We present a single-photon source based on the stimulated four-wave mixing process with
adjustable linear state of polarization. This source allowed us to generate non-orthogonal
states of polarization, that can be used for quantum key distribution experiments. The
average number of photon counts as a function of the angle of the analyzer was obtained
for two non-orthogonal linear states of polarization. The results show an accurate detection
after propagation through a standard single-mode optical fiber with a length equal to
20 km. We also employed a master/slave configuration between two avalanche photodiodes,
in order to check the probability of our single-photon source to emit pulses with
more than one photon, for an average number of photons per pulse, μ ∼ 0.2, and consequently
the probability of a photon to choose one of the paths. Results show that our
experimental scheme is suitable for polarization-encoding experiments.QuantTel - Quantum Secure TelecommunicationsQuantPrivTel - Quantum Private Telecommunications - PTDC/EEATEL/ 103402/200

Almeida, Álvaro J.

Muga, Nelson J.

Pinto, Armando N.

Silva, Nuno A.

Repositório Institucional da Universidade de Aveiro

Fiber-Optical Communication SystemUsing Polarization-encoding PhotonsA. J. Almeida1, N. A. Silva1,2, N. J. Muga1,3 and A. N. Pinto1,21Instituto de Telecomunicações, Universidade de Aveiro, Campus Universitário de Santiago,3810-193 Aveiro, Portugal, Tel: +351 234 377 900, Fax: +351 234 377 9012Dp.to de Electrónica, Telecomunicações e Informática, Universidade de Aveiro, CampusUniversitário de Santiago, 3810-193 Aveiro, Tel: +351 234 377 900, Fax: +351 234 377 9013Dp.to de Física, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro,Portugal, Tel: +351 234 377 900, Fax: +351 234 377 901E-mails: aalmeida@av.it.pt, nasilva@av.it.pt, muga@av.it.pt, anp@ua.ptWe present a single-photon source based on the stimulated four-wave mixing process withadjustable linear state of polarization. This source allowed us to generate non-orthogonalstates of polarization, that can be used for quantum key distribution experiments. Theaverage number of photon counts as a function of the angle of the analyzer was obtainedfor two non-orthogonal linear states of polarization. The results show an accurate detec-tion after propagation through a standard single-mode optical fiber with a length equal to20 km. We also employed a master/slave configuration between two avalanche photo-diodes, in order to check the probability of our single-photon source to emit pulses withmore than one photon, for an average number of photons per pulse, μ ∼ 0.2, and con-sequently the probability of a photon to choose one of the paths. Results show that ourexperimental scheme is suitable for polarization-encoding experiments.1. IntroductionIn order to transmit information between two parties, most quantum protocols requiresingle-photon sources [1]. These can be obtained from a variety of devices, likecolor centers in diamond, quantum dots, or from single atoms and molecules. Thereare, however, some practical problems with these sources. Low collection efficiency,technical complexity or molecule stability issues are some of them [2]. Recently,the stimulated four-wave mixing (FWM) process has been used to generate single-photons in optical fibers [3–6]. The stimulated FWM process is a third-order nonlinearprocess that occurs when light of two or more frequencies (known as pump and signalfields) are launched into an optical fiber, given rise to a new frequency known as idler[7]. Using the stimulated FWM process, we took advantage of generating the photonsalready inside the optical fiber [3–7]. This avoids the losses introduced by the couplingcomponents used in another techniques [8]. This paper contains five sections. Insection 2 we describe our single-photon source, which was used for generating singlephotons in two non-orthogonal linear states of polarization (SOPs). In section 3 wepresent a theoretical model to describe the photon counts obtained in two detectors,in two different configurations. First, using two detectors working as master, andsecond using a master/slave configuration between them. In section 4 we present anddiscuss the experimental results obtained in the two different configurations. Finally,in section 5 we present our conclusions.2. Single-Photon Source Based on Stimulated Four-Wave Mixing ProcessA schematic of the experimental setup used to generate, transmit and detect singlephotons, is shown at Fig. 1. A pump at λ1, from an external cavity laser (ECL), passesthrough a polarization controller (PC1) before being coupled to another optical signal,λ2, from a tunable laser source (TLS). This second optical signal passes througha polarization controller (PC2), and is then externally modulated to