Quantum non-local effects with Bose-Einstein condensates
Résumé
We study the properties of double Bose-Einstein condensates in different spin states, represented quantum mechanically by double Fock states. We assume that individual measurements of the spins of the particles are performed in transverse directions (perpendicular to the spin quantization axis), giving access to the relative phase of the condensates. Initially, this phase is completely undefined, and the first measurements provide purely random results. But a fixed value of this phase rapidly emerges value under the effect of the successive quantum measurements, giving rise to a quasi-classical situation where all spins have parallel transverse orientations. If the number of measurements reaches its maximum value (the number of particles), this classical phase disappears and quantum effects show up again. These effects can give rise to substantial violations of Bell type inequalities, comparable to those obtained with two spins in singlet state, even if the total number of particles involved is very large.
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