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VARIOUS APPROACHES TO PHOTON ANTIBUNCHING IN SECOND-HARMONIC GENERATION 1

Adam Miranowicz, J. Bajer

Published Jan 1, 1998• 1 citation
OpenAlex

Abstract

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,

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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,
The study investigates antibunching, sub-Poissonian statistics, and photon correlation functions in the pump and harmonic modes of the seventh harmonic generation process.We investigated various approaches to photon antibunching by solving the generalised interaction Hamiltonian in the Heisenberg picture using short-time approximation.It is inferred that the number of pump photons, coupling of the field strength, and interaction times significantly influence photon antibunching.It is observed that third-order antibunching in the pump mode has greater nonclassicality than second-and first-order antibunching.In the harmonic mode, the nonclassical effect is found to be less pronounced and becomes more evident as the interaction time decreases.The first-order Hamiltonian interaction induces a stronger nonclassical effect than the second-order interaction.The interaction of a coherent pump field with a nonzero harmonic field leads to photon clustering and bunching effects.Finally, photon antibunching appears most pronounced, indicating nonclassicality, as the second-order correlation function decreases.This confirms that antibunching is a fundamental quantum property of light.
We studied photon antibunching in the pump and the harmonic modes of the sixth harmonic generation process. The generalized interaction Hamiltonian is solved for several particular cases in the Heisenberg picture, and the possibility of observing photon antibunching is investigated using the short-time approximation technique. It is shown that the photon antibunching in the pump field depends on the number of pump photons, the interaction time, and the coupling of the field between the modes. With the same amount of pump photons, we deduced that third-order photon antibunching is more nonclassical than second- and first-order photon antibunching. In this process, the effect of photon antibunching is not seen in the harmonic mode over pump mode. It is shown that photon antibunching is more noticeable with shorter interaction times as the depth of nonclassicality increases and the second-order correlation function decreases. The first-order Hamiltonian interaction, which stimulates both pump and harmonic fields, is demonstrated to be more nonclassical than the second-order Hamiltonian interaction. It is clear that the coherent state, or vacuum state, of a pump field with a nonzero harmonic field creates photon clusters because the pump field causes interaction, which leads to bunching effects. It is interpreted that the degree of photon antibunching is maximum in the regions where the second correlation function is minimum. Photon antibunching has been shown to be one of the quantum properties of light.
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.
Abstract We report on a step-by-step-series of experiments from statistical optics with classical light to undergraduate quantum optics with single-photon states, particularly suitable to paving an introductory way to quantum phenomena. We build up a progressive process analysing temporal variations of the irradiance of light discerned by measuring the value of the non-delayed second-order correlation function g (2) ( τ = 0). We demonstrate how Poisson distributed photoelectron counts from constant irradiance ( g (2) (0) = 1) can be used to calibrate the apparatus. Measurements with harmonically modulated irradiance of Poissonian light give an introduction to g (2) (0) correlation analysis. After these introductory steps, we demonstrate photon bunching with (pseudo-) thermal light ( g (2) (0) ≈ 2), and finally show quantum antibunching of photons in Fock states ( g (2) (0) ≈ 0). All measurements are in excellent agreement with the theoretical predictions.
A great deal of effort has been devoted during the last decade to the theory of nonclassical states of the radiation field. From a practical point of view some of the most interesting predictions of these theories concern the generation of light with sub-Poissonian photon counting statistics for which Such light is evidently less noisy than laser radiation with obvious implications for the improved performance of optical systems. When the temporal autocorrelation function of the photon counts increases as the delay time increases from zero the light is also said to be antibunched.
The concepts listed in the title are introduced and clarified. The relations among them are pointed out. It is shown that the corresponding optical phenomena are definitely of a quantum nature. The basic quantities which are measured in correlation optical experiments are discussed. Manifestations of photon antibunching and of sub-Poisson photon statistics in the recording of delayed coincidences, in the distribution of photon counts, and in intensity fluctuation spectra are analyzed. (More precisely, what is involved is the spectrum of fluctuations in the photocurrent; all the results of the theoretical analysis in this review are expressed in terms of directly measurable quantities.) A diagram technique for calculating the correlation characteristics of the radiation from a polyatomic system is outlined. Photon correlations in nonlinear resonance fluorescence are analyzed. There is a discussion of approaches to the development of macroscopic sources of radiation with sub-Poisson photon statistics: the production of a squeezed state of a field in phase-sensitive parametric effects in nonlinear optics and the introduction of repulsive statistics in luminescence excitation events and in the pumping of a laser. Experiments in these directions which had been reported through April 1986 are discussed. The practical importance of reducing the quantum noise in radiation for extremely precise measurements and for optical data transmission is pointed out.