produce opticalpulses with a width at half maximum of 1.6 ns and a repetition rate, r = 550530 Hz.After the modulation, λ2 passes through another polarization controller (PC3), in orderto assure that it will be co-polarized with λ1. After the coupling, the two optical fieldsare launched into a dispersion-shifted fiber (DSF) with a length equal to 8400 m. Dueto the stimulated FWM process, the new optical field is generated inside the DSFat λ3 =λ1λ2/(2λ2−λ1) [7]. Next, a filter blocks the pump and signal waves, while theidler photon’s polarization can be aligned with the rotating linear polarizer (RLP) usinga new polarization controller (PC4). After transmission through the quantum channel(optical fiber), the idler photons pass through a 50/50 polarization beam splitter (PBS).Adjusting the PCs, PC5 and PC6, the photons with the input SOPs, θ=0◦ or 45◦, thatcan be chosen with the polarization analyzer (PA), can be redirected to detectors D1or D2, respectively, and polarization changes inside the optical fiber be compensated[9]. The linear polarizers, P1 or P2, work as analyzers, and their transmission axesangle, θ, can be tuned with the PA. The detectors D1 and D2 are two InGaAs/InPavalanche photodiodes (APDs) from IdQuantique, operating in the so-called Geigermode [10]. Detector D1 (id200) has a dark count probability per time gate, tg =2.5 ns,of Pdc <5×10−5 ns−1, and a quantum detection efficiency, ηD∼10% [11]. Detector D2(id201) has a dark count probability per time gate, tg =2.5 ns, of Pdc ∼ 1×10−6 ns−1,and a quantum detection efficiency, ηD ∼ 10% [12]. The average number of photonsper pulse at the single-photon source output was μ∼0.2, and the measurements wereperformed during a period time of 10 s.PBS50/50PC4PC1Pumpλ1 = 1549.32 nmSignalλ2 = 1550.92 nm PC3MZ modulatorPC2DC VoltagePAPulse Pattern GeneratorDSF (L = 8400 m)FilterQuantumChannelCoupler50/50PC5 P1P2PC6D1D2RLPFigure 1: Experimental setup used to generate, transmit and detect single photons with quantuminformation, encoded into polarization. Using this setup we were able to analyze two non-orthogonallinear SOPs (θ=0◦ and 45◦).3. Theoretical ModelIn this section we present a theoretical model to describe the photon counts that canbe registered in the APDs (D1 and D2), as a function of the PA angle, θ, as presentedin Fig. 1.Assuming that the photon distribution of our single-photon source follows a Poisso-nian statistics, the probability of a pulse carries n photons is given by,P (n, μ) =μnn!e−μ , (1)where μ is the average number of photons per pulse [8]. After the photons passthrough a single-mode fiber (SMF), the quantum channel, the probability that thepulse carries at least one photon can be written as,P = 1− e−ηF μ , (2)with ηF =10−αL/10, where α and L are the fiber losses and the fiber length, respectively[13]. When the beam passes through a 50/50 beam splitter, it will generate two beamswith independent Poissonian statistics. Then, we will have in each arm [14],P = 1− e−ηF μ/2 . (3)Next, the beam will pass through a PA, which transmits photons in the state, |Tθ〉,given by,|Tθ〉 = cos(θ)|H〉+ sin(θ)|V 〉 , (4)where |H〉 and |V 〉 represents the horizontally and vertically polarized SOPs, respec-tively, and the transmission axis forms and angle θ with the horizontal [15]. Theprobability of transmission of a photon in a state |ψφ〉 is given by,Pt = |〈Tθ|ψφ〉|2 , (5)where the general input photon state can be written as,|ψφ〉 = cos(φ)|H〉+ sin(φ)eiξ|V 〉 , (6)being ξ = ξy−ξx the phase between the quantum states [16]. Substituting (4) and (6)in (5), we obtain that,Pt = cos(θ)2 cos(φ)2 + sin(θ)2 sin(φ)2 + 2 cos(θ) cos(φ) sin(θ) sin(φ) cos(ξ) . (7)From (3) and (7) we can write the probability of detection in an APD as,Pd = (1− e−ηF ηBηDμ/2)Pt , (8)where ηB = 10−LB/10, and LB represents the total losses in each arm, between thebeam splitter and the APD, and ηD is the quantum efficiency of the APD.The probability of a detector to click can be denoted by,Pclick = Pd + Pdc − PdPdc , (9)where Pdc is the probability of a click due to detector’s dark counts [13]. In terms of adetector count, (9) results in,C = rPclick , (10)where r is the pulse repetition frequency per second [13].In case of employing a master/slave configuration between two APDs, (10) can bewritten as, {CM = rPMclickCS = CMPSclick ,(11)(12)where CM and CS are the average number of photon counts in master and slavedetectors, respectively, and PMclick and PSclick are the probabilities of having a click inmaster and slave detectors, respectively.4. Experimental Polarization-encoding Photons4.1 Two Non-orthogonal Linear SOPs DetectionBefore transmission through a SMF with a length equal to 20 km we performed aback-to-back measurement, i.e., without using the quantum channel, in order to verifythe feasibility of our