This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.

Coherence Properties of Optical Fields

The production of pairs of entangled photons simply by focusing a laser beam onto a crystal with a nonlinear optical response was used to test quantum mechanics and to open new approaches in imaging. The development of the latter was enabled by the emergence of single-photon-sensitive cameras that are able to characterize spatial correlations and high-dimensional entanglement. Thereby, new techniques emerged, such as ghost imaging of objects — in which the quantum correlations between photons reveal the image from photons that have never interacted with the object — or imaging with undetected photons by using nonlinear interferometers. In addition, quantum approaches in imaging can also lead to an improvement in the performance of conventional imaging systems. These improvements can be obtained by means of image contrast, resolution enhancement that exceeds the classical limit and acquisition of sub-shot-noise phase or amplitude images. In this Review, we discuss the application of quantum states of light for advanced imaging techniques. Using quantum states of light for imaging both reveals quantum phenomena and enables new protocols that result in images that surpass classical limitations. Such systems require both quantum light sources and often the ingenious use of detector technologies.

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Imaging with quantum states of light

In this paper we start from our Quantum Noise IV model of a homogenously broadened maser and specialize to the case in which the number of photons and the population difference are the slowest changing variables In spite of the high coherence of the system, we find that by eliminating all other variables adiabatically we obtain the usual rate equations plus a set of noise sources with precisely those moments appropriate to shot noise Thus we justify McCumber's model for amplitude noise in a laser, and after making a quasi-linear approximation obtain his amplitude spectrum Comparison with exact calculations of Hempstead and Lax for the rotating wave van der Pol oscillator suggests that quasi-linear methods are accurate except within a factor 10 (in photon number) of threshold

Quantum noise VII: The rate equations and amplitude noise in lasers

The amplitude and phase noise spectra of the internal and external fields of a laser oscillator are calculated using the quantum mechanical Langevin equations. The outgoing field spectra are demonstrated to be different from the internal field spectra. The outgoing photon flux \hat{N} from a laser oscillator operating at far above the threshold has a spectral density equal to the classical shot noise level, 2\langle\hat{N}\rangle . On the other hand, the internal photon number spectrum is Lorentzian, and the variance is equal to the average photon number, \langle\hat{N}\rangle . The difference stems from the quantum mechanical interference between the transmitted internal field and the reflected zero-point fluctuation at the output coupling mirror. The relation between the present analysis and the previous noise theory of a laser is also discussed.

Internal and external field fluctuations of a laser oscillator: Part I--Quantum mechanical Langevin treatment

The production of pairs of entangled photons simply by focusing a laser beam onto a crystal with a non-linear optical response was used to test quantum mechanics and to open new approaches in imaging. The development of the latter was enabled by the emergence of single photon sensitive cameras able to characterize spatial correlations and high-dimensional entanglement. Thereby new techniques emerged such as the ghost imaging of objects - where the quantum correlations between photons reveal the image from photons that have never interacted with the object - or the imaging with undetected photons by using nonlinear interferometers. Additionally, quantum approaches in imaging can also lead to an improvement in the performance of conventional imaging systems. These improvements can be obtained by means of image contrast, resolution enhancement that exceed the classical limit and acquisition of sub-shot noise phase or amplitude images. In this review we discuss the application of quantum states of light for advanced imaging techniques.

/pdf/imaging-with-quantum-states-of-light-36gwijxgti.pdf

L. Mandel

Papers

Physical Significance of Operators in Quantum Optics