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Applied Optics

Measuring Stokes parameters by means of unitary operations

Zhi-Kun Su, Jiahui Wang

Published Oct 12, 2021• 3 citations
Publisher

Abstract

We propose an improved scheme to measure the Stokes polarization parameters by making the to-be-measured state evolve unitarily. An optical setup able to implement the scheme is presented theoretically and experimentally. Theoretical results indicate that at least two unitary operators should be employed to determine the Stokes parameters of light with arbitrary degrees of polarization. Compared with the results acquired by a commercial polarimeter, the proposed scheme is used to obtain the Stokes parameters of 13 representative states with degrees of polarization r = 1 and r = 0.5 , experimentally. The fidelity between the two states gained by the above methods is in the range of 0.9802 ± 0.0046 to 1.0000 ± 0.0000 .

DOI
10.1364/ao.439420

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We propose an improved scheme to measure the Stokes polarization parameters by making the to-be-measured state evolve unitarily. An optical setup able to implement the scheme is presented theoretically and experimentally. Theoretical results indicate that at least two unitary operators should be employed to determine the Stokes parameters of light with arbitrary degrees of polarization. Compared with the results acquired by a commercial polarimeter, the proposed scheme is used to obtain the Stokes parameters of 13 representative states with degrees of polarization r = 1 and r = 0.5 , experimentally. The fidelity between the two states gained by the above methods is in the range of 0.9802 ± 0.0046 to 1.0000 ± 0.0000 .
We demonstrate experimental excitation-manifold-resolved polarization characterization of quantum states of light ranging from the few-photon to the many-photon level. In contrast to the traditional characterization of polarization that is based on the Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a given photon number do the methods coincide. For states with an indeterminate photon number, for example Gaussian states, the employed method gives a richer and more accurate description. We apply the method both in theory and in experiment to some common states to demonstrate its advantages.
We present the experimental results for a method used to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two-level systems. The setup has no moving parts and is sensitive to weak sources (emitting single photons) of light as it relies on photon counting, and has potential applications in both classical polarization measurements and quantum communication scenarios. In our implementation, we are able to reconstruct the Stokes parameters of pure polarization states with an average fidelity of 99.9%.
We show that the quantum Stokes parameters aptly describe the nonclassical two-polarization-mode Fock states and the transformation of their polarization states. In this description, the two-polarization-mode Fock states are the simultaneous eigenstates of the first and second Stokes parameters. Transformations of the polarization states, which are caused, for example, by optically active media, are described by the rotations in the Stokes vector space, which are given by unitary operators generated from the Hermitian Stokes parameters. The SU(2) symmetry of the Stokes parameters provides two independent degrees of freedom of polarimetric measurements that can exceed the standard quantum limit.
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.
We propose a new method for performing continuous quantum nondemolition measurements (QNDM) of the polarization characteristics of light, the signal photon number, and the Stokes parameters of light. For devices that implement such measurements we take cubically nonlinear double-filament optical fibers with tunnel coupling of the filaments. Such a system employs a four-mode mixing of the waves (two probe modes and two signal modes). Linear optical elements needed for preliminary and subsequent conversion of the Stokes parameters are also used. We show that measurements of one Stokes parameter can be used for QNDM of the phase difference between the two initial modes. Here the accuracy of such measurements is determined by the initial fluctuations of the Stokes parameters of the probe modes and by the size of the nonlinear mode conversion coefficient in the optical fibers.