experimental setup (see Fig. 1). In Fig. 2a) we plot the aver-age number of photon counts registered by detectors D1 and D2 as a function of thePA angle, θ (degrees), in a back-to-back configuration, and the theoretical predictiongiven by (10). As described by (4), we have a maximum when the photon’s polar-ization is aligned with the transmission axis of the linear polarizers, and a minimumwhen they are orthogonal. As can be seen in Fig. 2a), (10) describes correctly theexperimental results that were obtained. In Fig. 2b) we plot the average number ofphoton counts registered in detectors D1 and D2, as a function of the PA angle, θ (de-grees), after transmission through a standard SMF with a length equal to 20 km, andthe theoretical prediction given by (10). As can be seen, there is a decrease in thenumber of counts registered in both detectors, which is due to fiber attenuation. The45◦ separation between the two SOPs remain, since polarization rotations performedby the optical fiber could be compensated adjusting PC5 and PC6 in order to alignthe SOPs at the fiber link output with the linear polarizers P1 and P2, respectively.The theoretical equation given by (10) also describes correctly the obtained experi-mental results. According to Fig. 2, we can see that it is possible to code informationin photons polarization, transmit it through an optical fiber with a length up to 20 km,and detect it correctly.0 30 60 90 120 150 1800300600900120015001800   	    θ b)0 30 60 90 120 150 180010002000300040005000   	    Average Number of Photon Counts (Hz)θ a)Figure 2: Average number of photon counts (Hz) as a function of the polarization analyzer angle, θ(degrees), for the linear SOPs with angles θ = 0◦ and 45◦, a) in a back-to-back configuration, and b)after propagation through a standard SMF with a length equal to 20 km. The pump and signal opticalpowers at the DSF input were P1=0.69 mW, and P2=0.39 mW, respectively.4.2 Master/Slave ConfigurationIn order to check the probability of our single-photon source to emit pulses with morethan one photon, for μ∼ 0.2, we implemented a master/slave configuration betweentwo APDs, where the slave detector only works when the master detector counts atleast one photon. In this case only when the pulse carries at least two photons wewill be able to have a count in slave’s detector. In Fig. 3 we present the experimentalsetup used to obtain a master/slave configuration between two APDs, D1 and D2. Themaster detector trigger was directly connected to the pulse pattern generator. Slavedetector trigger is connected to the master detector D1 through a NIM output. Thedelay line (DL) in slave detector arm is a 10 m optical fiber, which allows compensatingof the electronic delay between the two detectors. The quantum channel that wasused to transmit the photons was a standard SMF with a length equal to 20 km.PBS50/50Single-photon sourceRLPQuantum ChannelP1P2D1D2PC5PC6Pulse Pattern GeneratorExternalTriggerD1 TriggerNIM OutPADLFigure 3: Experimental setup used to obtain a master/slave configuration between two APDs, usingtwo non-orthogonal linear SOPs (θ=0◦ and 45◦).In Fig. 4a) we plot the average number of photon counts as a function of the PA angle,θ (degrees), when detector D1 worked as master and detector D2 as slave, and thetheoretical predictions given by (11) and (12). As can be seen, detector D1 collectsalmost all the photons with SOP angle, θ = 0◦, and only a few goes to detector D2,that is prepared to receive the photons with SOP angle θ = 45◦. It can be seen inFig. 4a) that the master detector shows the same behavior as in Fig. 2, while thecounts registered by the slave detector shows some difference. Results show that theslave detector presents two minimums, one in 90◦ and other in 135◦. Since the slavedetector is only able to count when the master detector receives at least one photon,when its polarization is orthogonal to the transmission axis of the linear polarizer, themaster detector will have a minimum number of counts, and consequently, the slavedetector too, since it uses the master detector’s counts as trigger. As the 45◦ SOPwas maximized using PC6, in order to be detected in D2, it will be also a minimumat 135◦, as the maximum will be at 22.5◦. The theoretical predictions given by (11)and (12) describes with good accuracy the experimental results, being the slightlydifferences due to experimental constraints. In Fig. 4b) we plot the average numberof photon counts as a function of the PA angle, θ (degrees), when detector D1 workedas slave and detector D2 as master, and the theoretical predictions given by (11) and(12). From comparison with Fig. 4a), we can see that the behavior do not dependson choosing D1 or D2 as master detector. This indicates that a photon has the sameprobability to go to each