High-visibility nonclassical interference
of photon pairs generated in
a multimode nonlinear waveguide
MichałJachura,1∗MichałKarpi´nski,1,2Czesław Radzewicz,1and
Konrad Banaszek1
1Faculty of Physics,University of Warsaw,Ho˙z a69,00-681Warsaw,Poland
2Clarendon Laboratory,University of Oxford,Parks Road,Oxford OX13PU,UK
∗
Abstract:We report measurements of two-photon interference using
a cw-pumped type-II spontaneous parametric down-conversion source
bad on a multimode perodically poled potassium titanyl phosphate
(PPKTP)waveguide.We have ud the recently demonstrated technique of
controlling the spatial characteristics of the down-conversion process via
flossintermodal dispersion to generate photon pairs in fundamental transver
modes,thus ensuring their spatial indistinguishability.Good overlap of
photon modes within the pairs has been verified using the Hong-Ou-Mandel
interferometer and the preparation of polarization entanglement in the
Shih-Alley configuration,yielding visibilities consistently above90%.
©2014Optical Society of America
设计说明英文
OCIS codes:(270.0270)Quantum optics;(190.4390)Nonlinear optics,integrated optics;
(230.7370)Waveguides.
References and links
1.J.L.O’Brien,A.Furusawa,and J.Vuˇc kovi´c,“Photonic quantum technologies,”Nat.Photon.3,687–695(2009).
2.M.˙Zukowski,A.Zeilinger,M.A.Horne,and A.K.Ekert,“‘Event-ready-detectors’Bell experiment via entan-
glement swapping,”Phys.Rev.Lett.71,4287-4290(1993).
3. B.G.Christenn,K.T.McCusker,J.B.Altepeter,B.Calkins,T.Gerrits,A.E.Lita,A.Miller,L.K.Shalm,
Y.Zhang,S.W.Nam,N.Brunner,C.C.W.Lim,N.Gisin,and P.G.Kwiat,“Detection-loophole-free test of quantum nonlocality,and applications,”Phys.Rev.Lett.111,130406(2013).
4.M.D.C.Pereira,F.E.Becerra,B.L.Glebov,J.Fan,S.W.Nam,and A.Migdall,“Demonstrating highly sym-
metric single-mode,single-photon heralding efficiency in spontaneous parametric downconversion,”Opt.Lett.
38,1609-1611(2013).
5.K.Banaszek,A.B.U’Ren,and I.A.Walmsley,“Generation of correlated photons in controlled spatial modes by
downconversion in nonlinear waveguides,”Opt.Lett.26,1367–1369(2001).
6. A.B.U’Ren,C.Silberhorn,K.Banaszek,and I.A.Walmsley,“Efficient conditional preparation of high-fidelity
single photon states forfiber-optic quantum networks,”Phys.Rev.Lett.93,093601(2004).
7.M.Fiorentino,S.M.Spillane,R.G.Beausoleil,T.D.Roberts,P.Battle,and M.W.Munro,“Spontaneous
parametric down-conversion in periodically poled KTP waveguides and bulk crystals,”Opt.Express15,7479–7488(2007).
8. A.Martin,V.Cristofori,P.Aboussouan,H.Herrmann,W.Sohler,D.B.Ostrowsky,O.Alibart,and S.Tanzilli,
thetimes“Integrated optical source of polarization entangled photons at1310nm,”Opt.Express17,1033–1041(2009).
9.T.Zhong,F.N.C.Wong,T.D.Roberts,and P.Battle,“High performance photon-pair-source bad onfiber-
coupled periodically poled KTiOPO4waveguide,”Opt.Express17,12019–12030(2009).
10.G.Harder,V.Ansari,B.Brecht,T.Dirmeier,C.Marquardt,and C.Silberhorn,“An optimized photon pair source
for quantum circuits,”Opt.Express21,13975–13985(2013).
