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Journal of the Optical Society of America B

Antibunching and photoemission waiting times

Reeta Vyas, Surendra Singh

Published Apr 1, 2000• 14 citations
Publisher

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.

DOI
10.1364/josab.17.000634

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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.
Antibunching is defined to be when the conditional waiting time in the photodetection is longer than the unconditional one. However, when this criterion is used on the waiting times for the closed-system detection of one photon from the so-called odd-shadowed thermal state, it shows no antibunching, although the state is proven to be non-classical. It does show antibunching in the waiting times for two-photon detection. This provides the motivation for extending the concept of photon antibunching to the detection of more than one photon. The general expressions for the expectation values of unconditional and conditional waiting times for multiphoton detection are derived. Then it is rigorously proven that multiphoton antibunching implies non-classicality which is defined to be when the P function is not positive definite.
We analyze the most popular approaches to photon antibunching as exemplified in a sim-ple model of second-harmonic generation. We find the exact evolution of the fundamental and harmonic fields for initial Fock states with small photon numbers. We show explicitly that definitions of photon antibunching based on the unnormalized, G(2)(t, t′), and normal-ized, g(2)(t, t′), two-time correlation functions describe distinct phenomena for nonstationary fields. For completeness, we also compare antibunching effects defined by the two-time and single-time correlations. 1 Photon antibunching Photon antibunching and sub-Poisson photon statistics (also called antibunching) reveal the quan-tum nature of light and therefore have received a great deal of attention during the last decades. The first detection of antibunched light by Kimble, Dagenais and Mandel [1] and first detection of sub-Poisson light by Short and Mandel [2] are regarded as milestones in the progress in quantum optics. In spite of many experimental and theoretical achievements, a deeper analysis of these effects seems to be necessary, particularly in the case of nonstationary fields. We shall clarify some of these aspects by referring to an example of second-harmonic generation. There are several commonly used definitions of photon antibunching for a single-mode radiation field (e.g., Refs. [1]–[9]): Definition I: The photon antibunching (see, e.g., Ref. [3]) occurs if the two-time light intensity correlation function G(2)(t, t+ τ) increases from its initial value at τ = 0,
Two standard criteria of the photon antibunching for non-stationary fields are compared. A new criterion, obtained by direct application of the Cauchy-Schwarz inequality, is proposed. All three definitions, based on the two-time correlation functions, are equivalent for stationary fields. However, the photon antibunching in the non-stationary regime is demonstrated to be not uniquely defined, since different criteria can lead to self-contradictory predictions. As an example, photon correlations of the signal mode in the parametric frequency converter are analysed analytically.
Wait-time distributions for the nthn\mathrm{th}nth photodetection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a photodetection, are considered. Simple analytic expressions are presented for several classical and quantum sources of light and are used to quantify and compare photon sequences generated by them. These distributions can be measured in photon-counting experiments and are useful in characterizing and generating photon sequences with prescribed statistics. The effects of nonunit detection efficiency are also discussed, and curves are presented to illustrate the behavior.