integrated quantum optics, department of physics ... · 2 dence of the down-conversion e ciency...

High-performance source of indistinguishable entangled photon pairs based on hybridintegrated-bulk optics

Evan Meyer-Scott,∗ Nidhin Prasannan, Christof Eigner, Viktor

Quiring, John M. Donohue, Sonja Barkhofen, and Christine SilberhornIntegrated Quantum Optics, Department of Physics,

University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany

Entangled photon pair sources based on bulk optics are approaching optimal design and imple-mentation, with high state fidelities, spectral purities and heralding efficiencies, but generally lowbrightness. Integrated entanglement sources, while providing higher brightness and low-power op-eration, often sacrifice performance in output state quality and coupling efficiency. Here we presenta polarization-entangled pair source based on a hybrid approach of waveguiding and bulk optics,providing near optimal performance in every metric. We show 96 % fidelity to the singlet state,82 % Hong-Ou-Mandel interference visibility, 43 % average Klyshko efficiency, and a high brightnessof 2.9× 106 pairs/(mode·s·mW), while requiring only microwatts of pump power.

I. INTRODUCTION

Modern entangled photon pair sources based on para-metric down-conversion (PDC) are approaching the ideal:high state fidelity, spectral purity, and heralding effi-ciency are commonly demonstrated, enabling applica-tions such as tests of Bell’s inequality [1, 2], probing theboundaries of quantum physics [3, 4], quantum commu-nication over long distance [5–7], and quantum metrol-ogy beyond classical limits [8–10]. However, sources us-ing bulk nonlinear crystals suffer an intrinsic three-waytradeoff between brightness, fiber-coupling efficiency, andspectral purity [11]. This deficiency is now becomingcritical, as many new experiments and applications relyon the interference of multiple photons. For high rate,high quality multi-photon experiments, all three of theaforementioned parameters must be maximized simulta-neously [12–18]. This is because the overall rate in multi-photon experiments with N pairs scales with probabilityp of producing and detecting a single pair as pN , requiringboth high brightness and coupling efficiency. The qual-ity of multi-photon interference is determined by spectralpurity and indistinguishably as only pure, indistinguish-able photons are able to interfere with high visibility.

In contrast to bulk sources, integrated sources pro-vide high brightness due to strong confinement in waveg-uides and long interaction lengths, and can be designedto be spatially and spectrally single-mode, enabling si-multaneously high fiber-coupling efficiency, spectral pu-rity, and brightness. Many examples exist of high-brightness integrated sources, for example based on PDCin waveguides [19–21], or four-wave mixing in opticalfibers [22, 23]. However, these sources have not yetdemonstrated simultaneous high performance in all otherparameters comparable to their bulk-optical counter-parts. Entangled pairs from quantum dots, while promis-ing [24, 25], also do not yet reach the performance of pairsfrom nonlinear optical sources.

∗ [email protected]

Here we solve the performance problem of integratedoptics while retaining the coupling and brightness bene-fits by employing a hybrid bulk-waveguide solution: pho-ton pairs are produced in a single-mode waveguide, thenmade to interfere and coupled to optical fiber using bulkoptics. Our source combines for the first time excellentperformance in all parameters simultaneously.

II. INTEGRATED SINGLE-MODE PHOTONPAIR SOURCES

Over the last two decades, efforts in improving en-tangled photon-pair sources based on bulk crystals andbulk optics have resulted in impressive performance inmany measures (see end of document for comparisontable). Entanglement fidelities above 99 % are readilyachieved [1, 2, 17, 26], and even above 99.9 % is possi-ble [4]. Klyshko (heralding) efficiency [27], defined asthe ratio of coincidence to singles counts, can reach 75 %[1, 2, 26, 28, 29]. The spectral purity, required to in-terfere photons from separate sources for multi-photonexperiments, has been shown above 99 % [30].

