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Journal of Physics A Mathematical and General

Antibunching: more than one kind in two-photon absorption

G. P. Hildred, A G Hall

Published Aug 1, 1978• 7 citations
Publisher

Abstract

Properties of the second moment of the photon distribution and intensity autocorrelation function are examined in a system undergoing only two-photon transitions. These properties are interpreted in terms of two kinds of antibunching, strict and temporal. It is shown that antibunching is a richer class of phenomena than usually supposed and that temporal antibunching may be easier to observe than the strict antibunching usually considered.

DOI
10.1088/0305-4470/11/8/007

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•Jan 1, 1998•1 citation
Properties of the second moment of the photon distribution and intensity autocorrelation function are examined in a system undergoing only two-photon transitions. These properties are interpreted in terms of two kinds of antibunching, strict and temporal. It is shown that antibunching is a richer class of phenomena than usually supposed and that temporal antibunching may be easier to observe than the strict antibunching usually considered.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.
We analyze the most popular approaches to photon antibunching as exemplified in a sim-ple model of second-harmonic generation. We find the exact evolution of the fundamental and harmonic fields for initial Fock states with small photon numbers. We show explicitly that definitions of photon antibunching based on the unnormalized, G(2)(t, t′), and normal-ized, g(2)(t, t′), two-time correlation functions describe distinct phenomena for nonstationary fields. For completeness, we also compare antibunching effects defined by the two-time and single-time correlations. 1 Photon antibunching Photon antibunching and sub-Poisson photon statistics (also called antibunching) reveal the quan-tum nature of light and therefore have received a great deal of attention during the last decades. The first detection of antibunched light by Kimble, Dagenais and Mandel [1] and first detection of sub-Poisson light by Short and Mandel [2] are regarded as milestones in the progress in quantum optics. In spite of many experimental and theoretical achievements, a deeper analysis of these effects seems to be necessary, particularly in the case of nonstationary fields. We shall clarify some of these aspects by referring to an example of second-harmonic generation. There are several commonly used definitions of photon antibunching for a single-mode radiation field (e.g., Refs. [1]–[9]): Definition I: The photon antibunching (see, e.g., Ref. [3]) occurs if the two-time light intensity correlation function G(2)(t, t+ τ) increases from its initial value at τ = 0,