Abstract

Single-photon interference experiments are attempted in the time domain using true single-photon streams. Self-heterodyning beats are clearly observed by letting the field associated with a single photon interfere with itself on a field-quadratic detector, which is a time analogue of Young’s two-slit interference experiment. The temporal first-order coherence of single-photon fields, i.e., transient interference fringes, develops as cumulative detection events are mapped point-by-point onto a virtual capture frame by properly correlating the time-series data. The ability to single out photon counts at a designated timing paves the way for digital heterodyning with faint light for such use as phase measurement and quantum information processing.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. W. E. J. Lamb and M. O. Scully, The photoelectric effect without photons (Presses Universitaires de France, 1969).
  3. P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
    [Crossref]
  4. D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
    [Crossref]
  5. F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
    [Crossref]
  6. M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
    [Crossref]
  7. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
    [Crossref]
  8. D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
    [Crossref]
  9. P. A. M. Dirac, The Principles of Quantum Mechanics, Fourth Edition (Oxford University, 1958).
  10. N. A. Massie, R. D. Nelson, and S. Holly, “High-performance real-time heterodyne interferometry,” Appl. Opt. 18, 1797–1803 (1979).
    [Crossref] [PubMed]
  11. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
    [Crossref] [PubMed]
  12. M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
    [Crossref] [PubMed]
  13. J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
    [Crossref]
  14. E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
    [Crossref]
  15. L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
    [Crossref]
  16. L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
    [Crossref] [PubMed]
  17. X. Guo, Y. Mei, and S. Du, “Testing the bell inequality on frequency-bin entangled photon pairs using time-resolved detection,” Optica 4, 388–392 (2017).
    [Crossref]
  18. R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
    [Crossref]
  19. L. Mandel, “Coherence and indistinguishability,” Opt. Lett. 16, 1882–1883 (1991).
    [Crossref] [PubMed]
  20. S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
    [Crossref]
  21. J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
    [Crossref]

2017 (2)

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

X. Guo, Y. Mei, and S. Du, “Testing the bell inequality on frequency-bin entangled photon pairs using time-resolved detection,” Optica 4, 388–392 (2017).
[Crossref]

2014 (1)

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

2008 (1)

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

2007 (1)

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

2004 (2)

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
[Crossref]

2003 (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

2001 (1)

1999 (1)

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

1991 (2)

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

L. Mandel, “Coherence and indistinguishability,” Opt. Lett. 16, 1882–1883 (1991).
[Crossref] [PubMed]

1986 (1)

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
[Crossref]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

1979 (1)

1976 (1)

L. Mandel, “II the case for and against semiclassical radiation theory,” Prog. Opt. 13, 27–68 (1976).
[Crossref]

1970 (1)

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Alaimo, M. D.

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

Andrews, F. A.

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Aspect, A.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
[Crossref]

Beck, M.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Bergreen, G. S.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
[Crossref]

Davies, R. E.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, Fourth Edition (Oxford University, 1958).

Donato, V. W.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Du, S.

Eberhardt, F. J.

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Ekert, A. K.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
[Crossref]

Emplit, P.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Ferri, F.

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

Goedgebuer, J.-P.

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Grangier, P.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
[Crossref]

Guo, X.

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Holly, S.

Huntington, E. H.

E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
[Crossref]

Ichimura, T.

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

Inaba, H.

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

Karpinski, M.

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Kondo, M.

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

Lamb, W. E. J.

W. E. J. Lamb and M. O. Scully, The photoelectric effect without photons (Presses Universitaires de France, 1969).

Magatti, D.

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

Mandel, L.

L. Mandel, “Coherence and indistinguishability,” Opt. Lett. 16, 1882–1883 (1991).
[Crossref] [PubMed]

L. Mandel, “II the case for and against semiclassical radiation theory,” Prog. Opt. 13, 27–68 (1976).
[Crossref]

Massar, S.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Massie, N. A.

Mazurenko, Y.

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Mei, Y.

Merolla, J.-M.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Mérolla, J.-M.

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Nagata, T.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

Neel, M. S.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Nelson, R. D.

O’Brien, J. L.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

Okamoto, R.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Olislager, L.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Phan Huy, K.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Potenza, M. A. C.

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

Ralph, T. C.

E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
[Crossref]

Rhodes, W. T.

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Roger, G.

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
[Crossref]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

Sasaki, K.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

Scully, M. O.