Unfortunately, bulk sources suffer from an intrinsictradeoff between the brightness, or emitted photon rateper pump power, and the Klyshko efficiency [11]; for ex-ample setting the pump focus to enable coupling photonpairs to single mode fiber with 95 % efficiency necessar-ily reduces the brightness by a factor of ten from themaximum [31]. This tradeoff arises due to conflictingrequirements on the focusing conditions: high brightnessrequires a tight focus which decreases the effective area ofthe interaction and therefore increases its strength. Highcoupling efficiency, however, requires a weak focus whichmore strongly correlates the spatial modes of signal andidler photons such that if one photon is coupled into fiber,the other is likely to be coupled too. This tradeoff meansthe fundamental performance limits of bulk sources havelargely been saturated. Furthermore, sources at telecom-munications wavelengths are much less bright than thosewith visible-range photons, due to the wavelength depen-

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dence of the down-conversion efficiency [32].

Integrated photon sources can surpass these limits, asthe waveguide, rather than spatial phasematching, de-fines the allowed modes into which photons are emit-ted [33]. Single-spatial-mode waveguides in particularcompletely decouple the brightness from the focusingconditions [34], and can be produced with appropriatechoice of the waveguide width and height. Then thethe maximum coupling efficiency depends only on themode overlap between the waveguide and fiber modes.While the brightness of bulk sources with optimal fo-cusing scales with increasing nonlinear crystal length Las√L [35] or constant [11], the brightness of waveg-

uide sources increases proportionally to L, as well as in-versely with the effective area [32]. This allows waveg-uide sources, beyond removing the brightness-efficiencytradeoff, to be significantly brighter overall [36], requiringmuch less pump power for reasonable photon pair proba-bilities (e.g. 2 mW average power for 0.1 pairs generatedper pulse [37]).

It is also desirable to have spectrally single-mode pho-tons, where a frequency measurement of the signal pro-vides no information on the properties of the idler, mean-ing each is in a pure spectral state. This is requiredfor interference between independent sources, essentialfor quantum networking [15, 16, 38, 39], boson sam-pling [12, 13] or linear optic quantum computing [12–14].This high spectral purity can be asymptotically accom-plished by narrowband filtering, but filtering both pho-tons unavoidably lowers the Klyshko efficiency [40, 41].Engineering the group velocities of the pump, signal,and idler avoids this problem by producing intrinsicallysingle-spectral-mode photons [42, 43]. However, for bulkcrystals, even a spectrally-engineered source has onlya certain range of focusing parameters where the spec-tral purity is maximized [11, 44, 45]. In waveguides,this spectral-spatial coupling is eliminated thanks to thesingle-spatial-mode propagation, allowing the spectralpurity to be independently optimized.

Yet to date the most advanced experiments do notuse waveguide sources, which can be understood inlight of the difficulty in optimizing performance in in-tegrated optics (see end of document for comparisontable). The brightness of integrated sources is ordersof magnitude larger than possible in bulk, reachingabove 108 pairs/(s·mW) [21, 23]. Entanglement fidelityover 95 % has been achieved in a few integrated sys-tems [20, 23, 46, 47], and while source engineering hasallowed high spectral purity in waveguided photon pairsources [34, 48, 49], so far it has not been combinedwith qubit entanglement. The biggest drawback of cur-rent implementations however is the Klyshko efficiency,which is often very low due to lossy integrated com-ponents and poor coupling between elements. Thoughhigh Klyshko efficiencies from unentangled waveguidesources have been demonstrated [37], only two examplesof an entangled pair source with efficiency >3 % exist sofar [20, 50].

By combining both integrated and bulk approaches webenefit from the advantages of waveguide photon pairsources – single mode operation, high brightness, inde-pendent optimization of parameters – and the flexibilityof efficient free-space coupling to fiber. We describe theexperimental setup and results below.

III. EXPERIMENT

Our hybrid source of entangled photon pairs is basedon a free-space-coupled waveguide in a periodically poledpotassium titanyl phosphate (KTP) crystal. In fact wetest two such chips, and find one has better entanglementproperties and the other better coupling efficiency. Wepresent a full data set for the latter, and discuss the differ-ences between the samples in Section III D. The periodicpoling is designed for type-II phasematching at 1550 nm,and the material KTP is chosen such that the group ve-locity of the pump is between that of the signal and idler.Matching the pump and phasematching bandwidths thenprovides intrinsic spectral purity of the photons [34, 51].

