Generation of photon pairs in highly nonlinear photonic crystal fibres for quantum information processing

Transcription

1 JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 8, No. 5, October 2006, Generation of hoton airs in highly nonlinear hotonic crystal fibres for quantum information rocessing XINZHU SANG *, CHONGXIU YU, M. K. ISLAM a, NAIGUANG LU b Key Laboratory of Otical Communication and Lightwave Technologies, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China a Otoelectronics Research Centre, City University of Hong Kong, Hong Kong b Deartment of Electronic Information Engineering, Beijing Institute of Machinery, Beijing, , China Flexible disersion characteristics and enhanced nonlinearity make the highly nonlinear hotonic crystal fibre(pcf) a good candidate to generate hoton airs for quantum information rocessing. Theoretical background and research rogress of hoton airs generated in highly nonlinear PCFs by means of four wave mixing are resented. With a 8.5 m PCF with zero disersion wavelength near 1552 nm, quantum correlated hoton airs are created around 1550 nm. It may rove eventually feasible to realize efficient, reliable, and low cost hoton air sources for ractical alications. (Received Setember 4, 2006; acceted Setember 13, 2006) Keywords: Nonlinear otics, Quantum information rocessing, Photonic crystal fibre, Photon air 1. Introduction Quantum information rocessing is a new, exciting and raidly exanding field of interdiscilinary research, whose main goal is to exloit the remarkable roerties and henomena of quantum hysics to imrove dramatically all asects of information rocessing, which is changing the way we view information and hysical world. In the last twenty years, we have witnessed a dramatic develoment of quantum information rocessing, driven by the rosects of quantum information enhanced communication [1-5], recision metrology [6-10], comutation systems [11-15], clock synchronization [16-17] etc. Among available hysical systems for ractical realizations these novel functions of quantum information rocessing, hotons are the rimary candidates for constituting carriers of quantum information. Efficient generation and transmission of quantum-correlated or -entangled hoton airs lay imortant roles in ractical engineering alications. Over the ast ten years, various attemts have been made to develo efficient hoton air sources, and most of them are based on sontaneous arametric down-conversion (SPDC) in second-order [χ (2) ] nonlinear crystals[18-25], such as beta barium borate, eriodically oled lithium niobate, LiIO 3, KNbO 3, and quasi-hase-matched KTiOPO 4 etc. A um hoton (ω ) annihilates and generates a air of twin hotons: signal (ω s ) and idler(ω i ), where ω = ω s + ω i. It should be noted that hoton airs around 1532 were also achieved, in which the effective χ (2) of eriodically oled silica fibres was used [26]. The rocess of SPDC is subject to conservation of Energy and momentum. The latter is also called hase matching condition. Phase matching can be achieved in birefringent crystals if either both, or one of the down-converted hotons are olarized orthogonally with resect to the um hotons. The first tye is referred to as tye I hase matching, and the second tye as tye II hase matching. If the birefringence of the crystal can not be exloited, it is ossible to achieve so called quasi hase matching in crystal where the sign of the χ (2) nonlinear coefficient is eriodically reversed. Though great rogress has made using this method, crystal waveguides generally offer a relatively shorter interaction length and this hoton air creation rocess is inefficient. In addition, it is imortant to coule the hoton airs into standard otical fibres for transmission, storage, and maniulation over a distance for alications, but hoton airs based on SPDC in nonlinear crystals suffer from loss and mode matching roblems when couling to otical fibre[27-28]. Therefore, there has been a growing interest in direct generation of hoton airs in otical fibre recently. Another advantage of fibre-based hoton air sources over those based on SPDC in nonlinear crystals is that the satial mode of hoton air would be the guided transverse mode of the fibre[29-31], like a very ure Gaussian single satial mode in otical fibre, so it is ossible to multilex several quantum channel on existing fibre lant. In fact, entangled and correlated hoton airs generated in otical fibres have been roosed [32-37]. Generally seaking, it will take several hundred meters or kilometers to create hoton airs via nonlinear effects in the conventional otical fibre. The advent of new materials, nano-technology and nano-maniulation have allowed quantum henomena to extend to a wider range, which rovides more ossibility of alications of quantum effects and breathes life into quantum information rocessing[37-41]. Photonic band ga structures offer the ability to design new otical roerties in existing materials by wavelength scale eriodic microstructuring the material configuration. The hotonic crystal fibre (PCF, also called microstructured fibre and holey fibre) is a silica otical fibre with an ordered array of microscoic air holes running along its length. Unlike the conventional fibre, the guidance roerties of the PCF are determined by the size, attern of air holes and the solid-silica regions rather than by the roerties of otical glass. Light is guided through small

