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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 11, Iss. 6 — Jun. 1, 1994
  • pp: 1130– 1141

Semiclassical versus quantum behavior in fourth-order interference

Jeffrey H. Shapiro and Ke-Xun Sun  »View Author Affiliations

JOSA B, Vol. 11, Issue 6, pp. 1130- 1141 (1994)

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A theoretical construct is presented for fourth-order interference between the signal and the idler beams of a parametric downconverter. Previous quantum treatments of fourth-order interference have employed correlated single-photon wave packets. The introduced approach, however, relies on Gaussian-state field correlations, which were previously used to characterize quadrature-noise squeezing produced by an optical parametric amplifier and nonclassical twin-beam generation in an optical parametric oscillator. Three principal benefits accrue from the correlation-function formalism. First, the quantum theory of fourth-order interference is unified with that for the other nonclassical effects of χ(2) interactions, i.e., squeezing and twin-beam production. Second, the semiclassical photodetection limit on Gaussian-state fourth-order interference is established; a purely quantum effect can be claimed at fringe visibilities substantially below the 50% level. Finally, both photon-coincidence counting (within the low-photon-flux regime) and intensity interferometry (in the high-photon-flux limit) are easily analyzed within a common framework.

© 1994 Optical Society of America

Jeffrey H. Shapiro and Ke-Xun Sun, "Semiclassical versus quantum behavior in fourth-order interference," J. Opt. Soc. Am. B 11, 1130- 1141 (1994)

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  17. Because we have suppressed the spatial and polarization characteristics of these fields, we say that our parametric interaction is degenerate if ωs = ωI = ωP/2 and nonde-generate if |Ωs - ωI| » Δω, where Δω is the common bandwidth of the signal and the idler emissions. Our development implicitly assumes that the signal and the idler beams are nondegenerate in either space or in polarization when they are degenerate in frequency. Spatial nondegen-eracy is ordinarily the case in parametric downconverters, and type-II phase-matched OPA’s and OPO’s produce orthogonally polarized signal and idler beams, so little generality is lost through this implicit assumption.
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  24. This result does not depend on assuming that P (ω) is an even function.
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  26. This quantum preservation of joint Gaussian behavior is just like the well-known result for classical Gaussian random processes (see, e.g., Ref. 24, Chap. 3). It can be proved by performance of the state transformation implied by Eq. (39) with antinormally ordered characteristic functions.28 [CrossRef] [PubMed]
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  29. Strictly speaking, we are concerned with a coincidence-rate dip at T = 0, not with a white-light fringe. Thus an experimentalist might prefer to gauge the depth of the destructive interference that occurs at T = 0 by computing {maxT[C(T; τg)] - minT[C(T; τg)]}/maxT[C(T; τg)] rather than γ.
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  33. The configuration considered by Ou and Mandel32 is not that of the dispersion-cancellation experiment. Their principal assumption, however, is configuration independent; they require the coincidence-gate duration to be much longer than both the field- and the intensity-correlation times of the signal and the idler beams. Thus the Ou-Mandel proof can be adapted to the Fig. 1 configuration. [CrossRef] [PubMed]
  34. Y. H. Shih, A. V. Sergienko, M. H. Rubin, T. E. Kiess, and C. O. Alley, "Two-photon interference in a standard Mach-Zehnder interferometer," Phys. Rev. A (to be published).
  35. Our concluding analysis from Subsection 3.A can be adapted to show that the nonergodic classical-field model from Eqs. (65) and (66) does not predict high-visibility coincidence-rate fringes. The Ou-Mandel theory32 can be used to disqualify any ergodic model from producing high-visibility fringes.

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