Eur. Phys. J. Special Topics 203, 87-116 (2012)
https://doi.org/10.1140/epjst/e2012-01536-0

Regular Article

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

^a e-mail: alice.sinatra@lkb.ens.fr

Received: 13 January 2012
Revised: 21 February 2012
Published online: 11 April 2012

Abstract

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 ⟨N_nc⟩/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.