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Optics and Spectroscopy

Biphoton light with hidden polarization and its polarization tomography

Pavel A. Bushev, V. P. Karassiov, Anatoly Viktorovich Masalov, A. A. Putilin

Published Oct 1, 2001• 37 citations
Publisher

Abstract

Polarization properties of biphoton light, emitted by an optical parametric oscillator, are studied both theoretically and experimentally. The theoretical treatment is performed using the Stokes operator formalism; polarization density matrix of the light fields; and the quasi-probability function, which represents an analog of the field Wigner function. The hidden polarization of biphoton light is demonstrated experimentally with the help of elements of polarization tomography.

DOI
10.1134/1.1412666

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Polarization properties of biphoton light, emitted by an optical parametric oscillator, are studied both theoretically and experimentally. The theoretical treatment is performed using the Stokes operator formalism; polarization density matrix of the light fields; and the quasi-probability function, which represents an analog of the field Wigner function. The hidden polarization of biphoton light is demonstrated experimentally with the help of elements of polarization tomography.
Using the formalism of the Stokes operators, a Wigner-type polarization quasi probability function and related tomography techniques, we analyze polarization properties of the XY-type biphoton light produced by a cw optical parametric oscillator. An appropriate data processing allowed to reveal experimentally the properties of hidden polarization and polarization squeezing for the parametric radiation, as well as to manifest a similarity between the calculated polarization Wigner function and that obtained via polarization tomography of the light produced.
The essence and basic structural elements of the method of polarization tomography of quantum radiation (the reconstruction of the polarization states of a field solely from polarization measurements) are described. The essential features of the method are discussed in comparison with usual field and spin tomographies. A general scheme for experimentally implementing this method is suggested and its use in polarization tomography of biphotonic radiation with hidden polarization is briefly analyzed.
Conceptual and operational aspects of the description of the polarization of light in classical and quantum optics are discussed. Primary emphasis is placed on the concept of P -quasispin, which ensures an adequate analysis for arbitrary quantum light fields. In terms of this concept, the polarization density matrix, which is obtained by reduction of the total field density operator and which completely describes the polarization state of quantum radiation, as well as the operational (measured in polarization experiments) characteristics and the transformations of the polarization dynamics, are determined. Applications of the formalism developed to biphoton optics are discussed.
The works devoted to studying the polarization properties of a two-photon light generated upon spontaneous parametric down-conversion in the collinear frequency-degenerate regime are briefly overviewed, with emphasis on the studies carried out by us over a period from 1999 to 2001 within the framework of the project “Polarization Optics of Biphotons” of the Russian Foundation for Basic Research. In particular, the polarization state of a two-photon light was analyzed and its pictorial mapping onto the Poincaré sphere was proposed. The experiments on polarization transformations of a two-photon light were performed; based on these transformations, a method was suggested for ternary quantum information coding. A two-photon state with the orthogonal photon polarizations was synthesized experimentally from the two beams of identically polarized correlated photons, and the spectral properties of this state were investigated. Finally, a method was suggested for measuring the polarization state of a two-photon light in the collinear frequency-degenerate case (“tomography”).
The notion and main conceptual and operational characteristics of the polarization state of quantum radiation are defined within the framework of the P - quasispin formalism developed earlier by the author. This state is shown to be described fully by the polarization density matrix obtained via reducing the field density operator. Basic operational quantities (quantum polarization degree, polarization "noises" , etc.), measured in quantum experiments and displaying peculiarities of polarization states, are defined with the help of P - quasispin components. The idea and features of polarization nonclassical states of quantum light are discussed. In this approach a series of nonclassical states of the biphoton radiation, manifesting unusual (for classical optics) polarization features, are analyzed. Some of applied possibilities of such states are briefly discussed.