Abstract

A theory of spontaneous parametric downconversion in a nonlinear crystal that is placed inside a microcavity in the degenerate, collinear, type I arrangement is given. Both atom and field variables are fully quantized. The photon-correlation function for the entangled photon pairs produced has a much longer correlation time (∼0.4 ns) than that without the cavity (of the order of subpicoseconds) and can be measured directly with fast photodetectors. We also calculate the resonant suppression and enhancement in the photon-pair count rate as a function of cavity length. The results are in qualitative agreement with recent downconversion experiments [Phys. Rev. Lett. 85, 2556 (1999)] in a 4.5-mm cavity.

© 2001 Optical Society of America

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  1. D. C. Burnham, D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
    [CrossRef]
  2. Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
    [CrossRef] [PubMed]
  3. C. K. Hong, L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
    [CrossRef] [PubMed]
  4. Z. Y. Ou, L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
    [CrossRef] [PubMed]
  5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
    [CrossRef] [PubMed]
  6. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [CrossRef] [PubMed]
  7. S. L. Braunstein, H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [CrossRef]
  8. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
    [CrossRef] [PubMed]
  9. T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
    [CrossRef] [PubMed]
  10. Z. Y. Ou, Y. J. Lu, “Cavity enhanced spontaneous down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 85, 2556–2559 (1999).
    [CrossRef]
  11. M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
    [CrossRef]
  12. R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).
  13. R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
    [CrossRef]
  14. F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
    [CrossRef] [PubMed]
  15. B. Zysset, I. Biaggio, P. Gunter, “Refractive indices of orthorhombic KNbO3: dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
    [CrossRef]

1999

Z. Y. Ou, Y. J. Lu, “Cavity enhanced spontaneous down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 85, 2556–2559 (1999).
[CrossRef]

R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).

1998

R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
[CrossRef]

S. L. Braunstein, H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

1995

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

1994

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[CrossRef] [PubMed]

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

1993

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

1992

1991

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

1990

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

1988

Z. Y. Ou, L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

1985

C. K. Hong, L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

1984

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

1970

D. C. Burnham, D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Andrews, R.

R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).

R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Biaggio, I.

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein, H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

Burnham, D. C.

D. C. Burnham, D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Collett, M. J.

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Crescentini, L.

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

De Martini, F.

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

Gardiner, C. W.

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Gunter, P.

Herzog, T. J.

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

Hong, C. K.

C. K. Hong, L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Kimble, H. J.

S. L. Braunstein, H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Loudon, R.

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

Lu, Y. J.

Z. Y. Ou, Y. J. Lu, “Cavity enhanced spontaneous down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 85, 2556–2559 (1999).
[CrossRef]

Mandel, L.

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

Z. Y. Ou, L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

C. K. Hong, L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

Marrocco, M.

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

Mataloni, P.

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou, Y. J. Lu, “Cavity enhanced spontaneous down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 85, 2556–2559 (1999).
[CrossRef]

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

Z. Y. Ou, L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Pike, E. R.

R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).

R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
[CrossRef]

Rarity, G. J.

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

Sarkar, S.

R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).

R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
[CrossRef]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Vaidman, L.

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[CrossRef] [PubMed]

Wang, L. J.

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

Weinberg, D. L.

D. C. Burnham, D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

Zeilinger, Z.

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

Zou, X. Y.

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

Zysset, B.

J. Opt. B: Quantum Semicl. Opt.

R. Andrews, E. R. Pike, S. Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum Semicl. Opt. 1, 588–597 (1999).

J. Opt. Soc. Am. B

Phys. Rev. A

F. De Martini, M. Marrocco, P. Mataloni, L. Crescentini, R. Loudon, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991).
[CrossRef] [PubMed]

Z. Y. Ou, X. Y. Zou, L. J. Wang, L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[CrossRef] [PubMed]

C. K. Hong, L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[CrossRef] [PubMed]

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and travelling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Phys. Rev. Lett.

D. C. Burnham, D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

T. J. Herzog, G. J. Rarity, H. Weinfurter, Z. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72, 629–632 (1994).
[CrossRef] [PubMed]

Z. Y. Ou, Y. J. Lu, “Cavity enhanced spontaneous down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 85, 2556–2559 (1999).
[CrossRef]

Z. Y. Ou, L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, Y. H. Shih, “New high-intensity source of polarization–entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

S. L. Braunstein, H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

Pure Appl. Opt.

R. Andrews, E. R. Pike, S. Sarkar, “The role of second-order nonlinearities in the generation of localized photons,” Pure Appl. Opt. 7, 293–299 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a nonlinear crystal of length d inside a cavity of length d.

Fig. 2
Fig. 2

Photon-pair count rate (pairs per second) plotted versus the dimensionless quantity q = 1.18 × 1012 τ′.

Fig. 3
Fig. 3

Photon-pair count rate (pairs per second) plotted versus the cavity displacement.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

A2r1, r2, r3, t=-ih5-tdt1-t1dt2-t2dt3-t3dt4-t4dt5×a1, a2, s3|μa,1t1μb,2t2μc,3t3μd,3t4μe,3t5|g1, g2, g3×0, ak0λ0|Ear1, t1Ebr2, t2Ecr3, t3Edr3, t4Eer3, t5|0, αk0λ0+r1  r2,
Gcav2r1, t1; r2, t2=-ih5ωk0201/2αk0λ0-tdt1-t1dt2μa1g1eff,1μa2g2eff,2χeff2 expiωa1g1t1expiωa2g2t2×π2d1o*2o*  d3k1  d3k2ωk120ωk220exp-iωk1t1-iωk2t2×Rk1oDk1o*Rk2oDk2o*expik1·r1+k2·r2-k1d-k2dsink0-k1z-k2zd2k0-k1z-k2zd2×δωk0-ωk1-ωk2,
ki=ki*+kiωkiωki=ωki*ωki-ωki*+122kiωki2ωki=ωki*×ωki-ωki*2+,
ωk1*+ωk2*=ωk0,  k1*+k2*=k0*.
Dki=1-1o2o expi2kid,
Rkio=2o exp-ikid+1o2o2-2o2expikidDki.
Gcav2z1, t1; z2, t2=-ωk0/2ωk0/2dx expiτx×sindνx22dνx221|1-1o2o expi2dνx|2,
ν=kiωkiωki=ωki*,
ν=2kiωki*2ωki=ωki*.

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