Abstract

We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency.

© 2017 Optical Society of America

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References

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2017 (1)

J. G. Koefoed, J. B. Christensen, and K. Rottwitt, “Effects of noninstantaneous nonlinear processes on photon-pair generation by spontaneous four-wave mixing,” Phys. Rev. A 95, 043842 (2017).
[Crossref]

2016 (5)

2015 (1)

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “Effects of self-and cross-phase modulation on photon purity for four-wave-mixing photon pair sources,” Phys. Rev. A 92, 053849 (2015).
[Crossref]

2013 (2)

B. Fang, O. Cohen, J. B. Moreno, and V. O. Lorenz, “State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing,” Opt. Express 21, 2707–2717 (2013).
[Crossref] [PubMed]

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Investigation of Inter-Modal Four-Wave Mixing in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25, 539–542 (2013).
[Crossref]

2012 (2)

L. Cui, X. Li, and N. Zhao, “Spectral properties of photon pairs generated by spontaneous four-wave mixing in inhomogeneous photonic crystal fibers,” Phys. Rev. A 85, 023825 (2012).
[Crossref]

B. P.-P. Kuo, J. M. Fini, L. Grüner-Nielsen, and S. Radic, “Dispersion-stabilized highly-nonlinear fiber for wideband parametric mixer synthesis,” Opt. Express 20, 18611–18619 (2012).
[Crossref] [PubMed]

2011 (2)

A. Clark, B. Bell, J. Fulconis, M. M. Halder, B. Cemlyn, O. Alibart, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Intrinsically narrowband pair photon generation in microstructured fibres,” New J. Phys. 13, 065009 (2011).
[Crossref]

C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide,” Opt. Lett. 36, 3413–3415 (2011).
[Crossref] [PubMed]

2010 (2)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[Crossref] [PubMed]

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. S. J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A 81, 031801 (2010).
[Crossref]

2009 (4)

2008 (1)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref] [PubMed]

2007 (1)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photon. 1, 165–171 (2007).
[Crossref]

2006 (1)

2005 (3)

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534–544 (2005).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[Crossref] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

2004 (4)

J. E. Sharping, J. Chen, X. Li, P. Kumar, and R. S. Windeler, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks,” Phys. Rev. Lett. 93, 093601 (2004).
[Crossref]

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004).
[Crossref]

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuations on dual-pump fiber-optic parametric amplifiers,” IEEE Photonics Technol. Lett. 16, 1292–1294 (2004).
[Crossref]

2001 (4)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

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).
[Crossref]

W. Grice, A. U’ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001).
[Crossref]

1998 (1)

1991 (2)

I. Abram and E. Cohen, “Quantum theory for light propagation in a nonlinear effective medium,” Phys. Rev. A 44, 500 (1991).
[Crossref] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[Crossref] [PubMed]

1990 (1)

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[Crossref]

1987 (1)

C. K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

Abram, I.

I. Abram and E. Cohen, “Quantum theory for light propagation in a nonlinear effective medium,” Phys. Rev. A 44, 500 (1991).
[Crossref] [PubMed]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley and Sons Ltd., 1981).

Agrawal, G. P.

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuations on dual-pump fiber-optic parametric amplifiers,” IEEE Photonics Technol. Lett. 16, 1292–1294 (2004).
[Crossref]

Alibart, O.

A. Clark, B. Bell, J. Fulconis, M. M. Halder, B. Cemlyn, O. Alibart, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Intrinsically narrowband pair photon generation in microstructured fibres,” New J. Phys. 13, 065009 (2011).
[Crossref]

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004).
[Crossref]

Baek, B.

Baldi, P.

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004).
[Crossref]

S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

Banaszek, K.

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks,” Phys. Rev. Lett. 93, 093601 (2004).
[Crossref]

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).
[Crossref]

A. B. U’Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” arXiv preprint quant-ph/0611019 (2006).

Begleris, I.

S. M. M. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. J. Richardson, P. Horak, and F. Parmigiani, “Inter-modal four-wave mixing study in a two-mode fiber,” Opt. Express 24, 30338 (2016).
[Crossref]

F. Parmigiani, Y. Jung, S. M. M. Friis, Q. Kang, I. Begleris, P. Horak, K. Rottwitt, P. Petropoulos, and D. J. Richardson, “Study of Inter-Modal Four Wave Mixing in Two Few-Mode Fibres with Different Phase Matching Properties,” in “Proceesings ECOC 2016; 42nd Eur. Conf. Opt. Commun.”, (2016), 301–303.

Bell, B.

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “Effects of self-and cross-phase modulation on photon purity for four-wave-mixing photon pair sources,” Phys. Rev. A 92, 053849 (2015).
[Crossref]

A. Clark, B. Bell, J. Fulconis, M. M. Halder, B. Cemlyn, O. Alibart, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Intrinsically narrowband pair photon generation in microstructured fibres,” New J. Phys. 13, 065009 (2011).
[Crossref]

Beveratos, A.

