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Journal of Optics B Quantum and Semiclassical Optics

A comparative study of hyperbunching in the fluorescence from a bichromatically driven atom

Matthias Jakob, Yonatan Abranyos, János A. Bergou

Published Apr 27, 2001• 9 citations
Publisher

Abstract

Recently, Miranowicz et al compared three different definitions of antibunching in non-stationary fields and found that they are by no means equivalent. In particular, they may lead to contradictory predictions of the photon antibunching. We consider another violation of the Cauchy-Schwarz inequality in non-classical and non-stationary fields which we term as hyperbunching. Similarly, this leads to three different definitions of hyperbunching in non-stationary fields which, again, are by no means equivalent and may lead to contradictory predictions of this phenomenon. We analyse these different concepts of anti- and hyperbunching in the non-stationary resonance fluorescence from a bichromatically driven two-level atom.

DOI
10.1088/1464-4266/3/3/310

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Recently, Miranowicz et al compared three different definitions of antibunching in non-stationary fields and found that they are by no means equivalent. In particular, they may lead to contradictory predictions of the photon antibunching. We consider another violation of the Cauchy-Schwarz inequality in non-classical and non-stationary fields which we term as hyperbunching. Similarly, this leads to three different definitions of hyperbunching in non-stationary fields which, again, are by no means equivalent and may lead to contradictory predictions of this phenomenon. We analyse these different concepts of anti- and hyperbunching in the non-stationary resonance fluorescence from a bichromatically driven two-level atom.
Two standard criteria of the photon antibunching for non-stationary fields are compared. A new criterion, obtained by direct application of the Cauchy-Schwarz inequality, is proposed. All three definitions, based on the two-time correlation functions, are equivalent for stationary fields. However, the photon antibunching in the non-stationary regime is demonstrated to be not uniquely defined, since different criteria can lead to self-contradictory predictions. As an example, photon correlations of the signal mode in the parametric frequency converter are analysed analytically.
Previous work on the two-time photon-number correlations of quantum non-stationary fields has focused on the demonstration of self-contradictory predictions of the photon antibunching according to different definitions. In this paper we analyse the usefulness of the conventional and generalized definitions of photon bunching in a description of classical non-stationary light. It is proved that the generalized definition applied to classical fields predicts photon bunching but never antibunching. In contrast, the two conventional definitions are shown to improperly classify certain classical non-stationary fields as being antibunched.
We study the correlation between photons in the fluorescence light scattered from an atom driven by an intense bichromatic field having one strong and one weak component, with or without the use of frequency filters in front of the photodetectors. Depending on the filters used and on the spectral components selected, we predict signals corresponding either to bunching or to antibunching, and modulations at the driving field Rabi frequencies as well as at their sum and difference. In contrast with the case of monochromatic driving, the antibunching can occur between photons emitted into different (as well as the same) lines of the fluorescence spectrum.
Photon antibunching in resonance fluorescence - the emission from a single, resonantly driven two-level quantum emitter - is a paradigmatic signature of nonclassical light. Photon entanglement, by contrast, manifests as correlations that can defy any classical description and is typically regarded as a distinct quantum effect. Here, we experimentally extract pairs of narrowband, time-bin-entangled photons from the antibunched resonance fluorescence of a single trapped atom. We verify entanglement via violation of the CHSH Bell inequality and by reconstructing the two-photon density matrix. The observed correlations vanish when the coincidence time window exceeds the antibunching timescale, revealing underlying multimode entanglement in the emitted field. Our results establish a direct link between photon antibunching and photon-photon entanglement, unifying two canonical signatures of nonclassical light.
We identify discrepancies between two published predictions of the resonance fluorescence from a two-level atom driven by a strong bichromatic field [J. Opt. Soc. Am. B 8,8,8, 1163 (1991) and Phys. Rev. A 48,48,48, 3092 (1993)]. These discrepancies are shown to arise from subtleties in extracting the time-averaged resonance fluorescence from the expansions used to solve the optical Bloch equations. We construct a solution to these equations that corrects the results of the latter reference and reconciles the two predictions.