Abstract

Interference phenomena play a fundamental role in physics, and interferometric techniques have helped advance science and technology significantly. In this Letter, we observe spatial fringes in the interference of two beams, which are controlled by a third beam through the phenomenon of induced coherence without induced emission. We show that the interference pattern depends on the alignment of this third beam in an analogous way, as fringes created in a traditional division of amplitude interferometer depend on the relative alignment of the two interfering beams. We demonstrate that the pattern is characterized by an equivalent wavelength, which corresponds to a combination of the wavelengths of the involved light beams. Our results open up the possibility of developing new techniques, such as wavefront sensing and holography at wavelengths for which no suitable single-photon cameras are available.

© 2017 Optical Society of America

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References

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  1. R. P. Feynman, R. B. Leighton, and M. Sands, Quantum Mechanics, the Feynman Lectures on Physics (Addison-Wesley, 1965), Vol. 3.
  2. D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988).
    [Crossref]
  3. L. Mandel, Opt. Lett. 16, 1882 (1991).
    [Crossref]
  4. B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
    [Crossref]
  5. L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
    [Crossref]
  6. X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
    [Crossref]
  7. T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
    [Crossref]
  8. A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
    [Crossref]
  9. G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
    [Crossref]
  10. M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
    [Crossref]
  11. F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
    [Crossref]
  12. T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
    [Crossref]
  13. S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
    [Crossref]
  14. D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
    [Crossref]
  15. D. N. Klyshko, Sov. Phys. J. Exp. Theor. Phys. 28, 522 (1969).
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    [Crossref]
  17. X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
    [Crossref]
  18. G. A. Barbosa, Phys. Rev. A 48, 4730 (1993).
    [Crossref]
  19. T. P. Grayson and G. A. Barbosa, Phys. Rev. A 49, 2948 (1994).
    [Crossref]
  20. M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).
  21. A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).
  22. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), Ch. 7.
  23. P. Hariharan, Optical Interferometry (Academic, 2003), Ch. 2.
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    [Crossref]

2016 (2)

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

2015 (2)

A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
[Crossref]

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

2014 (2)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

2004 (1)

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

2000 (1)

H. M. Wiseman and K. Mølmer, Phys. Lett. A 270, 245 (2000).
[Crossref]

1996 (1)

B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
[Crossref]

1995 (1)

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

1994 (1)

T. P. Grayson and G. A. Barbosa, Phys. Rev. A 49, 2948 (1994).
[Crossref]

1993 (2)

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

G. A. Barbosa, Phys. Rev. A 48, 4730 (1993).
[Crossref]

1991 (3)

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

L. Mandel, Opt. Lett. 16, 1882 (1991).
[Crossref]

1988 (1)

D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988).
[Crossref]

1970 (1)

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[Crossref]

1969 (1)

D. N. Klyshko, Sov. Phys. J. Exp. Theor. Phys. 28, 522 (1969).

Barbosa, G. A.

T. P. Grayson and G. A. Barbosa, Phys. Rev. A 49, 2948 (1994).
[Crossref]

G. A. Barbosa, Phys. Rev. A 48, 4730 (1993).
[Crossref]

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

Borish, V.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), Ch. 7.

Boyd, R. W.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[Crossref]

Chekhova, M. V.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Cole, G. D.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Englert, B. G.

B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
[Crossref]

Feynman, R. P.

R. P. Feynman, R. B. Leighton, and M. Sands, Quantum Mechanics, the Feynman Lectures on Physics (Addison-Wesley, 1965), Vol. 3.

Grayson, T.

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

Grayson, T. P.

T. P. Grayson and G. A. Barbosa, Phys. Rev. A 49, 2948 (1994).
[Crossref]

Greenberger, D. M.

D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988).
[Crossref]

Hariharan, P.

P. Hariharan, Optical Interferometry (Academic, 2003), Ch. 2.

Herzog, T. J.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

Heuer, A.

A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
[Crossref]

Hochrainer, A.

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

Hudelist, F.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Iskhakov, T. S.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Jing, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Kalashnikov, D. A.

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Klyshko, D. N.

D. N. Klyshko, Sov. Phys. J. Exp. Theor. Phys. 28, 522 (1969).

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Krasheninnikov, V. N.

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Krivitsky, L. A.

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Kulik, S. P.

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Kwiat, P. G.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

Lahiri, M.

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

Lapkiewicz, R.

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

Leighton, R. B.

R. P. Feynman, R. B. Leighton, and M. Sands, Quantum Mechanics, the Feynman Lectures on Physics (Addison-Wesley, 1965), Vol. 3.

Lemieux, S.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Lemos, G. B.

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

Leuchs, G.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Liu, C.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Mandel, L.

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

L. Mandel, Opt. Lett. 16, 1882 (1991).
[Crossref]

Maslennikov, G. A.

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Menzel, R.

A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
[Crossref]

Merkulova, S. P.

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Milonni, P. W.

