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Journal of Experimental and Theoretical Physics

The method of polarization tomography of radiation in quantum optics

V. P. Karassiov, Anatoly Viktorovich Masalov

Published Jul 1, 2004• 26 citations
Publisher

Abstract

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.

DOI
10.1134/1.1787078

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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.
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.
We discuss a procedure of measurement of an arbitrary quantum state of an optical system in Hilbert space with the dimension d=4. Such states can be realized using a collinear frequency-nondegenerate regime of spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. A high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.
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”).