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New J. Phys. 6, 163 (2004).
[Crossref]

Brecht, B.

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. S. J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A 81, 031801 (2010).
[Crossref]

Cemlyn, B.

A. Clark, B. Bell, J. Fulconis, M. M. Halder, B. Cemlyn, O. Alibart, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Intrinsically narrowband pair photon generation in microstructured fibres,” New J. Phys. 13, 065009 (2011).
[Crossref]

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
[Crossref] [PubMed]

Chen, J.

Chraplyvy, A. R.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Investigation of Inter-Modal Four-Wave Mixing in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25, 539–542 (2013).
[Crossref]

Christensen, J. B.

J. G. Koefoed, J. B. Christensen, and K. Rottwitt, “Effects of noninstantaneous nonlinear processes on photon-pair generation by spontaneous four-wave mixing,” Phys. Rev. A 95, 043842 (2017).
[Crossref]

J. B. Christensen, C. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
[Crossref]

Clark, A.

A. Clark, B. Bell, J. Fulconis, M. M. Halder, B. Cemlyn, O. Alibart, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Intrinsically narrowband pair photon generation in microstructured fibres,” New J. Phys. 13, 065009 (2011).
[Crossref]

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
[Crossref] [PubMed]

Clark, A. S.

Cohen, E.

I. Abram and E. Cohen, “Quantum theory for light propagation in a nonlinear effective medium,” Phys. Rev. A 44, 500 (1991).
[Crossref] [PubMed]

Cohen, O.

B. Fang, O. Cohen, J. B. Moreno, and V. O. Lorenz, “State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing,” Opt. Express 21, 2707–2717 (2013).
[Crossref] [PubMed]

O. Cohen, J. S. Lundeen, B. J. Smith, G. Puentes, P. J. Mosley, and I. A. Walmsley, “Tailored photon-pair generation in optical fibers,” Phys. Rev. Lett. 102, 123603 (2009).
[Crossref] [PubMed]

Cui, L.

L. Cui, X. Li, and N. Zhao, “Spectral properties of photon pairs generated by spontaneous four-wave mixing in inhomogeneous photonic crystal fibers,” Phys. Rev. A 85, 023825 (2012).
[Crossref]

De Micheli, M.

S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

De Riedmatten, H.

S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[Crossref]

Duligall, J.

Dyer, S. D.

Eggleton, B. J.

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
[Crossref] [PubMed]

Erdmann, R.

A. B. U’Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” arXiv preprint quant-ph/0611019 (2006).

Essiambre, R.-J.

R.-J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental Investigation of Inter-Modal Four-Wave Mixing in Few-Mode Fibers,” IEEE Photonics Technol. Lett. 25, 539–542 (2013).
[Crossref]

Fang, B.

Fasel, S.

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Figures (8)

Fig. 1
Fig. 1 Possible setup for pure single-photon generation; the green and red dots are single photons at different wavelengths that are generated through SpFWM in the few-mode SIF.
Fig. 2
Fig. 2 (a) Diagram of relative IGV of the LP01-mode (solid blue) and LP11-mode (dashed red); the black dots denote the IGV of the pump modes at the central pump frequency; the solid gray lines lie on the pump IGV at the pump frequency but their slope value is the average of the LP01 and LP11 slope values; the gray dots denote the points on the grey lines that form a parallelogram with the black pump dots; (b) the same relative IGV diagram as in (a) but showing the skewed parallelogram of phase matching that satisfies Eq. (19).
Fig. 3
Fig. 3 The relative core radius variation along the fiber length (top) and the normalized absolute value of the resulting JSA (bottom) for (a) σa = 0, (b) σa/a0 = 0.25 %, (c) σa/a0 = 0.5 %, and (d) σa/a0 = 1.0 %.
Fig. 4
Fig. 4 (a) Phase-matched signal wavelength and (b) heralded single-photon purity versus core radius and Ge-doping concentration of a SIF; the solid black line denotes all positions where the phase-matched signal wavelength has a maximum in the core radius; the dashed black line is a contour line that represents a separation of 32 THz between the pump at λp = 1064 nm and the phase-matched wavelength.
Fig. 5
Fig. 5 (a) Phase-matched signal wavelength and (b) heralded single-photon purity versus core radius for selected values of the doping concentration, i.e. horizontal cross sections of Fig. 4(a) and 4(b), respectively; the Raman line denotes the wavelength above which Raman scattering is negligible; in (a), the filled black dots mark the maximum on each curve; in (b), they denote the purity associated with each maximum in (a); the black dotted line in each plot represents the function values of the solid black lines in Fig. 4(a) and 4(b), respectively; the legend in (a) applies also to (b).
Fig. 6
Fig. 6 Relative IGV versus wavelength for the LP01 and LP11-modes in a fiber with core radii (a) a0 = 3.86 μm, (b) a0 = 4.65 μm, and (c) a0 = 5.44 μm and doping concentration of 6.7 %; the gray area marks the Raman active zone of 32 THz separation from the pump.
Fig. 7
Fig. 7 Median heralded purity as a function of (a) core radius for different fluctuation strengths, with the value of σa/a0 indicated next to each curve and 1-ps-pump pulses, and (b) pump pulse duration for different core radii for 1 % CRF. Quantiles of the distribution are indicated such that half of the purities fall within the shaded region.
Fig. 8
Fig. 8 (a) Median purity of heralded photons from a source and HOM visibility of two sources with a0 = 4.0 μm as a function of correlation length. (b) Same as (a), but with a0 = 4.65 μm where the phase matching is stable. Half of the simulation results fall within the shaded regions and the dashed line indicates the correlation length used in previous simulations.