A. Setup

The KTP waveguide is placed in a Sagnac loop [52] asshown in Fig. 1(a). The pump (Coherent Mira 900f) at770 nm is coupled through a single-mode fiber for spatialmode cleaning, then its polarization is set with a half-wave plate (HWP), and it passes through a dichroic mir-ror (Thorlabs DMSP1180). The pump is split equally ata dual-wavelength polarization beam splitter (PBS, Op-toSigma), and propagates both ways around the Sagnacloop. In the counter-clockwise direction the pump po-larization is rotated to horizontal with a superachro-matic HWP (B. Halle), balanced with an identical HWPat 0◦ on the clockwise path to reduce distinguishablyfrom dispersion. Then the pump is coupled using achro-matic lenses of focal length 6 mm (Edmund Optics ACH-NIR 6 X 9 NIR-II) into the KTP waveguide (ADVR,Inc.) with length 9 mm. For producing a single spec-tral mode, this waveguide length requires a pump band-width of 1.8 nm, which we set using a 4f-line in thepump path. The same lenses couple out the photonpairs, where now the clockwise-propagating pairs are ro-tated 90◦ in polarization by the HWP. These interferewith the un-rotated counter-clockwise pairs at the dual-wavelength PBS, which divides signal and idler to the twooutput ports while creating the polarization entangled-state |ψ〉 = 1√

2

(|HV 〉+ eiφ |V H〉

). The phase φ of the

state is set to π in the signal arm using a Soleil-Babinetcompensator (Thorlabs, SBC-IR), and both photons passfilters to remove sinc lobes of the PDC spectrum and flu-orescence (signal: Semrock NIR01-1550/3, idler: Thor-labs FBH1550-12). Finally the entangled state is ana-lyzed with half- and quarter-wave plates and PBSs (notshown), then coupled into optical fiber for detection with

3

Pump in

Waveguide and coupling

Signal out

SBC

(a) Idler out

HWP

Achr. HWPAchr. HWP

Dual-wavelengthPBS

(b)

0 2 4 6 8 10KTP end facet reflectivity (%)

80

85

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100

Enta

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d st

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)

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Second chip

Theoretical boundExperimental data

Uncoated

FIG. 1. (a) Experimental setup of hybrid integrated-free-space source. We present the important optical and mechani-cal elements in the actual layout, to scale, such that the setupcan be easily reproduced. HWP - half-wave plate, PBS - po-larization beam splitter, SBC - Soleil-Babinet compensator.(b) Maximal theoretical bound of achievable entangled statefidelity given nonzero end facet reflectivity in the KTP waveg-uide, and experimental data points for different chips.

superconducting nanowire single photon detectors (Pho-ton Spot, Inc.).

B. Differences to bulk sources

The single-mode nature of the PDC in our waveguidebrings significant advantages over bulk optics. Since theclockwise and counterclockwise photons are necessarily inthe same spatial mode, interference at the PBS is simple,and alignment is straightforward. This also relaxes muchof the strict symmetry needed in the crystal position inbulk Sagnac sources with respect to the focusing lensesand PBS [53]. The high brightness of the source allowsfor low pump power, which means the pump spatial modecan be cleaned in standard single mode fiber withoutspectral broadening due to nonlinearities. One drawback

is the lenses used to couple light in and out of the waveg-uide are the same for pump and photon pairs, meaningthe focus is optimized only for the photons. Nonetheless,with achromatic lenses we can reach >40 % coupling ofthe pump through the waveguide.

