Higher-order Coherence Functions Research Articles

Coherences of accelerated detectors and the local character of the Unruh effect

We study the locality of the acceleration temperature in the Unruh effect. To this end, we develop a new formalism for the modeling of macroscopic irreversible detectors. In particular, the formalism allows for the derivation of the higher-order coherence functions, analogous to the ones employed in quantum optics, that encode temporal fluctuations and correlations in particle detection. We derive a causal and approximately local-in-time expression for an Unruh-DeWitt detector moving in a general path in Minkowski spacetime. Moreover, we derive the second-order coherence function for uniformly accelerated Unruh-DeWitt detectors. We find that the fluctuations in detection time for a single Unruh-DeWitt detector are thermal. However, the correlations in detection time between two Unruh-DeWitt detectors with the same acceleration but separated by a finite distance are not thermal. This result suggests that the Unruh effect is fundamentally local, in the sense that the notion of acceleration temperature applies only to the properties of local field observables.

Astronomical applications of quantum optics for extremely large telescopes

A programme has been started to investigate photon properties that are not currently exploited in astronomical instruments, namely second- and higher-order coherence functions encoded in their arrival time, and the orbital angular momentum. This paper expounds the first results achieved in the study of a novel astronomical photometer capable of pushing time tagging towards the picosecond region. This conceptual device has been developed as a possible focal plane instrument for the future OverWhelmingly Large Telescope (OWL) of the European Southern Observatory. This instrument has been named QuantEYE, that is, the Quantum Eye of OWL.

Modeling of high-frequency propagation in inhomogeneous background random media.

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.

Higher-order Coherence Functions in the Space-frequency Domain

Abstract Some years ago a new coherence theory in the space-frequency domain was formulated. Subsequent research has revealed some difficulties regarding the representation, in this theory, of the higher-order correlation functions. In the present paper the origin of these difficulties is discussed and a new representation of the higher-order correlation functions is introduced, in terms of the coherent modes of the second-order theory.

Higher-order coherence functions of phase states

We study the quantum mechanical degree of high order coherence of the radiation field in the phase states introduced recently by Barnett and Pegg and use them to evaluate the photon-counting distribution and factorial moments. The results so obtained have been compared with those obtained from the coherent and chaotic radiation.

Stochastic geometrical theory of diffraction

The localization of high-frequency sound-wave propagation around ray trajectories, and the reflection and(or) diffraction of these local plane-wave fields by boundaries, inhomogeneities, and(or) scattering centers has been combined via the geometrical theory of diffraction (GTD) into one of the most effective means of analyzing high-frequency wave phenomena in complex deterministic environments. These constructs are here incorporated into a stochastic propagation and diffraction theory for statistical moments of the high-frequency field when the propagation medium has weak random fluctuations superimposed upon an inhomogeneous background profile, subject to the assumption that the correlation length ln of the fluctuations is small compared with the scale of variation, but large compared with the local wavelength λ=2π/k=2πv/ω, in the fluctuation-free background, with k being the local wavenumber, v the local wave speed, and ω the radian frequency. Canonical problems of deterministic GTD furnish the propagators and, in the presence of interfaces, boundaries, or other types of scatterers, the local reflection, refraction, and diffraction coefficients that relate incoming to outgoing wave fields. The major analytical building blocks include propagators described in local coordinates centered on the curved GTD ray trajectories in the deterministic inhomogeneous background environment; multiscale expansions in these coordinates to chart and solve for the propagation properties of statistical measures of the parabolically formulated ray fields; Kirchhoff or physical optics (PO) approximations, generated by stochastic GTD incident fields, to establish initial conditions for fields reflected from, or transmitted across, extended smooth surfaces; and ‘‘point scatterer’’ solutions to establish GTD initial conditions for small scatterers and edges. In addition to the conventional second- and higher-order coherence functions, there are introduced as appropriate statistical objects two-point random functions and corresponding higher-order functions which are useful in treating correlation of incident and of backward reflected or diffracted fields that traverse the same propagation volume. By this solution strategy, one gains access to a much larger class of high-frequency problems in a random medium than at present. Expressions for the average field and higher moments have been obtained for forward propagation in a fluctuating medium with inhomogeneous and caustic-forming background, for reflection and refraction due to a plane or smoothly curved interface in such a medium, and for diffraction due to a wedge and a small scatterer.

Propagation of Higher-Order Coherence Functions in Random Media*

In this paper, a general result is given for the coherence of any order of a wave propagating through a random medium, provided that the phase and the logarithm of the amplitude are gaussian random variables. Because theoretical and experimental work concerned with optical waves propagating through the atmosphere are in good agreement with the prediction of a gaussian random variable for these quantities, such an assumption appears reasonable. For this case, all higher-order coherence functions can be expressed in terms of the autocovariance and cross-covariance functions of log amplitude and phase. The general expression for the higher-order coherence function is shown to agree with the results of other workers for the mutual coherence function and the fourth-order coherence function for a plane monochromatic wave in a homogeneous random medium. However, the general expressions given may be applied for any case in which the covariance functions of log amplitude and phase are known, e.g., spherical-wave or beam-wave propagation, or propagation through a random medium with smoothly varying characteristics as a function of space.

Coherence Properties of Optical Fields II Study of Experiments Described by Fourth-Order Coherence Functions

The higher-order coherence functions of optical fields involving phase fluctuations have not yet been studied extensively. We discuss here an experiment which can in principle yield the fourth-order coherence function. This experiment is a study of the correlation function of the irradiance fluctuations obtained in some interference experiments. Two kinds of delay are then used: optical delays in the interferometer and electrical delays with suitable variations in the correlator.The results of the experiment are calculated theoretically with a particular statistical model of laser light. The possibility of using a spectrum analyzer instead of a correlator is discussed.

Higher-Order Coherence Functions of Optical Fields and Phase Fluctuations

Some properties of the higher-order coherence functions of optical fields are reviewed. A few experiments on light, beat, and interference are discussed by using the fourth-order coherence functions. The higher-order coherence functions of the amplitude-stabilized laser are derived by assuming the gaussian process for the phase fluctuations.

Classical Coherence Formulation of Second-Harmonic Generation in the Optical Parametric Amplifier

In this paper we extend the formulation of the propagation of higher-order coherence functions in nonlinear media to include optical parametric amplification. It is shown that, in the strictly monochromatic limit the coherence formulation leads exactly to the solutions previously reported. This is demonstrated for complete phase matching. In addition, the quasi-monochromatic case is also considered and suggests that measurements of the higher-order coherence functions can give information about the nonlinear medium.

Propagation of Higher-Order Coherence Functions in Optically Lossy Media

In this paper we extend the calculation of the propagation of the mutual power spectrum, Γˆ(x1,x2,ν), for nonlinear dielectrics to the case of optically lossy media. In particular, in the quasi-monochromatic limit, the dependence of the mutual coherence function of the second harmonic wave on the full fourth-order coherence of the incoming radiant flux is discussed. An experiment utilizing this phenomenon is suggested.