GD

R’1

3 - 2

1.11

.201

3

Parametric interaction between single photons

A. Martin, T. Guerreiro, B. Sanguinetti, E. Pomarico, N. Sangouard, J. S. Pelc, C. Langrock, M. M. Fejer, H. Zbinden, R. T. Thew, N. Gisin!

!Group of Applied Physics, University of Geneva.!

E. L. Ginzton Laboratory, Stanford University.

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Sum Frequency Generation (SFG)

χ(2)

ωi

ωs

(ωi + ωs)

- Energy conservation

- Momentum conservation

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Outline

• Interest of SFG at the single photon level

• Experimental realization

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Entangled pairs source for Theoreticians

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Entangled pairs source for Experimentalists

Laser χ(2) &

| i =p

P0|00i+p

P1| �i+p

P2...

SPDC

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Heralded entangled pairs with linear optics

SPDC50/50

SPDC

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Heralded entangled pairs with linear optics

SPDC50/50

SPDC

Problem :

• P1 P1 = P2

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Heralded entangled pairs with linear optics

SPDC

SPDC

SPDC

50/50

r/t

Heralded noiseless amplifier

N. Gisin, S. Pironio and N. Sangouard (2010) PRL 105(7): 070501.!N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew and H. Zbinden (2011) PRL 106(12):.

|01i

rt| ih |

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Heralded entangled pairs with non-linear optics

SPDC

Heralded noiseless amplifier

N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew and H. Zbinden (2011).!"Faithful Entanglement Swapping Based on Sum-Frequency Generation." PRL 106(12).

SPDC

SFG

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Heralded entangled pairs with non-linear optics

SPDC

N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew and H. Zbinden (2011).!"Faithful Entanglement Swapping Based on Sum-Frequency Generation." PRL 106(12).

SPDC

SFG

Not sensitive to the double pairs contribution

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

Linear vs Non-linear heralding entangled pairs

Assuming : 100% coupling and 100% detection efficiency

Heralding probability :

• Linear optics : 10-11

• Non-linear optics : 10-5 x ηSFG

Other advantages:

- Non-linear filtering → fidelity not impaired by imperfections

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Nonlinear crystal for SFG

• To maximise the efficiency :

➡ Crystal with high nonlinearity ➡ Small temporal and spatial confinement ➡ Good temporal and spatial overlap ➡ Long length of interaction

4 cm long pigtail waveguide (Stanford)

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 SFG efficiency

Classical efficiency of a waveguide is: ⌘N ⇡ 100%/W/cm2

The power of a single photon: P� ⇡ h ⌫

⌧c

Crystal coherence time acceptance ➡limited by the group velocity mismatch GVM

GVM =1

vg(�1)� 1

vg(�2)= 2.3ps/cm

⌧c = 9.2 ps

Optimal coherence time for 4 cm PPLN

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

SFG efficiency characterization in the single photon regime

Classically, the efficiency of SFG is proportional to thepump power Ppump and the square of the crystal length L2.Commercially available nonlinear waveguides offer highnormalized SFG efficiencies !̂ ! 100%=ðW # cm2Þ [17].Consider that the pump power is reduced so that a singlephoton is present per temporal mode. In this regime, thepower of the input beam can be calculated as the energy ofeach photon divided by its coherence time, i.e., Ppump ¼h"!"=tbp, where !" is the photon bandwidth and tbp isthe time-bandwidth product. Furthermore, the bandwidth!" is limited by group velocity dispersion, and decreases

linearly with the length of the crystal, i.e., !" ¼ !̂"=L

where !̂" is the spectral acceptance of the crystal. Theoverall conversion efficiency when the full bandwidth

of the crystal is used, is given by !thSFG ¼ !̂ !̂" h"L=tbp.

We experimentally verified that this equation holdsby injecting a pair of one-photon-per-mode beams at1557 nm and 1563 nm into a 2.6 cm periodically poledlithium niobate waveguide with an acceptance bandwidth

of !̂" ¼ 300 GHz # cm and measuring the rate of 780 nmoutput photons [see Fig. 4].