arm of the beam splitter, and consequently, the non emptypulses carries in average one photon, when we use μ∼0.2.0 30 60 90 120 150 18001234θ 030060090012001500b)      	 	     0 30 60 90 120 150 180030060090012001500        	     	θ Average Number of Photon Counts (Hz)01234a)Figure 4: Average number of photon counts as a function of the polarization analyzer angle, θ (de-grees), for the linear SOPs with angles θ = 0◦ and 45◦, with a) detector D1 working as master, anddetector D2 as slave, and b) detector D1 working as slave, and detector D2 as master. Photons weretransmitted through a SMF with a length equal to 20 km. The pump and signal optical powers at theDSF input were the same as presented in Fig. 2.5. ConclusionsWe successfully implemented a single-photon source based on the stimulated FWMprocess, with adjustable linear SOP. This allowed us to generate single photons lin-early polarized, and transmit them through a standard SMF with a length equal to20 km. Results showed that it is possible to code information into photons polariza-tion, and decode it correctly after propagation through an optical fiber with a lengthof several kilometers. In order to verify the probability of our single-photon source toemit pulses with more than one photon, for an average number of photons per pulse,μ ∼ 0.2, we employed a master/slave configuration between two detectors. Resultsshowed that a photon has the same probability to choose one of the arms of the beamsplitter, and that non empty pulses carries in average one photon. The master/slaveconfiguration can also be used on entanglement-based quantum experiments.AcknowledgmentsThis work was partially supported by the Fundação para a Ciência e Tecnologia, FCT,through the Laboratório Associado (IT/LA) program, project “QuantTel - QuantumSecure Telecommunications” and “QuantPrivTel - Quantum Private Telecommunica-tions” project (PTDC/EEA-TEL/103402/2008), FEDER and PTDC programs.References[1] D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information, 2000.[2] M. Dusek, N. Lutkenhaus, and M. Hendrych, “Quantum Cryptography,” ArXiv Quantum Physics e-prints, Jan. 2006.[3] P. F. Antunes, A. N. Pinto, and P. S. André, “Single-Photon Source by Means of Four-Wave MixingInside a Dispersion-Shifted Optical Fiber,” Frontiers in Optics, OSA Technical Digest (CD) OpticalSociety of America, Oct. 10 2006.[4] A. J. Almeida, G. G. Fernandes, and A. N. Pinto, “Single-Photon Source With Adjustable Linear SOP,”Proc VII Symposium On Enabling Optical Networks and Sensors, Nokia Siemens Networks, Amadora,Portugal, Jun. 26 2009.[5] N. A. Silva, N. J. Muga, and A. N. Pinto, “Influence of the Stimulated Raman Scattering on the Four-Wave Mixing Process in Birefringent Fibers,” IEEE/OSA Journal of Lightwave Technology, vol. 27,no. 22, pp. 4979 – 4988, Nov. 15 2009.[6] ——, “Effective Nonlinear Parameter Measurement Using FWM in Optical Fibers in a Low PowerRegime,” IEEE Journal of Quantum Electronics, vol. 46, no. 3, pp. 285 – 291, Mar. 2010.[7] G. Agrawal, “Nonlinear Fiber Optics, 4th ed.” Academic Press, 2007.[8] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Reviews of Modern Physics,vol. 74, pp. 145–195, Jan. 2002.[9] N. J. Muga, A. Nolasco Pinto, M. F. S. Ferreira, and J. R. Ferreira da Rocha, “Uniform PolarizationScattering With Fiber-Coil-Based Polarization Controllers,” Journal of Lightwave Technology, vol. 24,pp. 3932–3943, Nov. 2006.[10] G. Ribordy, N. Gisin, O. Guinnard, D. Stucki, M. Wegmuller, and H. Zbinden, “Photon counting at tele-com wavelengths with commercial InGaAs/InP avalanche photodiodes: current performance,” Journalof Modern Optics, vol. 51, pp. 1381–1398, Sep. 2004.[11] idQuantique, id 200 Single-Photon Detector Module - Operating Guide, Version 2.2, 2005.[12] ——, id 201 Single-Photon Detector Module - Operating Guide, Version 4.0, 2008.[13] A. Trifonov, D. Subacius, A. Berzanskis, and A. Zavriyev, “Single photon counting at telecom wave-length and quantum key distribution,” Journal of Modern Optics, vol. 51, pp. 1399–1415, Sep. 2004.[14] P. D. Townsend and I. Thompson, “A Quantum Key Distribution Channel Based on Optical Fibre,”Journal of Modern Optics, vol. 41, pp. 2425–2433, Dec. 1994.[15] E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer,“Interference with correlated photons: Five quantum mechanics experiments for undergraduates,”American Journal of Physics, vol. 73, pp. 127–140, Feb. 2005.[16] J. N. Damask, Polarization Optics in Telecommunications, J. N. Damask, Ed., 2005.

Fiber-optical communication system using polarization-encoding photons

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Fiber-optical communication system using polarization-encoding photons

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Repositório Institucional da Universidade de Aveiro