I will discuss Bose-Einstein spinor condensates for F=1 atoms in the context of 87 Rb, as studied experimentally by the Stamper-Kurn group 1 . The dynamical quantum fluctuations of a sample that starts as a condensate of N atoms in a pure F=1, m F = 0 state may be described in analogy to the ``two-mode squeezing" of quantum optics. In our system the initial m F = 0 condensate acts as a source ("pump") for the creation pairs of m F =1,-1 atoms (via "4 wave mixing"). It will be shown that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the m F = +1 degree of freedom, obtained by tracing out the m F = -1,0 degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins. Our approach seeks to improve on the standard mean field description of the system by matching the fluctuations of our quantum states to the initial boundary conditions for the mean-field Gross Pitaevski equations.
. L. Sadler et al, Nature 443 , p193 (2006).