2 1896 Xinzhu Sang, Chongxiu Yu, M. K. Islam, Naiguang Lu solid core PCFs, where high intensities can be maintained for interaction lengths of several meters resulting in large nonlinear effects. In addition, PCFs allow a more flexible tailoring of the disersion roerties, which are crucial for many alications. Recently, we have discussed technical reasons behind great research interest of highly nonlinear PCFs in otical communication comonents[41]. Here we will discuss and review generation of hoton airs in highly nonlinear PCFs via FWM. The wavelengths of hoton airs achieved in mostly reorted exeriments are away from low loss window of the fibre. In theory, highly nonlinear PCFs can be used to generate hoton airs at any desired wavelength[42]. Exerimental results of generation of correlated hoton airs around 1550 nm in a PCF of 8.5 m are resented, which is exected for transmission in otical fibres. 2. Theoretical background FWM in the otical fibre is a scattering rocess, which has long been studied. A simlified energy diagram with four beams couling three virtual excited state a, b and e, and a ground state g is shown in Fig.1[36]. Two um hotons at frequency ω are absorbed, a air of signal ω s and idler hotons ω i are created. For efficient interaction, the following hase matching and conservation of energy should be met, and 2k k i k s + 2γ P 2γP + β ( ω ω ) 2 = 0 (1) s i ω ω = ω s + (2) where k s,i, are the wavevectors of the signal, idler and um hotons, β is the grou velocity disersion (GVD) coefficient; P is the eak um ower and γ is the nonlinear coefficient of the fibre, 2π λ A neff γ 2 = (3) Fig.1 Schematic energy diagram for hoton airs generation via FWM Quantum theory of twin hoton generation via FWM in otical fibres has been discussed in detail[29, 36], and the coincidence rate C r of signal-idler hoton airs with um ower, nonlinear coefficient and fibre length follows 2 C ( γp L) (4) r From the above equation, we can see that the coincidence rate scales quadratically with um eak ower. This is a distinct feature of FWM of the χ (3) interaction, comared with the linear deendence on um ower in χ (2) SPDC. 3. Exerimental demonstrations Recently, PCFs with high nonlinearity and relatively low loss have become ossible to manufacture, which oens u ossibilities for many new alications. Several research grous have carried out exerimental investigations of generation of hoton airs in highly nonlinear PCF of several meters, which shows the huge otential of alications of the PCF to generation of hoton airs. In addition to reviewing the state of the art status of research, an exerimental result of generation of hoton airs around 1550 nm is resented. where n 2 is the nonlinear refractive index of fibre core, A eff is the effective area of the fibre core mode and λ is the um wavelength. The rimary factors influencing FWM rocess in the fibre are : the nonlinear coefficient γ, the um ower P, the fibre length L, and the GVD β. By oerating near the zero-disersion wavelength and considering disersion, hase matching condition can be met. With a well-designed highly nonlinear PCF, efficient FWM can be achieved at any desired wavelength with a short fibre and relative low um ower[41]. 3.1 Generation of correlated hoton airs via sontaneous FWM High brightness sources of hoton airs are required in various alications of quantum information rocessing. Pumed a PCF in the normal disersion regime, the sidebands generated are widely saced at equal frequency intervals from the um, and a high brightness hoton air source can be achieved as shown in Fig.2(a)[43]. A mode-locked icosecond Ti:Sahire um laser is sent onto a rism P to remove in-band light from the um laser sontaneous emission. The in hole is used to imrove the um mode and the attenuators to reduce the ower down. A half wave-ate(hwp) is used to align the um olarization along one axis and revent olarization scrambling. The outut of the 2 m PCF with zero disersion wavelength at 715 nm is collimated using an asheric lens, followed by a removable mirror M, allowing to monitor the hoton air sectra to launch them into a