There is one point in waveguides that requires specialattention compared to bulk sources: the antireflectioncoating on the crystal surface. In bulk sources, photonsreflected internally at the end facets have a different focalposition when they reach the coupling fibers, and thuscouple poorly. In waveguides by contrast, photons re-flected at the end facets remain in the single spatial modeand couple well to the fibers. Unfortunately these pho-tons end up in exactly the wrong polarization comparedto their non-reflected partners, directly lowering the en-tanglement fidelity as in Fig. 1(b). We solve this using anion-assisted coating technique to deposit anti-reflectioncoatings for both wavelengths on both end facets. Thesecoatings reduce the end facet reflectivity to around 2 %for the first chip and below the measurement uncertaintyof 0.06 % for the second chip, giving a maximum achiev-able fidelities of 96 % and 99.9 % respectively.

C. Distinguishability in time and frequency

For any polarization-entangled photon pair source, it isessential that the two polarization paths are completelyindistinguishable in all other degrees of freedom. Thesingle-mode waveguide and output fiber coupling ensurethis indistinguishability in the spatial degree of freedom,but extra care must be taken to ensure time-frequencyoverlap, particularly as spectrally pure photons requirerelatively broadband pump pulses, especially comparedto continuous-wave sources. The Sagnac scheme does notrequire degenerate signal and idler emission, but does re-quire that the clockwise (c) and counter-clockwise (cc)paths remain indistinguishable. Even though both pathsencounter the exact same optical components, they en-counter them at different wavelengths and polarizations(e.g. pump vs photon wavelength, signal vs idler polar-ization). Any uncompensated dispersive or birefringentmaterials or coatings thereby reduce the polarization en-tanglement generated by coupling polarization informa-tion to the time-frequency degree of freedom.

This coupling can be modelled in the joint polarizationand time-frequency space for signal and idler photons in

modes defined by creation operators â and b̂, respectively,as

|ψ〉 = 1√2

∫dωsdωi

(fcc(ωs, ωi)â

†H,ωs

b̂†V,ωi (1)

− fc(ωs, ωi)â†V,ωs b̂†H,ωi

)|00〉 .

This model state always has perfect anti-correlations inthe rectilinear (H/V) basis. The projection probability

4

in the diagonal basis is∣∣∣∣( 〈H|+ 〈V |√2)(〈H| ± 〈V |√

2

)|ψ〉∣∣∣∣2 (2)

=1

8

∫dωsdωi |fcc(ωs, ωi)∓ fc(ωs, ωi)|2 .

If the joint spectral amplitudes for the clockwise andcounter-clockwise paths fc(ωs, ωi) and fcc(ωs, ωi) are ex-actly identical, the polarization and time-frequency de-grees of freedom are separable, and we obtain a “perfect”polarization entangled state, with anti-correlations in thediagonal (D/A) basis. For distinguishable paths withfc(ωs, ωi) 6= fcc(ωs, ωi), undesired coincidence countswill be measured when projecting on |DD〉, as describedby Eq. (2). Notably, this projection is sensitive to spec-tral phase differences between the two paths.

Indi

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FIG. 2. Investigating the distinguishability of photon pairsvia polarization-resolved joint spectra. We show the jointspectral intensity as simulated (top) and measured (bottom)when projecting onto the polarization state |HV 〉 or |DD〉.The |DD〉 plots have been scaled up in intensity by a fac-tor 10 for readability. These diagonal measurements exhibitfringing owing to time-frequency distinguishability betweenthe two paths of the Sagnac source, resulting in reduced over-all visibility since the detectors are not sensitive to this time-frequency information. By changing the wavelength of thePDC pump (left vs. right), we see a change in the orien-tation of the fringes, suggesting the presence of a direction-dependent chirp on the pump. To eliminate the distinguisha-bility and therefore the undesired counts in the D/A basis(plot shown to scale with the other D/A measurements) wefound a different waveguide with more uniform phasematch-ing.

