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Reports on Progress in Physics

Non-classical effects in the statistical properties of light

R. Loudon

Published Jul 1, 1980• 308 citations
Publisher

Abstract

Measurements on non-classical effects fall into two categories depending on whether the two intensities or photon counts to be correlated refer to a single light beam or to two different beams. The main experimental work in the single-beam case is on resonance fluorescence; the relevant theory is reviewed in some detail, with particular emphasis on the simpler aspects of the calculations. Alternative proposals for generating non-classical single beams by non-linear optical experiments are reviewed more briefly. A similar coverage of double-beam experiments is given, with a detailed account of the theory of non-classical correlations between the light beams generated in two-photon cascade emission, and a briefer survey of corresponding non-linear optical experiments.

DOI
10.1088/0034-4885/43/7/002

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Measurements on non-classical effects fall into two categories depending on whether the two intensities or photon counts to be correlated refer to a single light beam or to two different beams. The main experimental work in the single-beam case is on resonance fluorescence; the relevant theory is reviewed in some detail, with particular emphasis on the simpler aspects of the calculations. Alternative proposals for generating non-classical single beams by non-linear optical experiments are reviewed more briefly. A similar coverage of double-beam experiments is given, with a detailed account of the theory of non-classical correlations between the light beams generated in two-photon cascade emission, and a briefer survey of corresponding non-linear optical experiments.
Expressions are derived for the intensity correlations or degrees of second-order coherence within and between two light beams of different frequency generated by cascade emission from a three-level atom. The atoms are assumed to be excited by two monochromatic coherent light beams in resonance with the upper and lower pairs of levels that constitute the triplet. The two emitted beams individually show photon antibunching and the correlation between the beams shows another complementary kind of non-classical effect. It is suggested that measurements on the system described here would provide more detailed information on quantum effects in cascade emission than previous observations with direct excitation to the uppermost atomic level by electron bombardment.
Abstract We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach to this type of problem by considering a Kolmogorov equation for the probability distribution of the atomic state, which takes into account first the deterministic evolution of this state under the effect of the incoming laser beam and second the random emission of photons during the spontaneous decay of the excited state(s) to the ground state. This approach yields solvable equations in the two level atom case. For the three level atom case we set the problem and clearly define its frame. The results obtained are valid in both opposite limits of rare and frequent spontaneous decay, compared to the period of the optical Rabi oscillations due to the interaction between resonant excitation and atomic levels. Our analysis gives access to various statistical properties of the fluorescence light, including one showing that its fluctuations in time are not invariants under time reversal. This result makes evident the fundamentally irreversible character of quantum measurements, represented here by the emission of photons of fluorescence.
Abstract The single-mode theory of Chapter 5 is inherently limited to the description of experiments that use time-independent light beams. The light is essentially nonergodic, in that its statistical fluctuations may be described by an ensemble, but these are not apparent in a time series of experiments made on the single member of the ensemble corresponding to a practical realization of the state. Identical measurements always give the same results and there are no time-dependent correlations of the kind considered in the classical theory of Chapter 3. Many of the nonclassical properties of light can be understood in terms of single-mode theory but other properties involve excitations of two or more modes. Practical observations of nonclassical effects are usually made on time-dependent light beams.
A number of general features of non-classical states of light are reviewed. The phenomena of photon antibunching and sub-Poissonian photon statistics are then treated in more detail, including the experimental observations. Quantum effects in spontaneous parametric down-conversion are discussed, and recent experiments dealing with the time intervals between down-converted photons, with the intensity dependence of the cross-correlation function, and with the detection of a localized one-photon state are described. Finally, some quantum effects in the interference of light are discussed.
This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.
Since the first observation of two-point correlation effects in optical fields (Hanbury, Brown, and Twiss, 1957) there has been continuous theoretical and experimental interest in photon correlation. In this paper we examine the possibility of measuring similar effects involving massive particles. We first discuss the theory of correlations between noninteracting massive particles by using the formalism of second quantization. This theory is considerably simpler than that for light because we can treat particles in the strictly nonrelativistic limit. However, the theory provides a particularly interesting contrast with the photon case because we may choose particles that are either fermions or bosons. We then apply the theory to the case of beams of atoms and neutrons and consider the experimental parameters of existing beams. In particular, we consider the case of experiments with laser-cooled metastable helium.