 12, No. 16 / OPTICS EXPRESS 3744#4382 - $15.00 US Received 14 May 2004; Revised 21 July 2004; accepted 24 July 2004
