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Annalen der Physik

The Attributes of Nonclassical Light and their Mutual Relationship

Max Schubert

Published Jan 1, 1987• 6 citations
Publisher

Abstract

Abstract In the present paper the attributes of nonclassical light with respect to the theoretical basis, the experimental verification, and the applications are discussed and compared. If one ore more of the corresponding statistical measures (fluctuation excess, bunching excess, Poisson excess) attain negative values, surprising new properties of photon states occur. The analysis shows that under certain temporal and interaction conditions squeezing, antibunching, and sub‐Poisson behavior can accompany one or more of the other attributes. Also the connection of the attributes with the Glauber‐Sudarshan P‐representation of the corresponding states is studied and yields important assertions.

DOI
10.1002/andp.19874990104

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•Jun 18, 1984•1 citation
Abstract In the present paper the attributes of nonclassical light with respect to the theoretical basis, the experimental verification, and the applications are discussed and compared. If one ore more of the corresponding statistical measures (fluctuation excess, bunching excess, Poisson excess) attain negative values, surprising new properties of photon states occur. The analysis shows that under certain temporal and interaction conditions squeezing, antibunching, and sub‐Poisson behavior can accompany one or more of the other attributes. Also the connection of the attributes with the Glauber‐Sudarshan P‐representation of the corresponding states is studied and yields important assertions.
In 1963 Glauber /Phys. Rev. 130, 2529 and 131, 2766/ published a basic theoretical study that revealed the broad variety of possible photon states. Later on a quantum-statistical analysis showed that states with classical analog (this light Is termed classical light) as well as states without classical analog (so-called nonclassical light) can occur. Following the definition given by Teich, Saleh, and Perina /JOSAB2 (1985) 275) nonclassical light exhibits one or more of the attributes squeezed, antibunched, sub-Poissonian, what is connected with a negative value of the field-fluctuation excess, the bunching excess, or the Poisson excess. These negative values mean quantum fluctuations below the classical standard quantum limits of ideal laser light; thus, nonclassical light may yield an essential improvement of the optical measurement accuracy, in particular of the signal-to-noise ratio. There exists a common property of the three attributes concerning the Glauber-Sudarshan representation P(c ), which is the real weight function belonging to the incoherent mixture (density operators) of Glauber states with different complex amplitudes. In the case of classical light P(oç ) is a positive definite function, whereas nonclassical light requires a nonpositive definite function P(o.), which cannot be interpreted as a proper probability distribution - as it is possible in the case of light with a classical analog /M. Schubert, Ann. d. Phys. 4k (1987) 53/. In addition to its possible important applications nonclassical light yields a deep insight into the quantum nature of the radiation field.
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.
Light exists in many different forms that exhibit surprising properties. These properties can be harnessed to understand fundamental processes associated with subtle effects of light and help develop new kinds of devices capable of making high-precision measurements. To understand the different forms of light, there are two major theoretical frameworks: (1) semiclassical theory and (2) complete quantum theory. Although semiclassical theory offers simplicity, it does not account for quantum behavior, whereas quantum theory is capable of explaining almost all the existing forms of light including bunching, anti-bunching, and their variants. Such light is known to exhibit distributions that are not Poisson in nature and can exhibit sub- and super-Poisson behavior. In this chapter, we will also briefly discuss how to generate these unusual forms of light.
The generation of nonclassical light has recently received a great deal of attention because three forms of it have now been observed in the laboratory: antibunched light, photon-number-squeezed (or sub-Poisson) light, and quadrature-squeezed light. These characteristics may, but need not, accompany each other in any given light source. Nonclassical light has been produced in experiments using resonance fluorescence, the Franck-Hertz effect, parametric interact ions, and semiconductor light sources. It is likely to be useful in providing new insights in various physical and biological processes, and in applications such as lightwave communications. Some of the characteristics, methods of generation, and expected uses of squeezed light will be addressed.
A review is made of some quantum effects that have no classical analogs: antibunching and sub-Poisson statistics of photons, violation of the classical Cauchy-Schwarz inequality, and squeezed states of light. Nonclassical effects in the generation of harmonics and collective resonance fluorescence are investigated. Various schemes for generating squeezed states of light are proposed, and conditions for obtaining highly squeezed states are indicated. Possible applications of quantum light are also discussed.
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.