11.M.Karpi´n ski,C.Radzewicz,and K.Banaszek,“Experimental characterization of three-wave mixing in a multi-
mode nonlinear KTiOPO4waveguide,”Appl.Phys.Lett.94,181105(2009).
#205051 - $15.00 USD Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014 (C) 2014 OSA7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8624
12.R.Machulka,J.Svozil´ık,J.Soubusta,J.Peˇr ina Jr.,and O.Haderka,“Spatial and spectral properties offields gen-
erated by puld cond-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,”
Phys.Rev.A87,013836(2013).
13. B.Brecht,A.Eckstein,A.Christ,H.Suche,and C.Silberhorn,“From quantum pul gate to quantum pul
shaper–engineered frequency conversion in nonlinear optical waveguides,”New.J.Phys.13,065029(2011). 14.M.Karpi´n ski,C.Radzewicz,and K.Banaszek,“Dispersion-bad control of modal characteristics for parametric
down-conversion in a multimode waveguide,”Opt.Lett.37,878–880(2012).
15.P.J.Mosley,A.Christ,A.Eckstein,and C.Silberhorn,“Direct measurement of the spatial-spectral structure of
waveguided parametric down-conversion,”Phys.Rev.Lett.103,233901(2009).
16.M.Karpi´n ski,C.Radzewicz,and K.Banaszek,“Generation of spatially pure photon pairs in a multimode nonlin-
ear waveguide using intermodal dispersion,”Proc.SPIE8518,Quantum Communications and Quantum Imaging X,85180J(2012).
17. C.K.Hong,Z.Y.Ou,and L.Mandel,“Measurement of subpicocond time intervals between two photons by
interference,”Phys.Rev.Lett.59,2044–2046(1987).
18.W.P.Grice,R.Erdmann,I.A.Walmsley,and D.Branning,“Spectral distinguishability in ultrafast parametric
down-conversion,”Phys.Rev.A57,R2289–R2292(1998).
19.Y.H.Shih,and C.O.Alley,“New type of Einstein-Podolsky-Ron-Bohm experiment using pairs of light quanta
produced by optical parametric down conversion,”Phys.Rev.Lett.61,2921–2924(1988).
尚德学校20.M.H.Rubin“Transver correlation in optical spontaneous parametric down-conversion,”Phys.Rev.A54,
5349–5360(1996).
21.J.P.Torres,K.Banaszek,and I.A.Walmsley,“Engineering nonlinear optic sources of photonic entanglement,”
Progress in Optics56,227–331(2011).
22.T.Zhong,X.Hu,F.N.C.Wong,K.K.Berggen,T.D.Roberts,and P.Battle,“High-qualityfiber-optics polar-
ization entanglement distribution at1.3µm telecom wavelength,”Opt.Lett.35,1392–1394(2010).
23.H.Herrmann,X.Yang,A.Thomas,A.Poppe,W.Sohler,and C.Silberhorn,“Post-lection free,integrated
optical source of non-degenerate,polarization entangled photon pairs,”Opt.Express21,27981–27991(2013).
24. F.Steinlechner,P.Trojek,M.Jofre,H.Weier,D.Perez,T.Jennewein,R.Ursin,J.Rarity,M.W.Mitchell,J.P.
Torres,H.Weinfurter,and V.Pruneri,“A high-brightness source of polarization-entangled photons optimized for applications in free space,”Opt.Express20,9640–9649(2012).while和when的区别
1.Introduction
Multiphoton interference is a nonclassical effect widely utilized in optical realizations of quantum-enhanced technologies[1]and testing foundations of quantum mechanics.High visi-bility of multiphoton interference depends critically on the abnce of distinguishing informa-tion between the interfering photons[2].While early experiments relied on spatial and spectral filtering to fulfill this requirement,a great deal of effort is currently being expended on the development of sources that guarantee suitable characteristics of the collected photons already at the production stage.Such sources can offer substantially higher brightness,compatibility with integrated optics circuits,and strong photon number correlations,the last feature needed for example in device-independent quantum cryptography and randomness generation[3,4].