To diagnose sources of distinguishability, we spectrallyresolve the polarization correlations [54, 55]. In Fig. 2,we show the joint spectral intensities reconstructed us-ing time-of-flight spectrometers [56, 57] when projectingon polarization combinations in the rectilinear and di-agonal polarization bases. The results can be explainedby relative time delays τ` (` = p, s, i) between the twodirections for the signal, idler, and pump, defined as

fcc(ωs, ωi) = eiτiωi+iτsωs+iτp(ωs+ωi)fc(ωs, ωi), (3)

which could arise due to spectral phase profiles spe-cific to the vertical ports or facet coatings of the dual-wavelength PBS, or due to unpoled regions on one endof the waveguide. By projecting onto the diagonal ba-sis, these time delays will manifest as fringing across thesignal-idler joint spectral intensity oriented at an angle

θ = arctan(τp+τiτp+τs

). If a relative chirp exists between

the two paths, this will appear as a frequency-dependenttime delay, τ` = τ0 + 2A`δω`, and the angle of thefringes will change as the central frequencies are shifted,which we observe when the pump wavelength is shiftedin Fig. 2. The theoretical simulations in Fig. 2 corre-spond to a relative time delay of 600 fs between horizon-tal and vertical components (τs = −τi = 300 fs), equiva-lent to the birefringent delay of approximately 2.2 mm ofKTP. To describe the dependence on pump wavelength,a chirp on the pump for the counter-clockwise processof Ap = 5800 fs

2 is sufficient. To optimize the indistin-guishably, we use this polarization-resolved joint spectralcharacterization to identify waveguides with more uni-form poling, and obtain the results presented below.

D. Results

We measure the spectral purity of our source viathe joint spectral intensity (JSI) and Hong-Ou-Mandel(HOM) interference [58] between independent photons.The joint spectral intensity of Fig. 3 is reconstructed us-ing a time-of-flight spectrometer [56, 57], and returns anupper bound to the purity of 98 %.

To measure HOM interference we use the Sagnac loopto create two photon pairs without polarization entan-glement, one in each direction around the loop. Thisis accomplished by detecting two signal photons simul-taneously, one |V 〉s and one |H〉s, making use of bothoutput ports of the signal photon’s PBS. This heraldstwo idler photons |1H, 1V 〉i in the same spatial modeheading toward the idler’s PBS. To make these photonsinterfere we rotate the idler HWP, which at 22.5◦ leadsto the state (in a single spatial mode) 1√

2(|2H〉i − |2V 〉i)

due to the indistinguishability of the two heralded pho-tons [59]. Thus we should be able to tune the coincidenceprobability between the horizontal and vertical outputports of the idler’s PBS between 0 and 1 by rotating theHWP. This is in contrast to typical HOM interference,where distinguishability in the photons is introduced viaa time delay, and they impinge from separate ports on a50:50 beam splitter. In that case the coincidence proba-bility varies between 0 and 1/2. Changing the HWP inour case is like changing the splitting ratio of the beamsplitter from 100:0 to 50:50 to 0:100. Mapping the HOMvisibility from the temporal to the polarization case gives

VHOM =Nmax/2−Nmin

Nmax/2, where Nmax and Nmin are the

maximum and minimum number of fourfold coincidenceswe measure, respectively, and the factor one half comesfrom the maximum probability being 1 compared to 1/2

5

1540 1545 1550 1555Signal wavelength (nm)

1540

1545

1550

1555

Idle

r w

avel

engt

h (n

m)

(a)

0100200300400500600700800

0 20 40 60 80Polarizer Angle( )

0

500

1000

1500

2000

Four

-fol

d co

unts

\(1

20 s

econ

ds)

(b)

FIG. 3. (a) Joint spectral intensity measured from our KTPwaveguide including 8 nm spectral filters, giving an upperbound of the spectral purity of 98 %. (b) Hong-Ou-Mandelinterference of two independently heralded photons from ourwaveguide, with visibility (82± 2) %.

in the temporal case. This visibility depends on the spec-tral purity and indistinguishably of the photons [60], andcan also be degraded by higher-order down-conversionevents. Our measured value is VHOM = (82± 2) %, with-out background subtraction. That the HOM visibility islower than the upper bound given by the JSI’s purity isprobably due to chirp on the pump pulses, backreflec-tions as in Fig. 1(b), and residual distinguishability inthe photons due to being produced in different directionsin the waveguide.

