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.
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.
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.
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,
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.
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.
Being bosons, photons like to group together, with the behavior of photon bunching described as an attribute of classical light. At the other extreme, photons emitted by a single emitter are expected to antibunch, trickling out of the emitter one at a time. Although bunching and antibunching are well established behaviors of classical and nonclassical light, respectively, the transition between the two has not been observed. It is expected that as the number of emitters is increased, a smooth transition should occur. Using a high-quality cavity into which they can place a variable number of atoms, Hennrich et al. show that they can probe the transition systematically as the number of emitters (atoms in the cavity) is gradually increased. They observe that the antibunching behavior disappears when the average number of atoms in the cavity is one, and they are able to explain the experimental data well if the emitters are assumed to form an independent ensemble. — ISO