3 Generation of hoton airs in highly nonlinear hotonic crystal fibres for quantum information rocessing 1897 coincidence test bench. A dichroic mirror sreads the incoming beam into two arms, one corresonding to the signal and the other to the idler. Two band-ass filters F1 and F2 centered at 570 and 880 resectively are used to remove in-line um and background. The detected hotons by two silicon avalanche hotodiodes(apd) are counted in a dual-channel counter and the coincidences are analyzed by a time interval analysis system(tia).with the um laser oerating at nm, correlated hoton airs at 587 nm and 897 nm are created simultaneously. The coincidence rate as a function of um is lotted in Fig.2(b), from which we can see that u to net coincidences er second can be achieved. Another exeriment is carried out by this research grou with PCFs with zero disersion wavelength close to 1060 nm and a nanosecond Q-switched laser of 1047 nm as um laser[44]. With the PCF of 6 m long, air hoton rates u to s -1 are generated at 839 nm and 1392 nm resectively. different sectral regions can be detected on two hoton-counting modules(pcms). Proer choosing the um, signal and idler wavelengths, and careful alignment of the system are imortant to obtain the desired result, as shown in Fig.3(b). The choice of um resect to the fibre s zero disersion wavelengths influences dramatically the signal-idler hoton air roduction rate. The PCF s zero disersion wavelength is olarization deendent due to birefringence in the PCF, which means that olarization of the um also affects the signal/idler count rate. Fig.3(c) shows a lot of coincident counts as a function of the number of um hotons er ulse. Fig.2. (a) Otical layout of exerimental setu. (b) Net coincidence rate versus the um ower. A exerimental setu on measurements of correlations in the hoton airs generated in a birefringence PCF is deicted in Fig.3(a)[45]. Linearly olarized, icosecond um ulses are launched into a 5.8 m PCF such that the lane of olarization is aligned along one the olarization mode axes of the fibre. The resulting signal and idler hoton airs co-roagate along with the um and emerge from the PCF. The outut of the PCF consists of a number of um hotons that are searated in wavelength from the um by about 10 nm. For efficient detection of the signal-idler hoton airs, um-hoton is suressed by three diffraction gratings so that two Fig. 3. (a) Exerimental setu used to generate and detect hoton airs. (b) The idler count rate with three different um wavelengths. (c) Total coincidence counts(triangles) and accidental coincidence counts(boxes) versus the number of um hotons er ulse. 3.2 Generation of correlated hoton airs via a reversed degenerate FWM rocess

4 1898 Xinzhu Sang, Chongxiu Yu, M. K. Islam, Naiguang Lu In the reversed rocess of the degenerate FWM rocess, a air of signal ω s and idler ω i hotons can be annihilated to create two um hotons ω of the same color, 2ω = ω s +ω i. Two new hotons are generated simultaneously and hence are correlated[46]. The exerimental setu is shown in Fig.4(a). A Ti:sahire laser emitting ulses of 3 s at 835 nm drives the FWM rocess in a 1 m PCF1. The outut of PCF1 is collimated onto a diffraction grating. With two narrow slits, a air of signal at 837 nm and idler at 833 nm light is selected. By using two movable mirrors M1 and M2, the relative timing between the signal and idler ulses can be adjusted. The linearly olarized signal and idler ulses are adjusted to the same rincial axis of PCF2 and couled to it. The outut hotons are selected with another grating and filtered with a narrow slit, and only those hotons at the wavelength of nm are directed to a 50/50 nonolarizing beam slitter. The outut beams from the beam slitter are couled into two single-mode fibres and are detected by two hoton counters. Photonelectronic ulses are analyzed by gated logical units for coincidence measurements. The exerimental measured coincidence counting rate as a function of eak um ower is lotted in Fig.4(b) with filled circles. The theoretical values are also shown with the solid curve. in cross-olarized um scheme is lower than that in the above scheme. 3.3 Generation of correlated hoton airs around 1550 nm To distribute hoton airs in standard fibre efficiently, it is imortant to create them in fibre s low loss window. The exerimental setu is shown in Fig.5(a).The light with a wavelength of 1552 nm form an external cavity semiconductor is modulated into 90 s ulses by an intensity modulator(im). The modulated ulses are amlified by two EDFAs, with two tunable filters(tfs) to reduce the amlified sontaneous emission from EDFAs. The ulses are then inut into a 8.5 m high nonlinear PCF with zero disersion wavelength near 1552 nm after olarization controller(pc). In the PCF, correlated hoton airs are generated through sontaneous degenerate FWM rocess. The um ower can be adjusted by changing the um current of two EDFAs. The measured outut sectrum form the PCF on the otical sectrum analyzer with um ower of 80 mw is shown in Fig.5(b). We can see that the signal and idler in the sectrum are almost symmetrically distributed beside the um light. Fig.5(a) Exerimental setu to generate hoton airs around 1550 nm Fig.4 (a) Schematic exerimental setu via reversed degenerate FWM. (b) Coincidence rate versus eak um ower P. Fig.5(b) Sectrum from the PCF with um ower of 80 mw. With a similar exeriment setu erformed in the above, the generation of cross-olarized hoton airs with cross-olarized frequency-conjugate laser um ulses are roosed and exerimental demonstrated[47]. Exerimental result shows that the contrast ration between coincidence count rate and accident coincidence count rate