We plot the measured count rates and Klyshko effi-ciencies in Fig. 4. The rates scale linearly with pumppower (at low power), allowing us to plot also versusthe mean pair number per pulse produced in the crystal.We are limited to around 2 mW pump power and 1 mil-lion coincidences per second by saturation and latchingof our detectors. From Fig. 4(a) we extract a bright-ness of (3.5± 0.1)× 106 pairs/(s·mW), competitive withstate-of-the-art waveguide processes. The Klyshko effi-ciencies, as expected, drop at low power due to darkcounts, and at high power due to detector saturation.The average Klyshko efficiencies (excluding the first twoand last five points) are (38.0± 0.5) % and (46.8± 1.3) %respectively for signal and idler. We can compare thesevalues to those estimated from classical measurements:component transmission from waveguide to fiber forthe signal (85± 3) % (idler (79± 3) %), fiber couplingefficiency for the signal (66± 5) % (idler (84± 5) %),

fiber transmission to detectors (95± 5) %, detector effi-ciency (90± 5) %, giving a total expected efficiency of(48± 4) % for the signal and (57± 6) % for the idler.Waveguide losses partially account for the difference tothe measured efficiencies, as do losses due to the gen-tle filtering used to remove sinc lobes [41]. None of theselosses are fundamental: better coatings on our optics andlower loss waveguides would boost the efficiency dramat-

ically. Additionally, the heralded g(2)h (0), an indication of

noise photons in the system, is consistent with zero extranoise. For spectrally pure photons and low pump power,

g(2)h (0) = 2(2 − ηh)µ, where µ is the mean pair number

per pulse and ηh is the Klyshko efficiency of the heralding

signal photon. This gives g(2)h (0)/µ = 3.24, which agrees

with our experimental result of 3.19± 0.05.

0 500 1000 1500Coupled pump power ( W)

0.0

0.5

1.0

1.5

2.0

2.5

Coun

t rat

es (M

Hz)

(a)

100 101 102 103Coupled pump power ( W)

0

10

20

30

40

50

Klys

hko

effic

ienc

y (%

)

(b)

SignalIdlerCoincidences

0.00 0.02 0.04 0.06Pairs per pulse

10 4 10 3 10 2 10 1Pairs per pulse

FIG. 4. (a) Single and coincidence count rates vs pump powerexiting the waveguide, from which we extract a brightnessof (3.5± 0.2)× 106pairs/(s·mW). (b) Klyshko efficiencies vspump power, calculated from coincidences divided by singles.The average efficiencies are (38.0± 0.5) % and (46.8± 1.3) %for the signal and idler respectively. Uncertainties in bothcases are the standard deviations of the multiple data points.

Finally we present the entanglement visibility curvesand reconstructed two-qubit density matrix in Fig. 5. Wefind a maximum visibility of (96.0± 0.1) % in the rectilin-

6

ear basis and (94.3± 0.1) % in the diagonal basis, wherethe error bars come from Poissonian statistics. We thenperform overcomplete quantum state tomography [61]with an average coincidence rate of 59 000 pairs/s, findinga fidelity of F = 〈ψ−| ρ |ψ−〉 = (95.78± 0.04) %. The fi-delity and visibilities are limited by the small end facet re-flectivity as in Fig. 3(b), some residual temporal-spectraldistinguishability as in Section III C, and 30 accidentalcoincidences per second due to multi-pair emissions.

(b) (c)

(a)

-0.5

0

0.5

HHHVVHVV

VVVHHVHH

-0.5

0

0.5

HHHVVHVV

VVVHHVHH

0 100 200 300Bob polarizer setting ( )

0

10000

20000

30000

40000

50000

60000

70000

Coin

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ond

Alice 0Alice 45

Alice 90Alice 135

FIG. 5. (a) Correlation curves of coincidence counts. (b)Real, and (c) imaginary parts of the reconstructed densitymatrix, giving (95.78± 0.04) % fidelity to |ψ−〉.

