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AIP conference proceedings

Quantum field theory and distance effects for polarization correlations in waveguides

T. Ishiwatari, Andrei Yu. Khrennikov, B. Nilsson, Igor Vasil'evich Volovich, Börje Nilsson, Louis Fishman, Anders Karlsson, Sven Nordebo

Published Jan 1, 2009• 7 citations
Publisher

Abstract

Quantization of Maxwell’s equations in waveguides is considered together with an analysis of the quantum correlation functions of the radiation field. Both the spatial and temporal dependence of the polarization correlation functions for entangled states are evaluated. Predictions for experiments for the study of the spatial dependence of the polarization correlation functions for entangled photons are given.

DOI
10.1063/1.3117105

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Quantization of Maxwell’s equations in waveguides is considered together with an analysis of the quantum correlation functions of the radiation field. Both the spatial and temporal dependence of the polarization correlation functions for entangled states are evaluated. Predictions for experiments for the study of the spatial dependence of the polarization correlation functions for entangled photons are given.
An investigation is made of the coherence of the electromagnetic field in a plane dielectric waveguide excited by an external field with specific coherence properties. The quantum theory of an electromagnetic field in one-dimensionally inhomogeneous media is employed to derive an expression which relates the correlation functions of the field inside the waveguide to the external field. This expression is used to study the variation of the coherence of the radiation at various distances z from the area where the radiation is coupled into the waveguide. If the external field has a finite line width, the spatial coherence is a periodic function of z when z ≪ z cr and tends to a constant value when z ≫ z cr . When z ≪ z cr , the temporal coherence is the same as for the external source, whilst when z ≫ z cr , the temporal coherence as a function of τ has maxima which move away from the point τ = 0 with increasing z . It is found that the coherence tunes τ 1 and τ 2 determined following Wolf and Mandel behave differently when z ≫ z cr : τ 1 2 increases quadratically with increasing z , whereas τ 2 tends to a constant value. The form of the radiation modulation spectrum is deduced. Curves are plotted for the spatial and temporal coherence by way of a specific example.
In this paper, we explore quantum control systems tuned by spatially varying functions, which are different from the broadly studied quantum control systems with time-dependent controls. Such control problems exist in the design of quantum waveguides and materials (e.g., fibers, photonic crystals, and metamaterials) and have not been considered from a control theoretic point of view. The spatial quantum control model is built from quantized Maxwell equations for dielectric waveguides, where the spatially varying dielectric parameters are taken as controls. The model can be applied to both passive and active dielectrics or their mixtures such as metamaterials. We derive the iterative equation for slab structures, which is analogous to a discrete-time control system. For homogeneous waveguides, the model is parallel with the well-known Langevin equation in the time domain. However, for inhomogeneous and dispersive waveguides, the control model becomes bilinear even for linear dielectric materials and hence is more complicated. The resulting input-output relation is derived in terms of irrational transfer functions, and the statistical properties of quantum noises are analyzed. This work provides a new perspective on modeling and analyzing quantum control systems, on the basis of which further design and optimization with spatial parameters can be explored.
The original quantum eraser scheme [Scully and Druhl, Phys. Rev. A 25, 2208 (1982)] is based on the entanglement of the two sequentially and spontaneously emitted photons. We consider the scheme in which the first emitted photon is largely detuned from resonance. We use the Schrodinger equation approach and the Laplace transform method to obtain the Raman Emission Doublet(RED) state vector. An exact analytical expression for the two-photon correlation function is derived in a general form that applies to any polarization of the two detectors located at any position, including the near field regime where the distances are comparable to the wavelengths of the photons. Frequency dependent refractive indexes of the RED photons are also included.
We analyze some aspects of recently performed Franson-type experiments with entangled photon pairs aimed to test Bell's inequalities. We point out that quantum theory leads to the coincidence rate between detectors which includes in fact a dependence on the distance. We study this dependence and obtain that for large distances the correlation function vanishes. Therefore with taking into account the space parts of wave functions of photons for large distances quantum mechanical predictions are consistent with Bell's inequalities. We propose an experimental study of space dependence of correlation functions in Bell-type experiments.
Abstract This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence are based on dynamical theries. The novel properties observed in the computations of such polarizations correlations, as predicted by QFT, is that they depend on the speed of the colliding particles, and, in some cases, even on coupling parameters ratios as well as on mass ratios of the underlying theory. These investigations clearly show that arguments based simply on combining spins to generate probabilities of such polarization correlations are not reliable. The novel properties obtained, with details of derivations provided here, hopefully would call for experiments on polarizations correlations which would monitor speeds of colliding particles, and, would, in turn, lead to new tests of the fundamental interactions of QFT such as of QED and of the Electroweak Theory.