A multi-photon Stokes-parameter invariant for entangled states

We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar invariant under the group realized by the transformations of stochastic local quantum operations and classical communications (SLOCC). This invariant is offered as a candidate entanglement measure for n-qubit states and discussed in relation to measures of quantum state entanglement for certain important classes of two-qubit and three-qubit systems. This invariant can be directly estimated via a quantum network, obviating the need to perform laborious quantum state tomography. We also show that this invariant directly captures the extent of entanglement purification due to SLOCC filters.Comment: 9 pages, 0 figures, Accepted for publication in Physical Review

Radio Astronomical Polarimetry and the Lorentz Group

In radio astronomy the polarimetric properties of radiation are often modified during propagation and reception. Effects such as Faraday rotation, receiver cross-talk, and differential amplification act to change the state of polarized radiation. A general description of such transformations is useful for the investigation of these effects and for the interpretation and calibration of polarimetric observations. Such a description is provided by the Lorentz group, which is intimately related to the transformation properties of polarized radiation. In this paper the transformations that commonly arise in radio astronomy are analyzed in the context of this group. This analysis is then used to construct a model for the propagation and reception of radio waves. The implications of this model for radio astronomical polarimetry are discussed.Comment: 10 pages, accepted for publication in Astrophysical Journa

Propagation of transverse intensity correlations of a two-photon state

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly-correlated photon pairs in an EPR-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anti-correlation, or no correlation, depending on the sum of the orders $\alpha$ and $\beta$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state, and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between theory and experiment.Comment: 9 pages, 7 figures, to appear PR

X-ray Coherent diffraction interpreted through the fractional Fourier transform

Diffraction of coherent x-ray beams is treated through the Fractionnal Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the Huygens-Fresnel theory is first discussed and a generalized uncertainty principle is introduced.Comment: 7 pages, 8 figure

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

Determination des fonctions spheroidales généralisées par méthode optique iterative

On rappelle que les modes de résonance d'une cavité optique confocale sont de nature sphéroîdale. En plaçant dans la cavité un élément amplificateur de lumière il devient possible d'obtenir ainsi physiquement ces modes et par conséquent l'ensemble des fonctions sphéroîdales auxquelles ils correspondent. Les lasers sont un exemple classique de réalisation physique d'un tel oscillateur. Cependant la présence dans ce cas d'un couplage entre oscillation et résonance impose, sur les dimensions de la cavité, des contraintes qui conduisent à ne considérer qu'un aspect asymptotique du problème sphéroîdal initial. On montre que la réalisation d'un résonateur utilisant un cristal de BSO (Oxyde de Bismuth Silicium) comme milieu actif, est par contre parfaitement bien adaptée à une détermination générale de ces fonctions. On présente enfin un certain nombre de modes sphéroîdaux obtenus selon ce principe et l'on discute de l'intérêt général d'une telle approche pour le calcul des fonctions sphéroîdales

orrélateur joint op tique appliqué à la détection multicible

On discute des avantages et inconvénients de l'utilisation d'un corrélateur joint non linéaire sous l'angle de la séléctivité et de la robustesse. On propose une implantation optique basée sur l'utilisation d'une valve optique à cristal liquide ferroélectrique. Du fait de ses temps de commutation rapides et de sa bistabilité, ce composant permet le traitement de plusieurs cibles, aussi bien qu'une modification de sa réponse non linéaire à une intensité. L'ajustement de cette non linéarité et son influence sur la sélectivité et la robustesse du corrélateur sont démontrés expérimentalement