We also measured a different waveguide chip with thesame design, but from a different batch. Due to bet-ter end coatings, the entanglement fidelity of this chipwas (98.82± 0.05) %, and the Hong-Ou-Mandel visibil-ity was (89± 2) %. Unfortunately the waveguide andcoupling losses were higher, resulting in Klyshko efficien-cies of (26.3± 0.3) % and (28.2± 0.5) %. Thus we choseto focus on the chip with best Klyshko efficiency, at thecost in this case of entanglement and Hong-Ou-Mandelvisibility. However both the reduced visibility of the firstchip and the reduced efficiency of the second chip aretechnical, rather than fundamental problems, and nei-ther prevents these sources from being used in cutting-edge experiments.

E. Comparison with other sources

It is instructive to compare the properties and perfor-mance of our source to previous work. Compared to bulksources (see Table I), our waveguide source provides 1−3orders of magnitude higher brightness, as well as higherKlyshko efficiency than the bright bulk sources due to thewaveguide decoupling the brightness and efficiency. Ourentanglement fidelity and HOM interference visibility arecomparable to many of the best bulk sources.

Compared to integrated sources (see Table II), oursource has by far the highest Klyshko efficiency, insome cases by nearly two orders of magnitude. Ourhigh spectral purity leads to an interesting brightnesscomparison: instead of the typical pairs/(s·mW), wecan compare the brightness additionally per spectralmode. Our brightness by this metric is still veryhigh (2.9× 106 pairs/(mode·s·mW)), while CW pumpedsources and those without spectral engineering drop byorders of magnitude. Our source is the brightest to emitentangled pairs into a single spectral-temporal mode,suitable for multi-photon interference.

IV. CONCLUSION

We have demonstrated a source of entangled photonpairs that has nearly ideal polarization entanglement,spectral purity, and brightness, and shown for the firsttime high Klyshko efficiency in a waveguided entangledpair source. Further optimization of optical coatings andbeam reshaping to maximize the overlap between waveg-uide and fiber modes [62] will allow coupling efficienciesapproaching 100 %, independent of the source brightness.Our use of spectral engineering to produce pure, indis-tinguishable photons is a great advantage over spectralfiltering for quantum networking, and could be furtherenhanced by apodization of the nonlinearity as shownin bulk sources [63–65]. Overall we have taken a signifi-cant step towards the ideal integrated source of entangledphotons, and laid out the straightforward optimizationsnecessary for maximum performance.

Looking forward, the high brightness, fidelity and pu-rity of our source make it an excellent candidate for mul-tiplexing to create multi-photon entangled states [17, 18],and for time-multiplexed multi-photon experiments [66].The wavelength is also compatible with telecommunica-tions infrastructure, making the source suitable for quan-tum communications in optical fiber, in particular tele-portation and entanglement swapping. Another excit-ing application is polarization squeezing [67], which re-quires simultaneously high brightness and coupling effi-ciency, to produce squeezed and entangled continuous-variable states that can be detected without a local os-cillator [68, 69].

7

FUNDING

Natural Sciences and Engineering Research Coun-cil of Canada (NSERC); European Union’s Horizon2020 research and innovation program (665148 QCUM-bER); European Commission, European Research Coun-

cil (ERC) (725366 QuPoPCoRN).

ACKNOWLEDGMENTS

We would like to thank Johannes Tiedau, Geoff Pryde,Morgan Weston, Deny Hamel, Thomas Jennewein, andSergei Slussarenko for helpful discussions.

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TABLE I. Comparison of high-performance entangled-pair sources based on bulk optics. † denotes photons attelecommunications wavelengths; * denotes values inferred from published data. In particular, entanglementfidelity is approximated from reported visibilities as F = 1− (1− V )/2, where V is the highest reported averagevisibility in rectilinear and diagonal bases without subtracting accidental coincidences, and HOM visibilitybetween two individually heralded photons is upper bounded by the spectral purity. The brightness encom-passes the filtered source bandwidth, and all losses are removed to give the brightness inside the crystal. TheKlyshko efficiency is the average of the signal and idler photons, evaluated as the coincidence rate divided bythe singles rate. Values that could not be estimated are indicated with –.

