Abstract

We discuss antibunching of photons in terms of the distributions of waiting between successive photoemissions and compare it with definitions of antibunching based on the two-time intensity correlation function. We illustrate our results for photon sequences emitted by parametric oscillators. Curves are presented to illustrate the behavior.

© 2000 Optical Society of America

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References

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  1. See H. J. Kimble and D. F. Walls, eds., feature on squeezed states of the electromagnetic field, J. Opt. Soc. Am. B 4, 1450–1741 (1987); P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” At. Mol. Opt. Phys. 28, 75–142 (1991).
    [CrossRef]
  2. H. J. Carmichael and D. F. Walls, “Proposal for the measurement of the resonant Stark effect by photon correlation techniques,” J. Phys. B 9, L43–L46 (1976); H. J. Kimble and L. Mandel, “Theory of resonance fluorescence,” Phys. Rev. A 13, 2123–2144 (1976).
    [CrossRef]
  3. R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983); L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
    [CrossRef] [PubMed]
  4. H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
    [CrossRef]
  5. G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
    [CrossRef] [PubMed]
  6. H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982); D. F. Walls, “Evidence for the quantum nature of light,” Nature 280, 451–454 (1979).
    [CrossRef]
  7. L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986); X. T. Zou and L. Mandel, “Photon-antibunching and sub-Poissonian statistics,” Phys. Rev. A 41, 475–476 (1990).
    [CrossRef] [PubMed]
  8. P. Rice and H. J. Carmichael, “Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit,” IEEE J. Quantum Electron. 24, 1351–1366 (1988).
    [CrossRef]
  9. G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
    [CrossRef] [PubMed]
  10. A. B. Dobson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
    [CrossRef]
  11. C. Cohen-Tannoudji and J. Dalibard, “Single-atom laser spectroscopy. Looking for dark periods in fluorescence light,” Europhys. Lett. 1, 441–448 (1986); P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
    [CrossRef] [PubMed]
  12. B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).
  13. R. Vyas and S. Singh, “Quantum statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989); “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989); “Waiting-time distributions in the photodetection of squeezed light,” Phys. Rev. A PLRAAN 38, 2423–2430 (1988).
    [CrossRef] [PubMed]
  14. H. J. Carmichael, S. Singh, R. Vyas, and P. R. Rice, “Photoelectron waiting times and atomic state reduction in resonance fluorescence,” Phys. Rev. A 39, 1200–1218 (1989); H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
    [CrossRef] [PubMed]
  15. R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–949 (1980); The Quantum Theory of Light (Oxford Science, Oxford, 1983).
    [CrossRef]
  16. F. Davidson and L. Mandel, “Photoelectric correlation measurements with time-to-amplitude converters,” J. Appl. Phys. 39, 62–66 (1968).
    [CrossRef]

1993 (1)

A. B. Dobson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
[CrossRef]

1992 (1)

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef] [PubMed]

1990 (1)

G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

1988 (1)

P. Rice and H. J. Carmichael, “Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit,” IEEE J. Quantum Electron. 24, 1351–1366 (1988).
[CrossRef]

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[CrossRef]

1968 (1)

F. Davidson and L. Mandel, “Photoelectric correlation measurements with time-to-amplitude converters,” J. Appl. Phys. 39, 62–66 (1968).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef] [PubMed]

Carmichael, H. J.

P. Rice and H. J. Carmichael, “Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit,” IEEE J. Quantum Electron. 24, 1351–1366 (1988).
[CrossRef]

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[CrossRef]

Davidson, F.

F. Davidson and L. Mandel, “Photoelectric correlation measurements with time-to-amplitude converters,” J. Appl. Phys. 39, 62–66 (1968).
[CrossRef]

Dobson, A. B.

A. B. Dobson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
[CrossRef]

Kimble, H. J.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[CrossRef]

Mandel, L.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[CrossRef]

F. Davidson and L. Mandel, “Photoelectric correlation measurements with time-to-amplitude converters,” J. Appl. Phys. 39, 62–66 (1968).
[CrossRef]

Rempe, G.

G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Rice, P.

P. Rice and H. J. Carmichael, “Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit,” IEEE J. Quantum Electron. 24, 1351–1366 (1988).
[CrossRef]

Schmidt-Kaler, F.

G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Tara, K.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef] [PubMed]

Vyas, R.