A promising route to photon sources with well-defined,controllable characteristics is bad on spontaneous parametric down-conversion inχ(2)nonlinear waveguides[5–10].Compared to bulk crystals,the pha matching conditions that define the nonlinear process in a waveg-uide assume a different form owing to the discreteness of transver spatial modes propagating through the structure[11,12].This opens up new possibilities to engineer properties of the pro-duced nonclassical radiation[13].In particular,generation of spatially pure photon pairs in a multimode waveguide has be
en recently reported in[14],with a high degree of spatial coher-ence verified via a heralded photon counting measurement of the beam quality factors bad on free-space diffraction.Single spatial modes for the generated photons were lected by ex-ploiting the effects of intermodal dispersion in the down-conversion process.This technique overcomes waveguide manufacturing limitations for shorter wavelengths.Prospectively,it can also be ud to produce spatial photonic entanglement[15,16].
In this paper,we study experimentally two-photon interference using a periodically poled potassium titanyl phosphate(PPKTP)waveguide source of spatially pure photon pairs that #205051 - $15.00 USD Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014 (C) 2014 OSA7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8625
Measurements performed in two configuration [18]and a visibilities consistently exceeding any spatial filtering of the generated The results provide a compelling generated photons,paving the way
towards employing them in more complex multiphoton interference experiments.
This paper is organized as follows.First,in Sec.2we briefly review parametric down-conversion in a nonlinear multimode waveguide and discuss operating conditions that ensure generation of indistinguishable photon pairs.Next,Sec.3describes the experimental tup and alignment procedures.Results of two-photon interference measurements are prented and dis-cusd in Sec.4.Finally,Sec.5concludes the paper.2.Method
We begin by reviewing the technique to control the spatial characteristics of photon pairs gen-erated in a multimode nonlinear waveguide and discussing the operation of the source that ensures high-visibility two-photon interference.The waveguide is chon to realize a type-II down-conversion process in which a pump photon P is converted into a pair of orthogonally polarized photons H and V .The basic object in our analysis is the pha matching function,which in the quantum picture of parametric down-conversion is interpreted as the probability amplitude that a pair of photons with wa
velengths λH and λV will be generated from a pump photon with the wavelength defined by energy conrvation.While in a bulk medium the pha matching function depends also on continuous spatial degrees of freedom of the photons taking part in the process,parameterized for example with transver wave vectors [20],in the ca of a multimode waveguide the function depends on the specific triplet of spatial modes of the photons P ,H ,and V involved in the process.
Fig.1.(a)Numerical simulations of pha matching for spontaneous parametric down-
conversion in a 1mm long PPKTP waveguide analogous to the structure ud in the ex-美容美体学校
periment,with the pump field prepared in the fundamental spatial mode of the waveguide.
Separate pha matching bands correspond to different combinations of the spatial modes
of H and V photons.The energy conrvation condition is depicted with a solid white line.
(b)The joint and marginal spectra of the generated photon pairs.Application of coar
spectral filtering reprented by dashed lines allows one to lect the spectral region where
机器人瓦力主题曲
辞职的理由
both the photons are generated in the fundamental waveguide modes 00H and 00V .
As illustrated in Fig.1(a),intermodal dispersion between waveguide modes makes the pha #205051 - $15.00 USD
Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014(C) 2014 OSA 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8626
matching condition satisfied in general at different regions of the plane spanned by the wave-lengthsλH andλV,resulting in a ries of bands who width is inverly proportional to the waveguide length.In particular,if the pump is prepared in the fundamental waveguide mode 00P,then the pha matching function for generating down-converted photons in fundamental modes00H and00V is parated from process involving higher-order H and/or V modes, provided that the waveguide is long enough to sufficiently narrow the relevant bands.This condition is satisfied for the1mm long structure in our experiment,which was simulated in Fig.1(a).It needs to be stresd that this scheme relies critically on the pump beam prepared in the fundamental spatial mode:coupling the pump into modes other than00P generates contri-butions from pha matching bands involving higher-order spatial modes for H and V photons that overlap spectrally with the desired00P→00H+00V band.
