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Sub-Poissonian Photon Statistics and Squeezed Quantum States

L. Mandeļ

Published Jun 18, 1984• 1 citation
OpenAlex

Abstract

The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.

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The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
Nonclassical effects such as squeezing, antibunching, and sub-Poissonian statistics of photons have been attracting attention in quantum optics over the last decade. Up to now most theoretical and experimental investigations have been carried out exclusively in the time domain while neglecting the spatial aspects by considering only one spatial mode of the electromagnetic field. In many situations such an approximation is well justified. There are, however, problems that do not allow in principle a single-mode consideration. This is the case when one wants to investigate the quantum fluctuations of light at different spatial points in the plane perpendicular to the direction of propagation of the light beam. Such an investigation requires a complete description of quantum fluctuations of light in both time and space and cannot be done within a single-mode theory. This space-time description brings about a natural generalization into the spatial domain of such notions as the standard quantum limit, squeezing, antibunching, etc. It predicts, for example, the possibility of generating a light beam with sub-Poissonian statistics of photons not only in time but also in the beam's transverse plane. Of particular relevance to the applications is a situation in which the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons in each. Photodetection of such a beam produces several sub-shot-noise photocurrents depending on the number of independent areas with sub-Poissonian statistics. This is in marked contrast to the case of a single-mode sub-Poissonian light beam in which any attempt to collect light from only a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of interesting new applications in optical imaging, optical parallel processing of information, parallel computing, and many other areas in which it is desirable to have a light beam with regular photon statistics across its transverse area. The aim of this review is to describe the recent development in this branch of quantum optics.
It is pointed out that, although squeezing and sub-Poissonian photon statistics need not go together, in the sense that an electromagnetic field may exhibit one but not the other, the method that is normally used to detect a squeezed state automatically generates sub-Poissonian photon statistics. However, when these considerations are applied to the fluorescence from a coherently driven atom, which exhibits both squeezing and sub-Poisson fluctuations, one finds that the statistics of the emitted photons show even larger departures from classical field theory than the squeezing.
Two manifestations of the quantum nature of coherent, resonant light scattering from atoms are photon antibunching and sub-Poissonian statistics. The existence of both effects has been demonstrated previously; in the present work, using individual barium atoms, measurements of the dependence of the latter effect on the frequency of the radiation field are presented. The distinction between the two phenomena is demonstrated by data that exhibit antibunching, yet have a photon counting distribution with variance equal to the Poisson value.
The concepts listed in the title are introduced and clarified. The relations among them are pointed out. It is shown that the corresponding optical phenomena are definitely of a quantum nature. The basic quantities which are measured in correlation optical experiments are discussed. Manifestations of photon antibunching and of sub-Poisson photon statistics in the recording of delayed coincidences, in the distribution of photon counts, and in intensity fluctuation spectra are analyzed. (More precisely, what is involved is the spectrum of fluctuations in the photocurrent; all the results of the theoretical analysis in this review are expressed in terms of directly measurable quantities.) A diagram technique for calculating the correlation characteristics of the radiation from a polyatomic system is outlined. Photon correlations in nonlinear resonance fluorescence are analyzed. There is a discussion of approaches to the development of macroscopic sources of radiation with sub-Poisson photon statistics: the production of a squeezed state of a field in phase-sensitive parametric effects in nonlinear optics and the introduction of repulsive statistics in luminescence excitation events and in the pumping of a laser. Experiments in these directions which had been reported through April 1986 are discussed. The practical importance of reducing the quantum noise in radiation for extremely precise measurements and for optical data transmission is pointed out.
A number of general features of non-classical states of light are reviewed. The phenomena of photon antibunching and sub-Poissonian photon statistics are then treated in more detail, including the experimental observations. Quantum effects in spontaneous parametric down-conversion are discussed, and recent experiments dealing with the time intervals between down-converted photons, with the intensity dependence of the cross-correlation function, and with the detection of a localized one-photon state are described. Finally, some quantum effects in the interference of light are discussed.