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Quantum Electronics and Laser Science Conference

Preparation and measurement of biphotons in given polarization state

A. V. Burlakov, Maria V. Chekhova, O.A. Karabutova, S. P. Kulik, Georgy O. Rytikov

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. Consider a pair of collinear frequency-degenerate photons-a biphoton, which can be obtained by spontaneous parametric down-conversion (SPDC). Its state vector/sup 1/ is |/spl Psi/>=C/sub 1/|2,0>+C/sub 2/|0,2>+C/sub 3/|1,1>, (1) with |n,m>, n+m=2 denoting n H-polarized photons and m V-polarized photons. The first and the second terms describe type-I biphotons (correlated photons have similar H or V polarizations), and the third one describes type-II biphotons (correlated photons have orthogonal polarizations). In the present work we study an anticorrelation properties of the artificially synthesized type-II biphotons.

DOI
10.1109/qels.2001.961869

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Summary form only given. Consider a pair of collinear frequency-degenerate photons-a biphoton, which can be obtained by spontaneous parametric down-conversion (SPDC). Its state vector/sup 1/ is |/spl Psi/>=C/sub 1/|2,0>+C/sub 2/|0,2>+C/sub 3/|1,1>, (1) with |n,m>, n+m=2 denoting n H-polarized photons and m V-polarized photons. The first and the second terms describe type-I biphotons (correlated photons have similar H or V polarizations), and the third one describes type-II biphotons (correlated photons have orthogonal polarizations). In the present work we study an anticorrelation properties of the artificially synthesized type-II biphotons.
Summary form only given. Consider a pair of collinear frequency-degenerate photons-a biphoton, which can be obtained by spontaneous parametric down-conversion (SPDC). Being a three-state quantum system, it is a ternary analog of a qubit. Its state vector is |/spl psi/>=c/sub 1/|2,0>+c/sub 2/|0,2>+c/sub 3/|1,1>, with |n,m>,n+m=2 denoting n X-polarized photons and m Y-polarized photons. The first two terms describe type-I biphotons (correlated photons have similar polarizations), and the third one type-II biphotons (correlated photons have orthogonal polarizations). An arbitrary biphoton state is given by four parameters.
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 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).
We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non-entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d =4, which differentiates them significantly from the often used two-qubit model ( d =2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.