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Journal of Physics B Atomic and Molecular Physics

Antibunching phenomena on single-scatterer fluorescence in the weak-field limit

A. A. Villaeys

Published Apr 14, 1980• 3 citations
Publisher

Abstract

Antibunching phenomena have been extensively discussed previously (1979) in the case of an intense driving field. Previously the intensity correlation function has been obtained in the so-called weak-field case by a limiting procedure. The author gives a description of weak light beams from a general light scattering point of view which has not been given previously. He shows that some specific phenomena like the indistinguishability of the photons or the wavepacket structure of the weak light beam have been neglected in earlier works by the use of their limiting procedure. He describes the scatterer rigorously, so the dynamical evolution is not restricted to the particular case of two-level atoms as in all previous work. Even with weak fields and a two-level system his result exhibits a supplementary contribution associated with the boson character of the photon. In addition the theory is extended to cover near-resonant phenomena.

DOI
10.1088/0022-3700/13/7/009

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Annual Meeting Optical Society of America•Jan 1, 1993•2 citations
Antibunching phenomena have been extensively discussed previously (1979) in the case of an intense driving field. Previously the intensity correlation function has been obtained in the so-called weak-field case by a limiting procedure. The author gives a description of weak light beams from a general light scattering point of view which has not been given previously. He shows that some specific phenomena like the indistinguishability of the photons or the wavepacket structure of the weak light beam have been neglected in earlier works by the use of their limiting procedure. He describes the scatterer rigorously, so the dynamical evolution is not restricted to the particular case of two-level atoms as in all previous work. Even with weak fields and a two-level system his result exhibits a supplementary contribution associated with the boson character of the photon. In addition the theory is extended to cover near-resonant phenomena.
The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.
The statistical properties of fluorescent light from a single two-level atom driven by nonclassical light beams that exhibit antibunching and squeezing are discussed in the weak-field limit. The fields produced in intracavity second-harmonic generation and those produced by superposing the light from a degenerate parametric oscillator with a coherent field are considered to be the models of nonclassical light beams. These fields can be described in terms of real Gaussian random processes with nonzero mean coherent components. Analytical expressions for the fluorescent light intensity, the second-order intensity correlation function, and the variance of the photon number in the steady state are obtained. The effects of driving-field correlations, detuning, and other parameters characterizing the atom-field interaction on the statistics of scattered light are investigated. It is found that for a certain range of parameters the second-order intensity correlation function may vanish at nonzero times. Under certain other circumstances the antibunching of the fluorescent photons is enhanced. These and other interesting features that appear in the scattered light are discussed.
Statistical properties of fluorescent light from a single two-level atom driven by a beam of antibunched light are discussed in the weak field limit. Fields generated by realistic open systems with pumping and dissipation are chosen to be the models for antibunched light. As examples, we consider fields produced in intracavity second harmonic generation and in the homodyned degenerate parametric oscillator. These fields can be described in terms of real Gaussian random processes with coherent components. Analytical expressions for fluorescent light intensity and second order intensity correlation function in the steady state are derived. Effects of driving field correlations, detuning, and parameters characterizing the driving field on the statistics of scattered light are investigated. It is found that over a certain range of parameters characterizing the driving field the second order intensity correlation function may vanish at non-zero time. These and other interesting features will be discussed.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.
Under usual laboratory conditions the absorption of a beam of light by a dilute two-level medium depends on the intensity and spectrum of the incident light. If the incident photon flux is small compared to the decay rate of the absorber’s excited state, saturation effects can be neglected and only the spectrum of the light is important; thus, weak-field absorption depends only on the firstorder correlation function of the incident light. This result relies, however, on a requirement that the incident beam cross-section be much larger than the absorption cross-section of an atom. Then individual atoms act as low efficiency scatterers and the statistics of the scattering process is governed by the law of large numbers applied to many scattering sites. In contrast, if it is arranged that just one atom significantly absorbs (scatters) a beam of photons, correlation functions of the incident light beyond the first-order must be considered. For a beam that is focused within an absorption cross-section, we might naively predict that every photon will be scattered and none transmitted. In fact, even for a very weak beam there is a finite probability for two photons to arrive at the atom within the excited state lifetime, and in this event at least one of them will be transmitted (statistical saturation). In this paper we calculate the transmitted photon flux for a weak beam of photons focussed strongly onto a single, resonant two-state atom. We study the dependence of the transmitted flux on the statistics of the incident photons. Photon beams derived from sources of coherent, chaotic, squeezed, coherent-antibunched, and broadband-antibunched light are considered. our calculations are based on a recently developed theory of cascaded open systems,1,2 and serve to illustrate the usefulness of this theory.