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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-mode simultaneous measurement of the light phase difference and the polarization states for quantum optical field

A. P. Alodjants, Sergei M Arakelyan

Published Jul 1, 1997• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.277665

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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.
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.
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.
A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincar\'e sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.
Quantum-state tomography is proposed as a means to achieve a complete measurement of the quantum polarization state of a light wave. A set of measurements using dual-polarization balanced homodyne detection is shown to be tomographi-cally complete with respect to the statistics of the SU(2) Stokes operators on the Poincaré sphere. Complete reconstruction of the polarization sector of the density matrix of a partially polarized optical field can be achieved while randomizing the overall phase of the dual-polarization local oscillator.