Abstract

We introduce the concept of higher-order super-Poissonian and sub-Poissonian statistics and show that higher-order sub-Poissonian statistics is a signature of a nonclassical field. Fields generated in intracavity second-harmonic generation and single-atom resonance fluorescence are shown to exhibit higher-order sub-Poissonian statistics.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. Kimble and D. F. Walls, eds., feature on squeezed states of the electromagnetic field, J. Opt. Soc. Am. B 4 (10), (1987).
  2. P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” Adv. At., Mol., Opt. Phys. 28, 75–142 (1991).
    [CrossRef]
  3. U. Fano, “Ionization yield of radiation. II. fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
    [CrossRef]
  4. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
    [CrossRef] [PubMed]
  5. 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]
  6. J. Perina, Quantum Statistics of Linear and Nonlinear Optical Phenonena, 2nd ed. (Kluwer, Dordrecht, The Netherlands, 1991).
  7. J. Perina, Jr., and J. Perina, “Quantum statistics of a nonlinear optical coupler,” in Progress in Optics, by E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. 41, pp. 361–419.
  8. C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721–1724 (1990).
    [CrossRef] [PubMed]
  9. R. Vyas and S. Singh, “Higher-order nonclassical effects in a parametric oscillator,” Phys. Rev. A 62, 033803 (5) (2000).
    [CrossRef]
  10. A. B. Dodson and R. Vyas, “Homodyne photon statistics of the subthreshold degenerate parametric oscillator,” Phys. Rev. A 47, 3396–3412 (1993).
    [CrossRef] [PubMed]
  11. P. D. Drummond and C. W. Gardiner, “Generalized P-representations in quantum optics,” J. Phys. A 13, 2353–2368 (1980).
    [CrossRef]
  12. R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–945 (1980).
    [CrossRef]
  13. P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
    [CrossRef]
  14. G. S. Holliday and S. Singh, “Enhancement of antibunching in second harmonic generation,” in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1990), pp. 509–512.
  15. Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
    [CrossRef] [PubMed]
  16. R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
    [CrossRef] [PubMed]
  17. R. Vyas and S. Singh, “Quantum Statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989).
    [CrossRef] [PubMed]
  18. R. Vyas and S. Singh, “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989).
    [CrossRef] [PubMed]
  19. R. Vyas and S. Singh, “Antibunching and photoemission waiting times,” J. Opt. Soc. Am. B 17, 634–637 (2000).
    [CrossRef]
  20. S. Singh, “Antibunching, sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence,” Opt. Commun. 44, 254–258 (1983).
    [CrossRef]
  21. S. Singh, “Photon statistics in resonance fluorescence with finite bandwidth excitation,” in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), pp. 457–463.
  22. 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).
    [CrossRef] [PubMed]
  23. H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
  24. H. F. Arnoldus and G. Nienhuis, “Photon statistics of fluorescence radiation,” Opt. Acta 33, 691–702 (1986).
    [CrossRef]

2000 (2)

R. Vyas and S. Singh, “Higher-order nonclassical effects in a parametric oscillator,” Phys. Rev. A 62, 033803 (5) (2000).
[CrossRef]

R. Vyas and S. Singh, “Antibunching and photoemission waiting times,” J. Opt. Soc. Am. B 17, 634–637 (2000).
[CrossRef]

1996 (1)

R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
[CrossRef] [PubMed]

1993 (1)

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

1992 (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]

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

1991 (1)

P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” Adv. At., Mol., Opt. Phys. 28, 75–142 (1991).
[CrossRef]

1990 (1)

C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721–1724 (1990).
[CrossRef] [PubMed]

1989 (3)

R. Vyas and S. Singh, “Quantum Statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989).
[CrossRef] [PubMed]

R. Vyas and S. Singh, “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989).
[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).
[CrossRef] [PubMed]

1986 (1)

H. F. Arnoldus and G. Nienhuis, “Photon statistics of fluorescence radiation,” Opt. Acta 33, 691–702 (1986).
[CrossRef]

1983 (1)

S. Singh, “Antibunching, sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence,” Opt. Commun. 44, 254–258 (1983).
[CrossRef]

1981 (1)

P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

1980 (2)

P. D. Drummond and C. W. Gardiner, “Generalized P-representations in quantum optics,” J. Phys. A 13, 2353–2368 (1980).
[CrossRef]

R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–945 (1980).
[CrossRef]

1979 (1)

1947 (1)

U. Fano, “Ionization yield of radiation. II. fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[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]

Arnoldus, H. F.