W. E. J. Lamb and M. O. Scully, The photoelectric effect without photons (Presses Universitaires de France, 1969).

Sergienko, A. V.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

Smith, B. J.

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

Söller, C.

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

Takeuchi, S.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
[Crossref]

Teich, M. C.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

Thorn, J. J.

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Toida, M.

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Woodhead, E.

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Wright, L. J.

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

Zeilinger, A.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
[Crossref]

Am. J. Phys. (1)

J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Toida, M. Kondo, T. Ichimura, and H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[Crossref]

Appl. Phys. Lett. (1)

D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. 92, 241101 (2008).
[Crossref]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Europhys. Lett. (1)

P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,” Europhys. Lett. 1, 173 (1986).
[Crossref]

J. Acoust. Soc. Am. (1)

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Nature (1)

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (2)

E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
[Crossref]

L. Olislager, E. Woodhead, K. Phan Huy, J.-M. Merolla, P. Emplit, and S. Massar, “Creating and manipulating entangled optical qubits in the frequency domain,” Phys. Rev. A 89, 052323 (2014).
[Crossref]

Phys. Rev. Lett. (3)

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref] [PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref] [PubMed]

J.-M. Mérolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Prog. Opt. (1)

L. Mandel, “II the case for and against semiclassical radiation theory,” Prog. Opt. 13, 27–68 (1976).
[Crossref]

Science (1)

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
[Crossref] [PubMed]

Other (3)

W. E. J. Lamb and M. O. Scully, The photoelectric effect without photons (Presses Universitaires de France, 1969).

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
[Crossref]

P. A. M. Dirac, The Principles of Quantum Mechanics, Fourth Edition (Oxford University, 1958).

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Figures (3)

Fig. 1
Fig. 1 (a) Frequency-labeled Mach-Zehnder interferometer (MZI) to observe single-photon self-heterodyne beats (SHBs); AOM, acousto-optic modulator; LP, long-pass filter; HWP, half-wave plate; NPBS, non-polarizing beam splitter; M, mirror; SPCM, single-photon counting module. (b)(c) Hanbury-Brown and Twiss-type two-photon interferometers (HBT-TPIs) for checking the anti-bunching status of single photons: (b) emanating from a type-II BBO (β-barium borate), and (c) undergoing 80-MHz up-conversion through the AOM. (d) HBT-TPI built with an AOM as NPBS for observing cross-frequency anti-bunching.
Fig. 2
Fig. 2 (a) Schematic modulo-T′ folding of time-series data, I(t). Single photon detection events are mapped point-by-point onto the virtual capture frame of a fixed width T′. (b) Visibility Vn (θ) (Eq. (6)) for modulo-T′ folding of n-times as a function of θ = 2π T/T where T is the true period. Only commensurate foldings (θ = 2; mZ) provide Vn (θ) = 1. (Inset) Cumulative photon counts over a large ensemble reconstruct the otherwise underdeveloped profile of the self-heterodyne beats.
Fig. 3
Fig. 3 Single-photon self-heterodyne beats (SHBs). Coincident counts were accumulated for 30 s without dark count correction. The solid line is the least-squares with visibility V = 0.91. Inset: the Poincaré sphere representation of Eq. (2). The digital heterodyning at a particular position (time) allows one to determine the azimuth angle ϕm ∈ [0, 2π).

Tables (1)

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Table 1 Singles count and heralded coincidence counts of SPDC photons receiving different anti-bunching tests. The left three columns correspond to normal HBT-TPI of Fig. 1(b). Note that multimode fibers were used for Δt = 7.3 and 18.8 ns while single mode fibers were used for Δt = 27.3 ns for collecting photons. The right two columns show the results for 80-MHz up-conversion through the AOM (Fig. 1 (c)) and cross-frequency anti-bunching (Fig. 1 (d)). Note that g(2)(0) = NGTRNG/NGTNGR.

Equations (6)

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| ψ AOM = α | 10 ω | 00 ω + Δ ω + β | 00 ω | 01 ω + Δ ω
| ψ ( ϕ ) = 1 2 ( | 1 ω | 0 ω + Δ ω + e i ϕ | 0 ω | 1 ω + Δ ω ) ,
I ( t ) = 1 2 n + 1 k = n n I ( t + k T )
= 1 + [ k = n n cos ( 2 π k T / T ) 2 n + 1 ] sin ( 2 π t T ) ,
V n ( θ ) = | k = n n cos ( k θ ) 2 n + 1 |
g ( 2 ) ( 0 ) = N G T R N G / N G T N G R

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