A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
[Crossref]

Mølmer, K.

H. M. Wiseman and K. Mølmer, Phys. Lett. A 270, 245 (2000).
[Crossref]

Ou, Z. Y.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Paterova, A. V.

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Penin, A. N.

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Perez, A.

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Radchenko, L. K.

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

Ramelow, S.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Sands, M.

R. P. Feynman, R. B. Leighton, and M. Sands, Quantum Mechanics, the Feynman Lectures on Physics (Addison-Wesley, 1965), Vol. 3.

Wang, L. J.

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[Crossref]

Weinfurter, H.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

Wiseman, H. M.

H. M. Wiseman and K. Mølmer, Phys. Lett. A 270, 245 (2000).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), Ch. 7.

Yasin, A.

D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988).
[Crossref]

Zeilinger, A.

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

Zhang, W.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Zou, X. Y.

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

J. Exp. Theory Phys. (1)

S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, J. Exp. Theory Phys. 98, 31 (2004).
[Crossref]

J. Mod. Opt. (1)

T. S. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, J. Mod. Opt. 63, 64 (2016).
[Crossref]

Nat. Commun. (1)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Nat. Commun. 5, 3049 (2014).
[Crossref]

Nat. Photonics (1)

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Nature (1)

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (2)

D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988).
[Crossref]

H. M. Wiseman and K. Mølmer, Phys. Lett. A 270, 245 (2000).
[Crossref]

Phys. Rev. A (6)

M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

A. Heuer, R. Menzel, and P. W. Milonni, Phys. Rev. A 92, 033834 (2015).
[Crossref]

X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, Phys. Rev. A 47, 2293 (1993).
[Crossref]

G. A. Barbosa, Phys. Rev. A 48, 4730 (1993).
[Crossref]

T. P. Grayson and G. A. Barbosa, Phys. Rev. A 49, 2948 (1994).
[Crossref]

Phys. Rev. Lett. (4)

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
[Crossref]

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[Crossref]

Sov. Phys. J. Exp. Theor. Phys. (1)

D. N. Klyshko, Sov. Phys. J. Exp. Theor. Phys. 28, 522 (1969).

Other (5)

M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin photon correlations in single-photon interference,” arXiv:1610.04298 (2016).

A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Quantifying the momentum correlation between two light beams by detecting one,” arXiv:1610.05529 (2016).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), Ch. 7.

P. Hariharan, Optical Interferometry (Academic, 2003), Ch. 2.

R. P. Feynman, R. B. Leighton, and M. Sands, Quantum Mechanics, the Feynman Lectures on Physics (Addison-Wesley, 1965), Vol. 3.

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (570 KB)      Justification of approximation used in main text

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Figures (3)

Fig. 1.
Fig. 1.

Setup of the experiment. Two nonlinear crystals NL1 and NL2 produce the signal (green, 810 nm) and idler (red, 1550 nm) photon pairs by type-0 SPDC. Using dichroic mirrors, the idler beam from NL1 is overlapped with the idler beam from NL2 such that the two beams are indistinguishable after NL2. The two signal beams are superposed at a beam splitter, and a camera detects the output at the focal distance of a positive lens (Lc). Confocal lens systems ensure identical pump spots at the crystals, indistinguishability of each mode of the idler beams at NL2, and the detection of the signal beams in the Fourier plane of both crystals. Coherence is induced between the respective modes of the signal beams.

Fig. 2.
Fig. 2.

Interference fringes in the signal beam for different idler beam configurations. (a) With perfect alignment, a uniform interference pattern is observed as a bright or a dark spot on the camera as the phase is shifted by π. (b) By tilting the idler beam, parallel fringes are produced on the camera. (c) If the imaging system is defocused, circular fringes occur.

Fig. 3.
Fig. 3.

Wavelength dependence of the interference pattern. (a) Examples of camera images obtained by introducing effective propagation distances d in the idler beam between the two crystals. (b) Evaluated radial positions ρn of the minima and maxima for d=9  mm (red), d=13  mm (green), and d=17  mm (blue). The error bars representing the standard deviation of the mean are smaller than the dots. The radial positions are subject to the condition aρn2+ϕ0=n, where n represents the orders of the maxima (n=1, 2) and minima (n=0.5, 1.5, 2.5). The solid lines are parabolic fits to the data, used to determine a. (c) The quadratic coefficients a (black points) determine how fast the relative phase between the two interfering beams varies with the distance from the center of the pattern. They show the expected linear dependence on the introduced propagation distance. The slope corresponds to an equivalent wavelength of 420±7  nm. The solid line shows the theoretical prediction for an equivalent wavelength of 423 nm.

Equations (4)

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|ψNLj=dkSjdkIjC(kS,kI)|kSj|kIj.
|ΨkS=dkIC(kS,kI)(|kS1+ei(ϕI(kI)+ϕ0)|kS2)|kI,
d2fc2ρn2+φ=nλeq,
λeq=λS2λI,

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