If a cw pump is employed to induce the down-conversion process,the wavelengths of the down-converted photons must satisfy the constraint of constant total energy,which is symmet-ric with respect to swappingλH andλV and for the wavelength range depicted in Fig.1(a) becomes a nearly straight line running in the antidiagonal direction with respect to the graph axes.In contrast,the slope of the pha matching bands is noticeably different,as the H and V photons are generated in the type-II process and they propagate as extraordinary and ordinary rays.Conquently,pairs of photons are produced for combinations of wavelengths that form a t of islands,shown in Fig.1(b),located at crossings of the energy conrvation line with pha matching bands.The island corresponding to the process00P→00H+00V can be pa-rated from other process by coar spectralfiltering of one or both of the generated photons. It is worth noting that overlap may occur between islands corresponding to generation of pho-ton pairs in higher-order spatial modes owing to approximate degeneracy with respect to their propagation constants.
While the above scheme ensures generation of photons in fundamental spatial modes,two-photon interference requires also spectral indistinguishability within the produced pairs.This condition is not satisfied automatically,as the paration between the spectra of the H and V photons will vary with the wavelength of the pump photons,which shifts the energy conrva-tion line in the diagonal directi
on of Fig.1(a).However,the graph indicates that for a suitable pump wavelength the regime of spectral degeneracy should be achievable.Becau our numer-ical simulation of the waveguide is nsitive to details of the actual refractive index profile,this regime of operation needs to be identified by experimental means.We found that a suitable procedure,described in detail in Sec.3,was to measure the individual photon spectra in the heralded regime and to carefully tune the pump wavelength until the spectral profiles of H and V photons were matched within the resolution of the measuring apparatus.
3.Experimental tup
The waveguide source of photon pairs ud in our experiments is shown schematically in Fig.2. Its heart was a1mm long PPKTP structure(AdvR Inc.)temperature stabilized at19.0±0.1◦C using a thermoelectric cooler.A ries of waveguides localized just beneath the surface had lateral transver dimensions of approx.2µm,effective depths of approx.5µm,and poling periods designed for efficient type-II cond harmonic generation in the800nm wavelength region.At the wavelengths the waveguides supported at least8transver spatial modes(4 for each polarization).The structure was placed between two infinity corrected50×microscope objectives with numerical apertures NA=0.55for incoupling and NA=0.8for outcoupling.A magnified image of the wav
eguide illuminated with incoherent white light along with measured spatial profiles of the fundamental pump,H,and V modes at their respective wavelengths is shown in Fig.3.
The down-conversion process was pumped by a narrowband(linewidth<0.0011nm)cw #205051 - $15.00 USD Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014 (C) 2014 OSA7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8627
Fig.2.The PPKTP waveguide source of photon pairs and tups for(a)characterization of
新视野大学英语视听说教程photon spectra,(b)measurement of two-photon interference,and(c)preparation of polar-
ization entanglement in Shih-Alley configuration.λ/2,half-wave plate;POL,Glan-Taylor
polarizer;IF,interferencefilter;DM,dichroic mirror;PBS,polarizing beam splitter;MMF,
multimodefiber;SMF,single modefiber;SPCM,single photon counting module;BSC,
Babinet-Soleil compensator;BS,non-polarizing beam splitter,NDF,neutral densityfilter;
CF,colorfilter.
