# Abstract:

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.

[1].

*L. Sadler et al, Nature*

**443**, p193 (2006).