Equations (23)

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E j = 1 2 e F j ( x , y , z ) 2 n j 0 c [ A j ( z , t ) e i ω 0 j t + c . c . ] , j = p , q ,
E ^ j ( z , t ) = 1 2 e F j ( x , y , z ) e i ω j 0 t 2 ω j 0 n j 0 0 c a ^ j ( z , t ) + H . C . , j = s , r ,
M ^ int ( z ) = 2 γ ( z ) d t A p ( z , t ) A q ( z , t ) a ^ s ( z , t ) a ^ r ( z , t ) + H . C . ,
γ ( z ) = 3 χ ( 3 ) ω s 0 ω r 0 f pspr ( z ) 4 0 c 2 n p n q n s n r ,
f psqr ( z ) = d x d y F p ( x , y , z ) F s * ( x , y , z ) F q ( x , y , z ) F r * ( x , y , z ) .
z j ( z , t ) + β 1 j ( z ) t j ( z , t ) = i β 0 j ( z ) j ( z , t ) , j = A p , A q , a ^ s , a ^ r .
j ( z , t ) = j ( 0 , t 0 z d z β 1 j ( z ) ) exp ( i 0 z d z β 0 j ( z ) ) , j = A p , A q , a ^ s , a ^ r ,
| ψ = d t s d t r 𝒜 ( t s , t r ) | t s | t r ,
𝒜 ( t s , t r ) = a ^ s ( L , t s ) a ^ r ( L , t r ) ( i 0 L d z M ^ int ( z ) ) ,
𝒜 ( t s , t r ) = 2 i γ ( z c ) A p ( 0 , t c 0 z c d z β 1 p ( z ) ) A q ( 0 , t c 0 z c d z β 1 q ( z ) ) × exp ( i 0 z c d z Δ β 0 ( z ) ) Θ ( z c ) Θ ( L z c ) ,
t c = t s z c L d z β 1 s ( z ) , t c = t r z c L d z β 1 r ( z ) .
V = 1 R 1 R 2 d t s d t s ( d t r 𝒜 1 ( t s , t r ) 𝒜 1 * ( t s , t r ) ) ( d t r 𝒜 2 ( t s , t r ) 𝒜 2 * ( t s , t r ) ) ,
P = n | λ n | 4 ( n | λ n | 2 ) 2 ,
𝒜 ( t s , t r ) = 2 i γ A p ( 0 , t c β 1 p z c ) A q ( 0 , t c β 1 q z c ) Θ ( z c ) Θ ( L z c ) ,
z c = L t s t r β 1 s β 1 r , t c = β 1 s t r β 1 r t s β 1 s β 1 r .
A j ( 0 , t ) = P j exp ( ( t Δ t j ) 2 2 T j 2 ) , j = p , q ,
T q 2 ( β 1 p β 1 r ) ( β 1 p β 1 s ) + T p 2 ( β 1 q β 1 r ) ( β 1 q β 1 s ) = 0 ,
Δ β = β ( 01 ) ( ω p 0 ) + β ( 11 ) ( ω p 0 ) β ( 01 ) ( ω s 0 ) β ( 11 ) ( ω r 0 ) ,
Δ β ( β 1 ( 01 ) β 1 ( 11 ) + β 2 ( 01 ) + β 2 ( 11 ) 2 Ω ) Ω ,
a ( z ) = a 0 + z d z N ^ ( z ) e ( z z ) / l corr ,
N ^ ( z ) N ^ ( z ) = 2 σ a 2 l corr δ ( z z ) ,
Δ ω PM Δ ω state = d ω PM d a | a = a 0 σ a T p + 1 2 d 2 ω PM d a 2 | a = a 0 σ a 2 T p .
l coll l corr = T p l corr | β 1 p β 1 q | .

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