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Japanese Journal of Applied Physics

Quantum-Stokes-Parameter Description of Nonclassical Polarimetric Measurements Using Two-Polarization-Mode Fock States

Kazuyuki Muroo, Yoshitaka Takubo

Published Feb 1, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.47.925

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We show that appropriate nonclassical photon states can attain Heisenberg-limited sensitivity in polarimetric measurements, in which the squared amplitudes of the photon states are measured. These photon states, which can be constructed from the two-mode Fock states, are found as the eigenstates of a Hermitian operator, which is closely related to the quantum Stokes operators. The algebraic property of the Hermitian operator governs the interferometric behavior in polarimetric interactions and provides the frequency of the interferometric fringes scaled by the total number of photons of the state. Thus, the polarimetry is able to achieve Heisenberg-limited sensitivity.
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 examine whether the Stokes parameters of a two-mode electromagnetic field results from the superposition of the spins of the photons it contains. To this end we express any n-photon state as the result of the action on the vacuum of n creation operators generating photons which can have may different polarization states in general. We find that the macroscopic polarization holds as sum of the single-photon Stokes parameters only for the SU(2) orbits of photon-number states. The states that lack this property are entangled in every basis of independent field modes, so this is a class of entanglement beyond the reach of SU(2) transformations.
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.