Reference Architecture Entanglementfidelity

HOM visibility Brightness(pairs/(s·mW))

Klyshko efficiency

CW-pumpedKwiat95 [70] BBO, rings 98.9%* – 1000* 10%*Kwiat99 [71] Crossed BBO 99.4%* - 2400* 6.5%*Fiorentino04 [72] PPKTP

Mach-Zehnder95%* - 370 000 18%

Kim06 [52] PPKTP Sagnac 99.1%* - 200 000* 16%*Steinlechner14[73]

PPKTP Sagnac 99.4% - 47 000 38%

Poh15 [4] BBO, rings 99.99%* - 9000* 6.3%*Chen18 [74] Crossed PPKTP

+ Sagnac99.2% - 4.7× 106 18.5%

Pulsed-pumpedChristensen13[26]

Crossed BiBO 99.8%* – – 75%

Giustina15 [1] PPKTP Sagnac 99.5%* – – 77%Shalm15 [2] PPKTP small

Mach-Zehnder†99.9%* – – 75%

Wang16 [17] Crossed BBO 99.5% 91% 12 000 42%*Spectrally engineered

Evans10 [75] PPKTP smallMach-Zehnder†

95%* 93%* 123 000 1.9%

Jin14 [76] PPKTP Sagnac† 97.3% 82%* (theory) 200 000* 10%Weston16 [30] PPKTP Sagnac† 99.0% 100% 1500* 52%This work PPKTP waveg-

uide + Sagnac†95.8% 82% 3.5× 106 43%

Second chip PPKTP waveg-uide + Sagnac†

98.8% 89% 5.6× 106 27%

12

TABLE II. Comparison of high-performance entangled pair sources based on integrated optics, with the sameconventions as above. For Jöns17, the Klyshko efficiency is replaced by the approximate extraction timesdetection efficiency, while for Huber17 it is upper-bounded by the extraction efficiency. The HOM visibilityfor Huber17 is given by the average two-photon interference visibility for QD2.

Reference Architecture Entanglementfidelity

HOM visibility Brightness(pairs/(s·mW))

Klyshko efficiency

CW-pumpedHerrmann13 [19] PPLN,

double-poling†97.5%* - 4× 105 2%*

Clausen14 [47] Free spaceMach-Zehnder

97.9%* 91%* 6.6× 105 5%

Autebert16 [77] AlGaAs Braggwaveguide†

93.4%* - – 1%*

Vergyris17 [21] PPLN + fiberSagnac†

92.6%* - 2.4× 108 3%*

Atzeni18 [78] 2x PPLNwaveguide + BS†

92.9% - 2.2× 109* 0.04%

Pulsed-pumpedLi05 [22] Fiber Sagnac† 65%* – 8× 107* 0.6%*Fan07 [23] Microstructure

fiber Sagnac96.3% – 8× 108* 0.6%

Lim08 [79] PPLN + fiberSagnac†

96.8% – – 0.6%*

Arahira11 [46] PPLN + fiberSagnac†

99.6%* – 5× 106* 0.6%*

Sansoni17 [20] PPLNMach-Zehnder†

97.3% 90%* 1.2× 106 4%*

Spectrally engineeredMeyer-Scott13 [50]

Crossed PM fiber 92.2% 70%* 1300* 20%

Quantum dotsHuber17 [24] GaAs quantum

dot94% 67% – � 1%

Jöns17 [25] InAsP quantumdot

81.7% – – 0.1%*

This work PPKTP waveg-uide + Sagnac†

95.8% 82% 3.5× 106 43%

Second chip PPKTP waveg-uide + Sagnac†

98.8% 89% 5.6× 106 27%

High-performance source of indistinguishable entangled photon pairs based on hybrid integrated-bulk opticsAbstractI IntroductionII Integrated single-mode photon pair sourcesIII ExperimentA SetupB Differences to bulk sourcesC Distinguishability in time and frequencyD ResultsE Comparison with other sources

IV Conclusion Funding Acknowledgments References

integrated quantum optics, department of physics ... · 2 dence of the down-conversion e ciency...

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