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Journal of Modern Optics

Quantum phase measurements and non-classical polarization states of light

A. P. Alodjants, Sergei M Arakelyan

Published Mar 1, 1999• 44 citations
Publisher

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.

DOI
10.1080/09500349908231279

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In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.
In our paper we consider the behavior of both the Hermitian (observable) Stokes parameters of light and the phases difference that describes the polarization state of optical field. In general case we introduce two pairs of phase operators associated with the phase angles in 3D picture for the polarization Stokes parameters of light on the Poincare sphere. The special eight-port polarization interferometer is presented for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phases and also of their fluctuations. It is shown that an anisotropic (spatio-periodically) Kerr-like nonlinear medium placed in the polarization interferometer can be used for generation and observation of the polarization-squeezed phase states of light.
In our paper we consider the behavior of both the Hermitian (observable) Stokes parameters of light and the phases difference that describes the polarization state of optical field. In general case we introduce two pairs of phase operators associated with the phase angles in 3D picture for the polarization Stokes parameters of light on the Poincare sphere. The special eight-port polarization interferometer is presented for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phases and also of their fluctuations. It is shown that an anisotropic (spatio-periodically) Kerr-like nonlinear medium placed in the polarization interferometer can be used for generation and observation of the polarization-squeezed phase states of light.
A possibility of formation of nonclassical polarization states of light in the case of interaction of two orthogonally polarized modes in a spatio-inhomogeneous nonlinear medium is considered. A procedure of the quantum nondemolition (QND) measurement both of the Stokes parameters and the phase difference of two orthogonally polarized modes of optical field is presented and analyzed for the first time. We also introduce a new nonlinear parameter to describe the light polarization (depolarization) in quantum optics. The general approach to the measurement procedure under study allows to propose the new scheme for the QND-measurement of the angular momentum of atomic system as well.
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.
A brief review of theoretical studies of the quantum state of polarization of light exhibiting the level of fluctuations in at least one of the Stokes parameters which is below the quantum noise limit is presented. Two approaches to generation of polarization-squeezed state of light are analyzed in detail: by propagating coherent radiation in a cubic nonlinear medium and by mixing radiation of two orthogonally polarized quadrature-squeezed modes. The degree of polarization of light is discussed. Other areas of quantum polarization optics, in particular, entanglement of quantum Stokes parameters and quantum polarization tomography, are also discussed.