diode lar(Toptica BlueTune)beam that could be tuned around the central wavelength of 400nm.The pump beam was delivered to the tup with a single-modefiber.The pump power and polarization were controlled using a Glan-Taylor polarizer placed between two half-wave plates.Typical pump power incident on the waveguide input facet was53µW,whereas the pump power coupled into the waveguide is estimated to be at least29µW.The estimate is bad on the power measured at the exit of the waveguide,assuming no propagation loss. This corresponds to coupling efficiency of at least55%,which is similar to the values reported in other experiments[9,22].Thisfigure could be improved by approx.8%by using a waveg-uide sample with an
ti-reflection coated facets.As preparing the pumpfield in the fundamental transver waveguide mode was crucial for the spatial purity of the generated photons,after the outcoupling objective the remainder of the pump beam was directed with a dichroic mirror to a CCD camera.Its purpo was to monitor the quality of the pump spatial mode through a comparison with a reference profile generated beforehand in the sum-frequency process[14]. An exemplary image of the pump beam mode is shown in Fig.3(b).Although the waveguide cross ction is elongated and asymmetric in the vertical direction,the fundamental pump beam mode,being well-confined within the structure,bears only a minor signature of this asymme-try.This enabled us to excite lectively the fundamental pump mode by direct coupling a lar beam spatiallyfiltered by a single modefiber and focud to an appropriate diameter with the microscope objective.
An auxiliary infrared beam from a modelocked Ti:sapphire lar,coupled predominantly into the fundamental spatial mode of the waveguide at the down-conversion wavelength,was ud to identify the waveguide with a suitable poling period and to align optical elements following the source.The profiles of H and V fundamental modes prented in Fig.3(c,d)were recorded with the help of this beam.
In order to verify the spectral indistinguishability of the generated photon pairs,in thefirst step we me
asured individual spectra of heralded photons using the tup depicted in Fig.2(a). Photon pairs were nt through a colorfilter(cut-off wavelength660nm)and parated on a polarizing beam splitter.The output paths for the photons could be swapped with the help of a half-wave plate placed before the polarizing beam splitter.At the output,one photon was ud #205051 - $15.00 USD Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014 (C) 2014 OSA7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8628
Fig.3.The image of the output facet of the PPKTP waveguide illuminated with spatially
incoherent white light(a)and transver profiles of the fundamental P mode excited with
the pump lar(b)as well as the fundamental H mode(c)and V mode(d)excited with the
auxiliary Ti:sapphire lar beam.The intensity distributions were obtained by imaging the
output facet of the waveguide onto a CCD camera using the outcoupling objective and a
200mm focal length lens.
as a herald,while the cond one was transmitted through a0.7nm full width at half max-imum(FWHM)interferencefilter mounted on a motorized rotation stage.The photons were subquently coupled using11mm focal length aspheric lens into100µm core diameter, 0.22NA multimodefibers connected to single photon counting modules(Perkin Elmer SPCM-AQRH-14-FC).Coincidence events were counted within a3ns window.The rotation angle of the interferencefilter was calibrated in terms of the transmitted central wavelength using a Ti:sapphire beam and a spectrometer.
Fig.4.Heralded spectra of individual photons measured by rotating a0.7nm FWHM band-
passfilter.Coincidence count rates(points,left scale)collected over5s intervals arefitted
有限公司 英文with Gaussian functions(solid lines)assuming Poissonian errors.Experimentally obtained
spectral profiles of the interferencefilters ud in measurements of two-photon interfer-
ence:11nm,dashed-dotted line;3nm,dotted line(right scale).
PPKTP pha matching properties make the spectral characteristics of the generated photons strongly dependent on the pump wavelength,as can be inferred from Fig.1(a).Using the over-lap of the single photon spectra as the optimization criterion,wefine-tuned the wavelength of the pump lar,obtaining the best match at400.63nm,shown in Fig.4.In the same graph, #205051 - $15.00 USD Received 20 Jan 2014; revid 11 Mar 2014; accepted 11 Mar 2014; published 3 Apr 2014 (C) 2014 OSA7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008624 | OPTICS EXPRESS 8629