In our experiment !̂ ¼ 15%=ðW # cm2Þ and tbp ¼ 0:66,so that the expected efficiency is !th

SFG ! 1& 10'8.We measured an efficiency of !meas

SFG ¼ 1:2ð0:2Þ & 10'8.Hence, with a more appropriate commercial waveguide,5 cm long and !̂ ¼ 100%=ðW # cm2Þ [17], one could real-istically get !th

SFG ! 1:5& 10'7. With the research devicepresented in Ref. [18] [10 cm, !̂ ¼ 150%=ðW # cm2Þ]the efficiency would increase to !th

SFG ! 5& 10'7. Notethat the efficiency could further be improved using groupvelocity matching [19], higher spatial confinement of

the modes [20], or the use of highly nonlinear organicmaterials [21].Conclusion.—In conclusion, we have shown how SFG

can make the entanglement resulting from entanglementswapping faithful. Despite long-held preconceptions, wehave demonstrated that the SFG efficiency is high enoughto provide efficient, yet simpler solutions to linear opticsbased protocols for the heralded production of entangledstates or for the implementation of DI-QKD.We thank M. Afzelius, J.-D. Bancal, C. Clausen, C.

Osorio, H. de Riedmatten, S. Pironio, Y. Silberberg, andC. Wagenknecht for helpful discussions. We acknowledgesupport by the ERC-AG QORE and the Swiss NCCRQuantum Photonics.

[1] M. Zukowski et al., Phys. Rev. Lett. 71, 4287 (1993).[2] P. Kok and S. L. Braunstein, Phys. Rev. A 62, 064301

(2000).[3] C. Wagenknecht et al., Nat. Photon. 4, 549 (2010); S. Barz

et al., Nat. Photon. 4, 553 (2010).[4] Y.-H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 86,

1370 (2001).[5] B. Dayan et al., Phys. Rev. Lett. 94, 043602 (2005).[6] A. Pe’er et al., Phys. Rev. Lett. 94, 073601 (2005); F. Zah

et al., Opt. Express 16, 16452 (2008).[7] S. Tanzilli et al. Nature (London) 437, 116 (2005); R. T.

Thew et al., Appl. Phys. Lett. 93, 071104 (2008).[8] C. Sliwa and K. Banaszek, Phys. Rev. A 67, 030101(R)

(2003).[9] N. Gisin, S. Pironio, and N. Sangouard, Phys. Rev. Lett.

105, 070501 (2010).[10] J. Brendel et al., Phys. Rev. Lett. 82, 2594 (1999).[11] For our purpose, the transmission losses and the nonunit

efficiency of the single-photon detectors are not relevant.[12] This formula and the one for the fidelity are extensions of

those given in Ref. [8] which take the four-pair emissioninto account.

[13] A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991); D. Mayersand A. C. Yao, Proceedings of the 39th Annual Symposiumon Foundations of Computer Science (IEEE ComputerSociety, New York, 1998), p. 503; J. Barrett, L. Hardy,and A. Kent, Phys. Rev. Lett. 95, 010503 (2005); A. Acinet al., Phys. Rev. Lett. 97, 120405 (2006); M. McKague,New J. Phys. 11, 103037 (2009); L. Masanes, Phys. Rev.Lett. 102, 140501 (2009).

[14] J F. Clauser et al., Phys. Rev. Lett. 23, 880 (1969).[15] A. Acin, N. Gisin, and L. Masanes, Phys. Rev. Lett. 98,

230501 (2007).[16] H. Hubel et al., Nature (London) 466, 601 (2010). Note

that it is not straightforward to extend this scheme for theheralded generation of remote entanglement.

[17] HC Photonics Corporation http://www.hcphotonics.com.[18] K. R. Parameswaran et al., Opt. Lett. 27, 179 (2002).[19] N. E. Yu et al., Opt. Lett. 27, 1046 (2002).[20] S. Kurimura et al., Appl. Phys. Lett. 89, 191123 (2006).[21] M. Jazbinsek et al., IEEE J Sel. Top. Quant. 14, 1298

(2008).

