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Optics and Spectroscopy

Polarization-squeezed light and quantum degree of polarization (A review)

A. S. Chirkin

Published Sep 1, 2015• 13 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x15090052

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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.
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.
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.
The propagation of partially coherent single-mode and two-mode radiations with orthogonal polarisations in media with a cubic optical nonlinearity is considered for the first time. Partially coherent light is regarded as a superposition of coherent and thermal radiations. It is shown that quantum and thermal fluctuations of a quadrature component may be suppressed in the self-interaction of partially coherent single-mode light. In the case of the self-interaction of incompletely polarised light can suppress fully only those fluctuations of the Stokes parameters (S 2 or S 3 ), which are associated with quantum fluctuations of the coherent component.
The quantum theory of polarizing light and the Stokes operators are applied to the study of the evolutions of polarization states of light in the processes of i nteraction with atoms in the case with or without Kerr medium. The non_classic b ehavior in the fluctuations of Stokes parameters for the polarizing light and th eir squeezing are investigated. The polarization ellipse, the degree of polariza tion of the field in quantum optics and the signal_to_noise ratio in the Stokes parameters are discussed. It is shown that the modulated oscillations appear in the evolutions of Stokes parameters and their fluctuations. These oscillations c ollapse and revive intermittently. The polarization ellipse does not vary in the interaction with atoms but the degree of polarization will oscillate. Kerr medi um changes these oscillations distinctly.