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Conference on Lasers and Electro-Optics

Continuous variable squeezing and entanglement with cold atoms

Aurélien Dantan, Vincent Josse, L. Vernac, Alberto Bramati, M. Pinard, E. Giacobino

Published Jan 1, 2004• 0 citations
Publisher

Abstract

We report on continuous variable polarization squeezing and entanglement generated using the interaction with cold atoms in cavity. Both quadrature and polarization entanglement are demonstrated using the i nseparability criterion [1] and the entanglement of formation.
DOI
10.1364/iqec.2004.itug3

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Quantum information with continuous variables conventionally exploits quantum variables with canonic: commutation relations, like position and momentum, or quadrature field components. In contrast, this contribution is devoted to quantum continuous polarization variables. The relevant observabIes are quantum Stokes operators which obey the SU(2) algebra with a commutator which is not a c-number but an operator. In this paper, we review the concept of polarization squeezing and the new concept of continuous-variable polarization entanglement using quantum Stokes parameters. We discuss the prospects and specific features of such nonclassical polarization states for quantum communication.
A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincar\'e sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.