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Optics and Spectroscopy

Quantum measurements of the parameters of the Gell-Mann optical field with an SU(3) interferometer

A. P. Alodzhants, Sergei M Arakelyan

Published Sep 1, 2004• 6 citations
Publisher

Abstract

The SU(3) polarization theory in the Hilbert space is developed for quantum Bose systems with Gell-Mann symmetry. The degrees of polarization and isopolarization are determined. An original SU(3) interferometer for measuring the phase-dependent Gell-Mann parameters of an optical field is considered, and the signal-to-noise measurements limiting in quantum noises and based on the use of entangled and squeezed states of light at the entrance of the optical system are analyzed. A new type of quantum (helical) states of optical radiation for which the correlation between the Hermitian quadratures and isospin operators plays a crucial role is revealed for one of these modes in the classical-field approximation.

DOI
10.1134/1.1803648

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The SU(3) polarization theory in the Hilbert space is developed for quantum Bose systems with Gell-Mann symmetry. The degrees of polarization and isopolarization are determined. An original SU(3) interferometer for measuring the phase-dependent Gell-Mann parameters of an optical field is considered, and the signal-to-noise measurements limiting in quantum noises and based on the use of entangled and squeezed states of light at the entrance of the optical system are analyzed. A new type of quantum (helical) states of optical radiation for which the correlation between the Hermitian quadratures and isospin operators plays a crucial role is revealed for one of these modes in the classical-field approximation.
We consider a new approach of the SU(3)-symmetry polarization in Hubert space for a quantum Bose-system with internal Gell-Mann symmetry in quantum and atomic optics. The operational determination of the SU(3) phase problem for a three mode optical field is discussed for the first time. The original twelve-port interferometer for simultaneous measurements of both the Gell-Mann parameters and the phase characteristics is proposed. The signal-to-noise ratio coefficients for coherent end entangled states of light are examined. In the paper we also discuss application ofour theory for the problems of quantum information as well.
We consider a new approach to describe a quantum optical Bose-system with internal Gell-Mann symmetry by the SU(3)-symmetry polarization map in Hilbert space. The operational measurement in density (or coherency) matrix elements for the three mode optical field is discussed for the first time. We have introduced a set of operators that describes the quantum measurement procedure and the behavior of fluctuations for the amplitude and phase characteristics of three level system. The original twelve-port interferometer for parallel measurements of the Gell-Mann parameters is proposed. The quantum properties of W-qutrit states under the measurement procedure are examined.
We consider a new approach for describing a quantum optical Bose system with internal Gell-Mann symmetry by means of the SU (3) symmetry polarization map in Hilbert space. The operational measurement of the density (or coherency) matrix elements for the three-mode optical field is discussed for the first time. We have introduced a set of operators that describe the quantum measurement procedure and the behaviour of fluctuations for the amplitude and phase characteristics of the three-level system. A novel twelve-port interferometer for making parallel measurements of the Gell-Mann parameters is proposed. The quantum properties of qutrit W-states in the measurement procedure are examined.
We consider a new approach to the SU(3) symmetry polarization in Hilbert space for a quantum-optical Bose system with internal Gell-Mann symmetry. The operational determination of the SU(3) amplitude and phase characteristics for a three-mode optical field is discussed for the first time. An original twelve-port interferometer for simultaneous measurements of both the Gell-Mann and the phase parameters is proposed. The quantum properties of various W-class qutrit states under the measurement procedure for quantum information purposes are examined.
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.
Quantum interferometric sensing plays a crucial role in a wide range of applications, including quantum metrology, quantum imaging, and quantum lithography, where minute phase shifts carry valuable physical information. The strength of quantum sensing lies in surpassing classical sensitivity limits, particularly through the use of quantum correlations and squeezing to suppress optical shot noise. Birefringence sensing is crucial for various applications, as it provides detailed information about the material's structure, stress, composition, and environmental conditions. We present an interferometric scheme for detecting unknown small birefringence beyond the shot-noise limit of sensitivity that leverages the hyper-squeezing (squeezed in both number-phase and polarization correlations) within a pair of polarized nonlinear SU(1,1) interferometers, coupled by the birefringence. Specifically, two pairs of crossed-polarization nonlinear media, both generate and measure two-mode quantum light that is squeezed and polarization-entangled. We present a complete theoretical analysis of the interferometer's sensitivity to small birefringence under realistic conditions of gain and internal loss, illuminating the potential for enhancement of the sensitivity by 3-15dB in practical, real-world experiments (the exact achievable enhancement is governed solely by the loss).