A. B. Dobson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
[CrossRef]

Walther, H.

G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

P. Rice and H. J. Carmichael, “Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit,” IEEE J. Quantum Electron. 24, 1351–1366 (1988).
[CrossRef]

J. Appl. Phys. (1)

F. Davidson and L. Mandel, “Photoelectric correlation measurements with time-to-amplitude converters,” J. Appl. Phys. 39, 62–66 (1968).
[CrossRef]

Phys. Rev. A (2)

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef] [PubMed]

A. B. Dobson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
[CrossRef]

Phys. Rev. Lett. (2)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[CrossRef]

G. Rempe, F. Schmidt-Kaler, and H. Walther, “Observation of sub-Poissonian photon statistics in a micromaser,” Phys. Rev. Lett. 64, 2783–2786 (1990).
[CrossRef] [PubMed]

Other (10)

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982); D. F. Walls, “Evidence for the quantum nature of light,” Nature 280, 451–454 (1979).
[CrossRef]

L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986); X. T. Zou and L. Mandel, “Photon-antibunching and sub-Poissonian statistics,” Phys. Rev. A 41, 475–476 (1990).
[CrossRef] [PubMed]

See H. J. Kimble and D. F. Walls, eds., feature on squeezed states of the electromagnetic field, J. Opt. Soc. Am. B 4, 1450–1741 (1987); P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” At. Mol. Opt. Phys. 28, 75–142 (1991).
[CrossRef]

H. J. Carmichael and D. F. Walls, “Proposal for the measurement of the resonant Stark effect by photon correlation techniques,” J. Phys. B 9, L43–L46 (1976); H. J. Kimble and L. Mandel, “Theory of resonance fluorescence,” Phys. Rev. A 13, 2123–2144 (1976).
[CrossRef]

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983); L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
[CrossRef] [PubMed]

C. Cohen-Tannoudji and J. Dalibard, “Single-atom laser spectroscopy. Looking for dark periods in fluorescence light,” Europhys. Lett. 1, 441–448 (1986); P. Zoller, M. Marte, and D. F. Walls, “Quantum jumps in atomic systems,” Phys. Rev. A 35, 198–207 (1987).
[CrossRef] [PubMed]

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

R. Vyas and S. Singh, “Quantum statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989); “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989); “Waiting-time distributions in the photodetection of squeezed light,” Phys. Rev. A PLRAAN 38, 2423–2430 (1988).
[CrossRef] [PubMed]

H. J. Carmichael, S. Singh, R. Vyas, and P. R. Rice, “Photoelectron waiting times and atomic state reduction in resonance fluorescence,” Phys. Rev. A 39, 1200–1218 (1989); H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
[CrossRef] [PubMed]

R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–949 (1980); The Quantum Theory of Light (Oxford Science, Oxford, 1983).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Random photon sequence, (b) bunched photon sequence, and (c) antibunched photon sequence.

Fig. 2
Fig. 2

(a) Normalized second-order intensity correlation g(2)(T) as a function of 2γT, showing violations of classical inequality (I) [inequality (4)]. (b) Waiting-time distribution w(T)/Iˆ as a function of 2γT for the HMDPO field [see the text following relation (6)]. The parameters for both of the curves are the following: mean photon number for the DPO, n¯d=0.28; mean photon number for the LO beam, n¯l=2; beam-splitter power transmissivity, T=0.75; DPO/LO phase angle, ϕ=90°.

Fig. 3
Fig. 3

(a) Normalized second-order intensity correlation function g(2)(T) as a function of 2γT, showing violations of classical inequality (II) [inequality (5)]. (b) Waiting-time distribution w(T)/Iˆ decreasing monotonically as a function of 2γ T for the HMDPO field. The parameters for both of the curves are as follows: mean photon number for the DPO, n¯d=0.28; mean photon number for the LO, n¯l=2; beam-splitter power transmissivity, T=0.75; DPO/LO phase angle, ϕ=90°.

Equations (6)

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w(T)=T:Iˆ(t){exp[-tt+T Iˆ(t)dt]}Iˆ(t+T):Iˆ,
w(0)<wc(0)
g(2)(T)=T:Iˆ(t)Iˆ(t+T):Iˆ2.
inequality(I)g(2)(0)1,
inequality(II)g(2)(0)g(2)(T).
g(2)(0)1w(0)wc(0).

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