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Bulletin of the Russian Academy of Sciences Physics

Polarization tomography of a narrow-band biphoton field

A. E. Mihailov, Латыпов Ильнур Зиннурович, Alexander A. Kalinkin, A. V. Shkalikov, А. А. Калачев, В. В. Самарцев

Published Dec 1, 2011• 1 citation
Publisher

Abstract

Narrow-band orthogonally polarized collinear frequency-degenerate biphotons are generated in the process of the spontaneous parametric down-conversion of light in a nonlinear BBO crystal placed in an optical resonator. Quantum polarization tomography and polarization transformation of the generated biphoton states are performed. The results from our experiment agree well with theoretical calculations.

DOI
10.3103/s1062873811120240

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Narrow-band orthogonally polarized collinear frequency-degenerate biphotons are generated in the process of the spontaneous parametric down-conversion of light in a nonlinear BBO crystal placed in an optical resonator. Quantum polarization tomography and polarization transformation of the generated biphoton states are performed. The results from our experiment agree well with theoretical calculations.
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).
The problem of generating a narrow-band biphoton field during spontaneous parametric down conversion of light in a quadratic nonlinear medium in a cavity is discussed. It is shown that, in the case of double resonance (for signal and idle fields), the form of the single-photon wave packet is biexponential and has a half-width determined by the photon life time in the cavity. An experiment is carried out on the generation of narrow-band biphotons in a crystal of lithium iodine with I-type matching in a frequency degenerate collinear regime. The second-order correlation function of the cavity-enhanced biphotons is measured using the electric nanosecond time delay line.
A method for reconstructing an arbitrary quantum state of an optical system in Hilbert space with dimension d = 4 is discussed. Such states can be realized using a collinear frequency-nondegenerate regime of generating spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. The 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.
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.
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.