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AIP conference proceedings

On the correlations of polarizations in the system of two photons

Vladimir Lvovich Lyuboshitz, Vladimir Lvovich Lyuboshitz

Published Jan 1, 2007• 2 citations
Publisher

Abstract

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two‐photon state is described by the one‐photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. The correlations between the Stokes parameters in the case of the two‐photon decays are considered.

DOI
10.1063/1.2750778

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The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two‐photon state is described by the one‐photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. The correlations between the Stokes parameters in the case of the two‐photon decays are considered.
The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π0 → 2γ, η → 2γ, K 0 → 2γ, K 0 → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.
A theoretical study of the angular correlation and angular variation of entanglement between a photoelectron and a fluorescent photon in photoionization of atoms is provided. The formulation is developed for experiments where spin polarization of a photoelectron and polarization of the subsequent fluorescent photon are detected in a coincidence measurement. The applied formalism of parameterization of all polarization sensitivities of the detectors using Stokes parameters and of the use of statistical and efficiency tensors provides straightforward implementation for any experimental geometry. The framework is demonstrated in the case of calcium photoionization followed by radiative decay.
Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as, e.g., for states with undefined photon numbers, the instances of its increased value contribute more to the parameters. One can introduce normalized quantum Stokes operators. Operationally, for a given single run of the experiment, their values are differences of measured intensities (or photon numbers) at the two exits of a polarizer divided by their sum. Effects of intensity fluctuations are removed. Switching to normalized Stokes operators results in more sensitive entanglement conditions. We also show a general method of deriving an entanglement indicator for optical fields which use polarization correlations, which starts with any two-qubit entanglement witness. This allows one to vastly expand the family of such indicators.
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.
We examine whether the Stokes parameters of a two-mode electromagnetic field results from the superposition of the spins of the photons it contains. To this end we express any n-photon state as the result of the action on the vacuum of n creation operators generating photons which can have may different polarization states in general. We find that the macroscopic polarization holds as sum of the single-photon Stokes parameters only for the SU(2) orbits of photon-number states. The states that lack this property are entangled in every basis of independent field modes, so this is a class of entanglement beyond the reach of SU(2) transformations.