Title
EinsteinPodolskyRosen argument and Bell inequalities for BoseEinstein spin condensates
Publication Date
2008
Journal or Book Title
PHYSICAL REVIEW A
Abstract
We discuss the properties of two BoseEinstein condensates in different spin states, represented quantum mechanically by a double Fock state. 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 two macroscopically occupied states. Before the first spin measurement, the phase is completely undetermined; after a few measurements, a more and more precise knowledge of its value emerges under the effect of the quantum measurement process. This naturally leads to the usual notion of a quasiclassical phase (Anderson phase) and to an interesting transposition of the EinsteinPodolskyRosen argument to macroscopic physical quantities. The purpose of this paper is to discuss this transposition, as well as situations where the notion of a quasiclassical phase is no longer sufficient to account for the quantum results, and where significant violations of Belltype inequalities are predicted. Quantum mechanically, the problem can be treated exactly: the probability for all sequences of results can be expressed in the form of a double integral, depending on all parameters that define the experiment (number of particles, number and angles of measurements). We discuss the differences between this case and the usual twospin case. We discuss the effect of the many parameters that the experimenters can adjust for their measurements, starting with a discussion of the effect of the angles of measurement (the “settings”), and then envisaging various choices of the functions that are used to obtain violation of BellClauserHorneShimonyHolt inequalities. We then discuss how the “sample bias loophole” (often also called “efficiency loophole”) can be closed in this case, by introducing a preliminary sequence of measurements to localize the particles into “measurement boxes.” We finally show that the same nonlocal effects can be observed with distinguishable spins.
Pages

Volume
77
Issue
2
Recommended Citation
Laloe, F and Mullin, WJ, "EinsteinPodolskyRosen argument and Bell inequalities for BoseEinstein spin condensates" (2008). PHYSICAL REVIEW A. 26.
Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/26
Comments
Published version is located at http://pra.aps.org/abstract/PRA/v77/i2/e022108