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Springer eBooks

Light Fields Represented by Binomial and Negative Binomial

H. C. Fan, Liyun Hu

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1007/978-981-95-1528-8_7

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The click statistics from on-off detector systems is quite different from the counting statistics of the more traditional detectors. This necessitates the introduction of new parameters to characterize the nonclassicality of fields from measurements using on-off detectors. To properly replace the Mandel Q(M) parameter, we introduce a parameter Q(B). A negative value represents a sub-binomial statistics. This is possible only for quantum fields, even for super-Poisson light. It eliminates the problems encountered in discerning nonclassicality using Mandel's Q(M) for on-off data.
The Glauber-Sudarshan P representation of negative binomial states is presented and its properties are discussed. It is shown that for the limiting cases the states approach the random-phase coherent state and the thermal noise state. Thus these states may allow a unified description of coherent and thermal states of the field. The two-dimensional representation of the P function is plotted on the complex-\ensuremath{\alpha} plane. The probability density function of waiting-time intervals between the arrivals of successive photons on a photodetector irradiated by a beam of the negative binomial light is also investigated.