Quantifying Entanglement Production of Quantum Operations

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described either by field operators, spin operators, or any other kind of operators, which is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analysed by the examples of Bose-Einstein condensation, superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analysed.Comment: 20 pages, Revte

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.Comment: Submitted to EPJ-ST Special Issue. 10 pages and 3 figure

Sur la théorie de l'effet Raman de résonance dans les cristaux présentant des défauts

The vibrational structure of the Raman resonance spectrum in the impure crystal is investigated. The following models of electron-phonon interaction are considered : the interaction with a single local mode, the interaction with two modes, the interaction with the crystal vibrational branch, the interaction with a single local mode and simultaneously with the crystal branch. It is shown that qualitatively Raman spectra resemble the luminescence spectra. In the case of the interaction with the vibrational branch there is a narrow Rayleigh peak on the continuous Raman background. Quantitatively the Raman spectra are more complicated than the luminescence spectra. In the case of the interaction with a single frequency the intensity of the multiphonon lines is not a monotonic function of the line order. In the case of the interaction with several modes the multiplication rule for the intensities, associated with the luminescence spectra, no longer holds. The selection rules for Raman scattering intensities, obtained by the group-theoretical methods, are discussed.On étudie le spectre de vibration dû à l'effet Raman de résonance dans des cristaux réels. On considère différents modèles de l'interaction des défauts avec les oscillations du réseau. On en tire des résultats numériques sur les intensités des répétitions des phonons par interaction des défauts avec une oscillation isolée au zéro absolu. Par effet de l'interaction avec une branche des vibrations du réseau, le spectre Raman consiste en une bande avec un pic de Rayleigh, qui présente une analogie optique avec l'effet Mossbauer. On compare la structure du spectre Raman avec celles des spectres d'émission et d'absorption infrarouges. Les particularités des règles de sélection de la théorie des groupes dans le cas de la résonance sont brièvement indiquées