Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size
1 Laboratoire Kastler Brossel, École Normale Supérieure, UPMC and CNRS, Paris, France
2 Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
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Revised: 21 February 2012
Published online: 11 April 2012
We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨Nnc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.
© EDP Sciences, Springer-Verlag, 2012