5 Generation of hoton airs in highly nonlinear hotonic crystal fibres for quantum information rocessing 1899 Fig.5(c) Coincidence rate versus um ower A diffraction grating is used to satially searate the signal the um and the idler hotons. The doubly diffracted signal and idler hoton are then recouled into two hotodiodes(pd) to count hotons in the counting system. The exerimentally measured coincidence counting rate as a function of um ower is given in Fig.5(c), which shows the coincidence rate increases with the square of the um ower. 4. Conclusion Generation of correlated hoton airs have been demonstrated exerimentally via FWM in highly nonlinear PCFs of several meters with different configurations. With a 8.5 m PCF with zero disersion wavelength near 1552 nm, quantum correlated hoton airs are created around 1550 nm. Most of the work is currently motivated by the otential alications to quantum information rocessing. The short device length will enhance system stability and reliability. Although the resent exerimental results need further imrovement, they are nonetheless romising for quantum information rocessing. It may rove eventually feasible to realize efficient, reliable, and low cost hoton air sources for ractical alications. Acknowledgement This aer is suorted by the National Basic Research Program of China(2003CB314906), Co-construction Program of Beijing Municial Commission of Education(XK ), Oen Grant of Beijing Key Lab of Electromechanical System Control and Measurement and the Initiating Grant For PH.D. of School of Electronic Engineering, BUPT. References [1] E. Diamanti, H Takesue, T. Honjo, K. Ioue, Yamanoto, Phys. Rev.A , [2] G. Bowen, Int. J. Quant. Info. 3(1) 123, [3] C. Kursiefer, P. Aarda, M. Halder, H. Weinfurter, P. M. Gorman, P.R. Taster, Nature , [4] T. Rudolh, L. Grover, Phys. Rev. Lett , [5] N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys , [6] T. Kim, J. Dunningham, K. Burnett, Phys. Rev. A , [7] V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. Lett , [8] G. M. D Ariano, P. L. Presti, M.G. A. Paris, Phys. Rev. Lett , [9] M.C. Booth, G. D. Giusee, B.E.A. Saleh, A.V. Sergienko, M. C. Tich, Phys. Rev. A , [10] A.F. Abouraddy, K.C. Toussaint, AV. Sergienko, B.E.A. Saleh, M.C. Teich, Ot. Lett. 26(21) [11] C.M. Dawson, H.L. Haselgrove, M.A. Nielsen, Phys. Rev. Lett., , [12] W. Mao, Phys. Rev. A , [13] M. terraneo, D.L. Sheelyansky, Phys. Rev. Lett , [14] L.B. Ioffe, M.V. Feigel man, Phys. Rev. B , [15] J. Gea-Banacloche, Phys. Rev. Lett , [16] M. D. Burgh, S.T. Bartlett, Phys. Rev. A , [17] R. Jozsa, D.S. Abrams, J.P. Dowling, C.P. Williams, Phys. Rev. Lett , [18] D.C. Burnham, D.L. Weinberg. Phys. Rev. Lett [19] P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, Y.H. Shih, Phys. Rev Lett , [20] K. Banaszek, A.b. U Ren, I.A. Walmsley, Ot. Lett , [21] C.E. Kuklewicz, M. Fiorentino, G. Messin, F.N.C. Wong, J.H. Shairo, Phys. Rev. A [22] F. Konig, E.J. Mason, F.N.C. Wong, M.A. Albota, Phys. Rev. A , [23] Z.D. walton, M.C. Booth, A.V. Sergienko, B.E.A. Saleh, M.C. Teich, Phys. Rev. A , [24] V. Giovannetti, L. Maccone, J.H. Shairo, F.N.C. Wong, Phys. Rev. Lett , [25] Y.H. Shih, A.V. Sergienko, M.H. Rubin, Phys. Rev. A [26] G. Bonfrate, V. Pruneri, P.G. Kazansky, P. Taster, J.G. Rarity, Al. Phys. Lett. 75(16) 2356, [27] C. Kurtsiefer, M. Oberarleiter, H. Weinfurter, Phys. Rev. Lett , [28] D. Ljunggren, M. Tengner, Phys. Rev. A , [29] J. Chen, X. Li, P. Kumar, Phys. Rev. A 72, , [30] K. Sanaka, K. Kawahara, T. Kuga, Phys. Rev. Lett. 86(24) 5620, [31] J. Kim, O. Benson, H. Kan, Y. Yamamto, Nature, , [32] Ch. Silberhorn, P.K. Lam, O.Weib, F. Konig, N. Korolkova, G. Leuchs, Phys. Rev. Lett. 86(19) 4267, [33] M. Fiorentino, P.L. Voss, J.E. Sharing, P. Kumar, IEEE Photon. Technol. Lett. 14(7) 983, [34] X. Li, P.L. Voss, J.E. Sharing, P. Kumar, Phys. Rev.

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