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Annual Meeting Optical Society of America

Nonclassical states of the radiation field

Mark S. Hillery

Published Jan 1, 1985• 0 citations
Publisher

Abstract

A nonclassical state of the electromagnetic field is a state whose P representation is not non-negative definite.1 Examples of such states are squeezed states and states with sub-Poissonian statistics. These states demonstrate the necessity of the quantum mechanical description of the radiation field.
DOI
10.1364/oam.1985.tht8

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The nonclassical measures of nonclassical properties of radiation fields are proposed in parallel with those of the nonclassical states. It is shown that the nonclassical measures of sub-Poissonian photon statistics and squeezing are bounded below 1/21/21/2 and their physical implications are discussed in comparison with the nonclassical measures of states.
A new operator-based condition for distinguishing classical from nonclassical states of quantized radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum-dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalization of the notion of sub-Poissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuations in quadratic combinations of mode annihilation and creation operators conserving the total photon number. This generalization is nontrivial and intrinsically two-mode as it goes beyond all possible single mode projections of the two-mode field. The nonclassicality of pair-coherent states, squeezed vacuum and squeezed thermal states is analysed and contrasted to one another, comparing the generalized sub-Poissonian statistics with extant signatures of nonclassical behaviour.
Recently, a new state of the quantized radiation field — the intermediate number squeezed state (INSS) — has been introduced in the literature: it interpolates between the number state |n> and the squeezed state |z, α>=Ŝ(z)|α>, and exhibits interesting nonclassical properties as antibunching, sub-Poissonian statistics and squeezing. Here we introduce a slight modification in the previous definition allowing us a proposal to generate the INSS. Nonclassical properties using a new set of parameters are also studied.
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.