Abstract

We propose and demonstrate a method for measuring the joint spectrum of photon pairs via Fourier spectroscopy. The biphoton spectral intensity is computed from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I downconversion source using a pair of common-path Mach–Zehnder interferometers based on Soleil compensators. The experimental results agree well with calculated frequency correlations that take into account the effects of coupling into single-mode fibers. The Fourier method is advantageous over scanning spectrometry when detectors exhibit high dark count rates leading to dominant additive noise.

© 2006 Optical Society of America

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    [CrossRef]
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2005 (4)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

J. P. Torres, F. Macia, S. Carrasco, and L. Torner, Opt. Lett. 30, 314 (2005).
[CrossRef] [PubMed]

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Y.-H. Kim and W. P. Grice, Opt. Lett. 30, 908 (2005).
[CrossRef] [PubMed]

2004 (3)

A. Dragan, Phys. Rev. A 70, 053814 (2004).
[CrossRef]

F. König and F. N. C. Wong, Appl. Phys. Lett. 84, 1644 (2004).
[CrossRef]

A. Valencia, G. Scarcelli, and Y. Shih, Appl. Phys. Lett. 85, 2655 (2004).
[CrossRef]

2003 (2)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, Quantum Inf. Comput. 3, 480 (2003).

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

2001 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
[CrossRef] [PubMed]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, Phys. Rev. A 64, 023802 (2001).
[CrossRef]

1976 (1)

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Banaszek, K.

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, Quantum Inf. Comput. 3, 480 (2003).

Carrasco, S.

Dragan, A.

A. Dragan, Phys. Rev. A 70, 053814 (2004).
[CrossRef]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Grice, W. P.

Harwit, M.

Kim, Y.-H.

König, F.

F. König and F. N. C. Wong, Appl. Phys. Lett. 84, 1644 (2004).
[CrossRef]

Kurtsiefer, C.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Lee, P. S. K.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
[CrossRef] [PubMed]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
[CrossRef] [PubMed]

Macia, F.

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Oberparleiter, M.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Resch, K. J.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Rudolph, T.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Scarcelli, G.

A. Valencia, G. Scarcelli, and Y. Shih, Appl. Phys. Lett. 85, 2655 (2004).
[CrossRef]

Schenck, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Sergienko, A. V.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Shih, Y.

A. Valencia, G. Scarcelli, and Y. Shih, Appl. Phys. Lett. 85, 2655 (2004).
[CrossRef]

Tai, M. H.

Teich, M. C.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Torner, L.

Torres, J. P.

U'Ren, A. B.

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, Quantum Inf. Comput. 3, 480 (2003).

Valencia, A.

A. Valencia, G. Scarcelli, and Y. Shih, Appl. Phys. Lett. 85, 2655 (2004).
[CrossRef]

van Exter, M. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Walmsley, I. A.

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, Quantum Inf. Comput. 3, 480 (2003).

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Weinfurter, H.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Woerdman, J. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Wong, F. N. C.

F. König and F. N. C. Wong, Appl. Phys. Lett. 84, 1644 (2004).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Zeilinger, A.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Valencia, G. Scarcelli, and Y. Shih, Appl. Phys. Lett. 85, 2655 (2004).
[CrossRef]

F. König and F. N. C. Wong, Appl. Phys. Lett. 84, 1644 (2004).
[CrossRef]

Nature (2)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, Nature 434, 169 (2005).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417 (2001).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (3)

A. Dragan, Phys. Rev. A 70, 053814 (2004).
[CrossRef]

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Quantum Inf. Comput. (1)

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, Quantum Inf. Comput. 3, 480 (2003).

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Simplified scheme of the double Fourier spectrometer applied to a source X of photon pairs. The photons enter interferometers with independently adjusted optical delays τ A and τ B and are counted by detectors D A and D B .

Fig. 2
Fig. 2

(a) Typical coincidence interferogram as a function of optical path differences τ A and τ B and (b) its Fourier transform. The dashed rectangle in (a) defines the scan range, which with suitable sampling density yields the region of interest in the frequency domain, outlined in (b).

Fig. 3
Fig. 3

(a) Experimental setup. X, BBO crystal; MZ1, MZ2, Mach–Zehnder interferometers; SPCM, single photon counting module, (b) Common-path Mach–Zehnder interferometer. HWP, half-wave plate; QP, quartz plate; QW, quartz wedges; P, polarizer; L, aspheric lens; F, single-mode fiber.

Fig. 4
Fig. 4

(a) Measured joint spectrum of photon pairs : I ̂ A ( λ A ) I ̂ B ( λ B ) : as a function of the wavelengths λ A and λ B ; (b) theoretical predictions of the joint spectral intensity; cross sections of the theoretical (dashed curve) and the experimental (solid curve with dots marking errors) distributions along the lines (c) λ A 1 + λ B 1 = constant and (d) λ A 1 λ B 1 = constant passing through the maximum.

Equations (2)

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p A B ( τ A , τ B ) 1 4 d ω A d ω B : I ̂ A ( ω A ) I ̂ B ( ω B ) : ( 1 + cos ω A τ A ) ( 1 + cos ω B τ B ) .
d τ A d τ B p A B ( τ A , τ B ) exp ( i Ω A τ A + i Ω B τ B ) δ ( Ω A ) δ ( Ω B ) : N ̂ A N ̂ B : + 1 2 δ ( Ω A ) : N ̂ A I ̂ B ( Ω B ) : + 1 2 δ ( Ω B ) : I ̂ A δ ( Ω A ) N ̂ B : + 1 4 : I ̂ A ( Ω A ) I ̂ B ( Ω B ) : ,

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