GDR’13 - 21.11.2013 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.
23
Embed
Parametric interaction between single photonsgdriqfa.unice.fr/IMG/pdf/Martin.pdf · PPLN LP DM LP DM laser sync 1560 nm 1551 nm 810 nm 807 nm 778 nm BS D3 Delay. DR ’13 Experimental
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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