H. F. Arnoldus and G. Nienhuis, “Photon statistics of fluorescence radiation,” Opt. Acta 33, 691–702 (1986).
[CrossRef]

Carmichael, H. J.

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).
[CrossRef] [PubMed]

Dodson, A. B.

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

Drummond, P. D.

P. D. Drummond and C. W. Gardiner, “Generalized P-representations in quantum optics,” J. Phys. A 13, 2353–2368 (1980).
[CrossRef]

Drumond, P. D.

P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

Fano, U.

U. Fano, “Ionization yield of radiation. II. fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[CrossRef]

Gardiner, C. W.

P. D. Drummond and C. W. Gardiner, “Generalized P-representations in quantum optics,” J. Phys. A 13, 2353–2368 (1980).
[CrossRef]

Holliday, G. S.

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

Kimble, H. J.

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

Lee, C. T.

C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721–1724 (1990).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–945 (1980).
[CrossRef]

Mandel, L.

McNeil, K. J.

P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

Milonni, P. W.

P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” Adv. At., Mol., Opt. Phys. 28, 75–142 (1991).
[CrossRef]

Nienhuis, G.

H. F. Arnoldus and G. Nienhuis, “Photon statistics of fluorescence radiation,” Opt. Acta 33, 691–702 (1986).
[CrossRef]

Qu, Y.

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

Rice, P. R.

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).
[CrossRef] [PubMed]

Singh, S.

R. Vyas and S. Singh, “Higher-order nonclassical effects in a parametric oscillator,” Phys. Rev. A 62, 033803 (5) (2000).
[CrossRef]

R. Vyas and S. Singh, “Antibunching and photoemission waiting times,” J. Opt. Soc. Am. B 17, 634–637 (2000).
[CrossRef]

R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
[CrossRef] [PubMed]

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” Adv. At., Mol., Opt. Phys. 28, 75–142 (1991).
[CrossRef]

R. Vyas and S. Singh, “Quantum Statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989).
[CrossRef] [PubMed]

R. Vyas and S. Singh, “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989).
[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).
[CrossRef] [PubMed]

S. Singh, “Antibunching, sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence,” Opt. Commun. 44, 254–258 (1983).
[CrossRef]

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.

R. Vyas and S. Singh, “Higher-order nonclassical effects in a parametric oscillator,” Phys. Rev. A 62, 033803 (5) (2000).
[CrossRef]

R. Vyas and S. Singh, “Antibunching and photoemission waiting times,” J. Opt. Soc. Am. B 17, 634–637 (2000).
[CrossRef]

R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
[CrossRef] [PubMed]

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

R. Vyas and S. Singh, “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989).
[CrossRef] [PubMed]

R. Vyas and S. Singh, “Quantum Statistics of broadband squeezed light,” Opt. Lett. 14, 1110–1112 (1989).
[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).
[CrossRef] [PubMed]

Walls, D. F.

P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

Wang, C.

R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
[CrossRef] [PubMed]

Xiao, M.

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

Adv. At., Mol., Opt. Phys. (1)

P. W. Milonni and S. Singh, “Some recent developments in the fundamental theory of light,” Adv. At., Mol., Opt. Phys. 28, 75–142 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

P. D. Drummond and C. W. Gardiner, “Generalized P-representations in quantum optics,” J. Phys. A 13, 2353–2368 (1980).
[CrossRef]

Opt. Acta (2)

P. D. Drumond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation. II. Quantum theory,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

H. F. Arnoldus and G. Nienhuis, “Photon statistics of fluorescence radiation,” Opt. Acta 33, 691–702 (1986).
[CrossRef]

Opt. Commun. (1)

S. Singh, “Antibunching, sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence,” Opt. Commun. 44, 254–258 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

U. Fano, “Ionization yield of radiation. II. fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[CrossRef]

Phys. Rev. A (8)

C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721–1724 (1990).
[CrossRef] [PubMed]

R. Vyas and S. Singh, “Higher-order nonclassical effects in a parametric oscillator,” Phys. Rev. A 62, 033803 (5) (2000).
[CrossRef]

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

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]

R. Vyas and S. Singh, “Photon-counting statistics of the degenerate parametric oscillator,” Phys. Rev. A 40, 5147–5159 (1989).
[CrossRef] [PubMed]

Y. Qu, M. Xiao, G. S. Holliday, S. Singh, and H. J. Kimble, “Enhancement of photon antibunching by passive interferometry,” Phys. Rev. A 45, 4932–4943 (1992).
[CrossRef] [PubMed]

R. Vyas, C. Wang, and S. Singh, “Homodyne detection for the enhancement of antibunching,” Phys. Rev. A 54, 2391–2396 (1996).
[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).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–945 (1980).
[CrossRef]

Other (6)

G. S. Holliday and S. Singh, “Enhancement of antibunching in second harmonic generation,” in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1990), pp. 509–512.

