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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Single-beam biphotons: polarization properties and propagation in fibers

Maria V. Chekhova

Published Feb 3, 2004• 0 citations
Publisher

Abstract

Most protocols of quantum information transmission are based on qubits, or two-level quantum systems. However, in certain cases, it is reasonable to use quantum systems of higher dimensionality, such as, for instance, qutrits - three-level systems. In the present paper, it is shown that single-mode entangled pairs of polarized photons (biphotons) can be used for this purpose. Polarization state of a single-mode biphoton is considered and its representation on the Poincare sphere is suggested. An orthogonality criterion for two biphotons in arbitrary polarization states is formulated. Experiments on polarization transformations of biphotons are described. Finally, propagation of biphotons through fibres is considered.

DOI
10.1117/12.505166

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Most protocols of quantum information transmission are based on qubits, or two-level quantum systems. However, in certain cases, it is reasonable to use quantum systems of higher dimensionality, such as, for instance, qutrits - three-level systems. In the present paper, it is shown that single-mode entangled pairs of polarized photons (biphotons) can be used for this purpose. Polarization state of a single-mode biphoton is considered and its representation on the Poincare sphere is suggested. An orthogonality criterion for two biphotons in arbitrary polarization states is formulated. Experiments on polarization transformations of biphotons are described. Finally, propagation of biphotons through fibres is considered.
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”).
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincaré sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement.
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincare sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement.
The polarization state of biphoton light generated via colinear frequency-degenerate spontaneous parametric down-conversion is considered. A biphoton is described by a three-component polarization vector, its arbitrary transformations relating to the SU(3) group. A subset of such transformations, available with retardation plates, is realized experimentally. In particular, two biphoton beams, formed by colinearly polarized photons (type I) are transformed into a single biphoton beam formed by orthogonally polarized photons (type II). Polarized biphotons are suggested as ternary analogs of two-state quantum systems (qubits).