FIG. 4 (color online). Probability !SFG that a signal photon(# ¼ 1563 nm, !# ¼ 0:3 nm) is upconverted when interactingwith a weak pump (# ¼ 1557 nm, !# ¼ 1:2 nm) inside thewaveguide, plotted against the number of photons per mode(equal for pump and signal). Experimentally pump and signalphotons are obtained by attenuating and filtering a light-emittingdiode. Upconverted photons are separated from the residualpump using a prism, they are then detected with a single photondetector (IDQ ID100, 6% efficiency). Dark counts (2.2 Hz) havebeen subtracted, and injection (3 dB), reflection (0.6 dB), andpropagation (0.2 dB) losses have been taken into account.

PRL 106, 120403 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending

25 MARCH 2011

120403-4

No pump depletion

LED att

LED att

Filters

WDM

Waveguide

⌘SFG = (1.5± 0.3)⇥ 10�8

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3

SFG efficiency characterization in the single photon regime

LED att

LED att

Filters

WDM

Waveguide

1555 1556 1557 1558 1559 15601555

1556

1557

1558

1559

1560

Signal wavelength (nm)

Idle

r wav

elen

gth

(nm

)⌘SFG = (1.5± 0.3)⇥ 10�8

SFG bandwidth ~ 0.4 nm

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Experimental setup

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

SPDC Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

BS

D3Delay

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Experimental setup

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

SPDC Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

BS

D3Delay

• SPDC sources

➡ 532 nm ➱ 1560 nm + 807 nm & 1551 nm + 810 nm ➡ Bandwidth: ~0.4 nm ➡ Coupling: >50% ➡ P1 ~0.03

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Experimental setup

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

SPDC Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

BS

D3Delay

• SFG

➡ 1560 nm + 1551 nm ➱ 778 nm ➡ Acceptance bandwidth: ~ 0.4 nm ➡ Transmission: > 70% ➡ ⌘SFG = (1.5± 0.3)⇥ 10�8

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Experimental setup

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

SPDC Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

BS

D3Delay

• Detector 1

➡ Free running ➡ Efficiency: ~ 60 % ➡ Noise: ~ 2 Hz

• Detectors 2 & 3

➡ Gated ➡ Efficiency: ~ 60 % ➡ Noise: ~ 10-6 /ns

arXiv:1208.4205

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Preliminary experimental setup

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

SPDC Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

BS

D3Delay

532 nm laser10 ps pulses430 MHz rep.

532 nm DWDM

DelayVariable delay

TDC

Pump laser

DFG Source

Sum Frequency Generation Detectors

PPLN-WG

D1

D2SPDC Source

PPLN

PPLN LP DM

LP DM

laser sync

1560 nm

1551 nm

810 nm

807 nm

778 nm

Seed Laser810 nm

DM

BS

D3Delay

• DFG Source SPDC source stimulated by a laser

➡ Single photon level coherent state at 1551 nm

➡ Avoid one detector

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Results

��� � ���

��

���

���� � ���������� ��

� ��������

�������������

� � � ��

��

��

��

��

�����������

�� �� �� � � � � ��

�

��

��

��

��

�

�

������������������� ���� ��

��� ���� �������������� ��������

� �

Rate: 25 coinc. per hour

For |α|2 ~ 1

Nature Com. 4, 2324 (2013)

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Conclusion & Perspective

• Photon-photon parametric interaction demonstrated

• With current nonlinearities this interaction is as efficient comparable to optimal linear optics.

Perspective :

• Improving the SFG efficiency

• Realisation of heralded entangled pairs

Para

metr

ic in

terac

tion

betw

een si

ngle

phot

ons -

GD

R’1

3 Thank you for your attention

Nicolas!Sangouard

Bruno !Sanguinetti

Enrico!Pomarico

Tommaso!Lunghi

Thiago!Guerreiro