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Physical Review A

Nonclassicality of vortex Airy beams in the Wigner representation

Rui‐Pin Chen, C. H. Raymond Ooi

Published Oct 28, 2011• 16 citations
Publisher

Abstract

The Wigner distribution function (WDF) of a vortex Airy beam is calculated analytically. The WDF provides intuitive pictures of the intriguing features of vorticity in phase space. The nonclassical property of the vortex Airy beam and the Airy beam is analyzed through the negative parts of the WDF. The study shows that destructive interference of certain classical waves can mimic nonclassical lights such as those due to quantum effects.

DOI
10.1103/physreva.84.043846

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The Wigner distribution function (WDF) of a vortex Airy beam is calculated analytically. The WDF provides intuitive pictures of the intriguing features of vorticity in phase space. The nonclassical property of the vortex Airy beam and the Airy beam is analyzed through the negative parts of the WDF. The study shows that destructive interference of certain classical waves can mimic nonclassical lights such as those due to quantum effects.
In the framework of the spatial coherence wavelets, different features of the first-order spatial coherence (Young's interference) are analysed by calculating the corresponding marginal power spectrum, a close related quantity to the classical Wigner Distribution Function (WDF) of the optical field. The consideration of radiant and virtual point sources evidences some effects, conventionally attributed to non-classical correlations of light, although such type of correlations are not explicitly included in the model. Specifically, a light state is produced that has similar morphology to the WDF of the well-known quantum Schrödinger cat state.
Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schr\"odinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.
We have considered optical beams with phase singularity and experimentally verified that these beams, although classical, have properties of two-mode entanglement in quantum states. We have observed the violation of Bell's inequality for continuous variables using the Wigner distribution function (WDF) proposed by P. Chowdhury et al. [Phys. Rev. A 88, 013830 (2013)]. Our experiment establishes an alternate form of Bell's inequality in terms of the WDF which can be used for classical as well as quantum systems.
The Wigner Distribution Function (WDF), defined for a phase space representation in quantum mechanics, offers an alternate form for representing signals simultaneously in Fourier reciprocal variables such as time, and frequency. A purely nonnegative function that is closely related to the WDF, is the so‐called ’’spectrogram’’. In this paper we describe three types of optical setups for the production of the spectrogram. They use coherent, partially coherent or temporally incoherent light as illumination. As application example speech signals are processed for a speaker verification.