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Physical Review A

Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: Preparation and testing

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

Published Sep 1, 2001• 38 citations
Publisher

Abstract

Two beams of collinear type-I biphotons generated via spontaneous parametric down-conversion (SPDC) from coherent pump beams are transformed without a loss into a state of correlated photons with orthogonal (in the general case, elliptical) polarizations. This alternative state manifests remarkable properties: while having the spectrum of type-I SPDC, it has polarization properties similar to type-II SPDC. To test the state, we use the anticorrelation effect (``anticorrelation dip'').

DOI
10.1103/physreva.64.041803

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Two beams of collinear type-I biphotons generated via spontaneous parametric down-conversion (SPDC) from coherent pump beams are transformed without a loss into a state of correlated photons with orthogonal (in the general case, elliptical) polarizations. This alternative state manifests remarkable properties: while having the spectrum of type-I SPDC, it has polarization properties similar to type-II SPDC. To test the state, we use the anticorrelation effect (``anticorrelation dip'').
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.
Polarization correlation measurement of two-photon state generated in type-II spontaneous parametric downconversion (SPDC) has been performed in a single input port beam splitter configuration. Two orthogonally polarized entangled photons with degenerate k vectors were directed to the single input port 50%-50% beam splitter. Polarization were measured with linear and circular polarization entangled state by the use of two polarization analyzers followed by two photon counting detectors. A strong correlation of polarization has been observed. The type of two-photon state generated in Type-II SPDC was tested. A strong dependence of the polarization correlation upon the spectral bandwidth of the detector spectral filter was found and a different correlation between linear and circular polarization entangled state were observed. It seems that the standard theoretical models for SPDC need to be improved in order to provide a comprehensive treatment for the result of the experiment.
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”).
Spontaneous parametric down-conversion (SPDC) is the most often used source of entangled photon states in quantum optics. Recently, it has been suggested in theory that the reduction of polarization entanglement between the photon pair generated via the type-II SPDC process pumped by a ultrafast laser is due to the asymmetry in the joint spectrum function, which is the indicative of the frequency entanglement between the two photons. In this paper, we report the measurement of the joint spectrum function (i.e., direct observation of the degree of frequency entanglement) of the two-photon state of type-II SPDC in both cw- and ultrafast-laser pumping conditions. We observed that, in agreement with the theory, the degree of frequency entanglement (the shape of the joint spectrum function) is indeed different for cw- and ultrafast-pumped type-II SPDC. Our results are of importance in "engineering" the two-photon state for specific quantum applications, such as quantum cryptography.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.