J. Perina, Quantum Statistics of Linear and Nonlinear Optical Phenonena, 2nd ed. (Kluwer, Dordrecht, The Netherlands, 1991).

J. Perina, Jr., and J. Perina, “Quantum statistics of a nonlinear optical coupler,” in Progress in Optics, by E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. 41, pp. 361–419.

H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).

S. Singh, “Photon statistics in resonance fluorescence with finite bandwidth excitation,” in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), pp. 457–463.

H. J. Kimble and D. F. Walls, eds., feature on squeezed states of the electromagnetic field, J. Opt. Soc. Am. B 4 (10), (1987).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic of the setup for homodyne detection of the light produced in IHSG: LO, coherent local oscillator; BS, lossless beam splitter; D, detector.

Fig. 2
Fig. 2

Parameter Sl for the HISHG light as a function of 2γT for l=27. Parameters are n¯o=106, n¯=0.2, n¯l=0.1998 (in units of n¯o), ϕ=π, and transmittivity T=0.5. Sl<0 indicates second- and higher-order sub-Poissonian statistics.

Fig. 3
Fig. 3

Parameter Sl for the light from a coherently driven single two-level atom as a function of βT for l=25 and Rabi frequency Ω=0.5. Sl<0 indicates second- and higher-order sub-Poissonian statistics.

Equations (35)

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

m(2)-m2<0.
m(l)=m=l m(m-1)(m-l+1)p(m, T),
Sl=m(l)ml-1.
m(l+k)m(j-k)m(l)m(j),
Sl+1=m(l)ml=m(l)m(l-1)mm(l-1)m(l-2)m×m(l-2)m(l-3)mm(2)mm.
Sl0.
β1=αT+|αl|exp(iϕ)R,
β2=|αl|exp(iϕ)T-αR,
β1*=α*T+|αl|exp(-iϕ)R,
β2*=|αl|exp(-iϕ)T-α*R.
G(s, T)=exp-sη 0T I(t)dt,
I(t)=2γ(β1β1*)=2γ {Tα*α+R|αl|2+RT |αl|[α exp(-iϕ)+α* exp(iϕ)]}.
m(l)=m=1 m(m-1)(m-l+1)p(m, T)=(-1)ldldslG(s, T)s=0.
α˙=-γ(α-E)-γα*α2no+iγno αξ,
α˙*=-γ(α*-E)-γαα*2no+iγno α*ξ*.
α=no[n¯+i(u1+u2)],
α*=no[n¯+i(u1-u2)].
ui(t)uj(t)=δijγn¯4noλi exp(-λi|t-t|),
i=1,2,
G(s, T)=Q1(s, T)exp[-f1(s, T)]Q2(s, T)×exp[-f2(s, T)],
Qi(s, T)
=exp(λiT/2)[cosh(ziT)+½(λi/zi+zi/λi)sinh(ziT)]1/2,
fi(s, T)
=KiTλi2zi24+λiT2+λiT+2λiBiT2+(2Bi-λi)T-2-2Biλizi2CiBiT-1,
Ci=cosh(ziT/2)+(λi/zi)(4+λiT/λiT)sinh(ziT/2)cosh(ziT/2)+(zi/λi)sinh(ziT/2),
zi2=λi2+(-1)i2sηnγ¯2T,
Bi=(-1)iγ2sηn¯Tλi
K1=2γsηn0(n¯T+n¯lR cos ϕ)2,
K2=2γsηn0n¯lR sin2 ϕ.
m(r)mr=r!Tr0T dtr0t2 dt1[1+λ(tr-tr-1)][1+λ(t2-t1)],
λ(τ)=-exp(-3βτ/2)cos(Ωβτ)+32Ω sin(Ωβτ),
Ω=[Ω/β)2-1/4]1/2,
Sl=m(r)mr-1=-1+2β2T21+Ω22β2r-1r!(3r-2)!.
Sl=m(r)mr-1=-1+r!n=1rr-1n-11n!-3/2βT1+Ω2/2β2r-n
=-3r(r-1)2βT11+Ω2/2β2+O(1/β2T2).

Metrics