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Nonlinear Optics

Semiclassical vs. quantum behavior in fourth-order interference

Jeffrey H. Shapiro, Ke-Xun Sun

Published Dec 17, 2002• 1 citation
Publisher

Abstract

We explore semiclassical and quantum descriptions of fourth-order interference that are built upon classical and quantum Gaussian-state models for the signal and idler outputs from a parametric down converter. Our approach unifies the analysis of fourth-order interference with those for squeezing and photon twins. It also demonstrates that a purely-quantum fourth-order interference effect can be claimed at fringe visibilities substantially below the commonly accepted threshold of 50%. We start with a pair of models - one quantum and one classical - for the signal and idler fields produced by parametric down conversion.>

DOI
10.1109/nlo.1994.470783

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We explore semiclassical and quantum descriptions of fourth-order interference that are built upon classical and quantum Gaussian-state models for the signal and idler outputs from a parametric down converter. Our approach unifies the analysis of fourth-order interference with those for squeezing and photon twins. It also demonstrates that a purely-quantum fourth-order interference effect can be claimed at fringe visibilities substantially below the commonly accepted threshold of 50%. We start with a pair of models - one quantum and one classical - for the signal and idler fields produced by parametric down conversion.>
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.
The interference of signal and idler waves produced by optical parametric down-conversion was the object of a classic paper by Ghosh and Mandel [Phys. Rev. Lett. 1987, 59, 1903–1905] many years ago. In this paper we investigate the problem in the continuous variable regime, with the aim of identifying quantum signatures that arise from the entanglement of signal and idler waves. By using a model which allows for analytical calculations we show first of all that no quantum features appear for the interference in the fourth-order correlation function in the high-gain regime of parametric down-conversion. The quantum signatures emerge instead from the spatio-temporal correlation function of a generic quadrature component, and we demonstrate that they are clearly linked to the signal/idler entanglement. Relevant and useful links with the theory of quantum images complete the picture.
It is shown that both the visibility V =1/2 predicted for two-photon interference experiments with two independent sources and the visibility V = 1 predicted for two-photon interference experiments with a parametric down-conversion source can be explained in terms of a locally causal, adaptive, corpuscular, classical (non-Hamiltonian) dynamical system. Hence, there is no need to invoke quantum theory to explain the so-called nonclassical effects in the interference of signal and idler photons in parametric down conversion and a revision of the commonly accepted criterion of the nonclassical nature of light is called for.
A number of multiphoton interference schemes involving independent fields from parametric down-conversion are analyzed. They include fourth-order (two-photon) interference between two fields from two independent parametric down-conversion processes, interference with two independent single photon Fock states (produced by gated parametric down-conversion), and quantum state teleportation and entanglement swapping. It is shown that the visibility in these interference experiments is related to a quantity that is responsible for the photon bunching effect in one of the fields (signal or idler) from the parametric down-conversion process. Besides the two-photon interference schemes, a four-photon interference scheme is discussed where we consider four-photon partition at a beamsplitter. It is found that probability distribution of the partition is dramatically changed by four-photon interference of six paths and the four-photon effect also depends on the same quantity responsible for photon bunching. We will discuss the difference between two-photon interference and four-photon interference.